The paper concerns slackened systems, i.e. discrete deformable systems with gaps (clearances) at structural joints. The mathematical model of such systems coincides with a FEM-oriented approximation of locking-elastic-plastic bodies. The theory describes a relatively wide class of systems made of time-independent materials. The problem of slackened systems has been developed during the last decade. The work presents the current state of knowledge in this field.

The available methods and solutions of problems in discrete optimum structural design are reviewed. They are classified into the following categories: branch and bound methods, dual approach, enumeration methods, penalty function approach, simulated annealing and other methods. For the majority of problems, none of the methods is guaranteed to give the exact solution from the mathematical point of view. However, "good practical'' solutions can be obtained at an acceptable cost.

We look directly into the phase space of experimental or numerical data to derive nonlinear equations of motion. Our example is the dynamics of viscous droplets. While the smallest useful dimension of phase space turns out to be three, we apply methods to visualize four, five, six dimensions and more. These methods are Poincairé sections and condensation of variables. The resulting equations of motion are extremely simple but nevertheless realistic.

In this paper, information on a sheet metal forming simulation program based on flow approach is provided and comparisons between numerical and experimental results are presented. Elastic spring-back effects and residual stresses are predicted by means of a large-strain elasto-viscoplastic finite element model recently proposed for this class of problems involving large deformations and changes in geometry. A wide experimental program performed in a sheet stamping factory is shortly described. Tests included the deep drawing of circular and rectangular blanks with cylindrical and prismatic tools, respectively. Different die and punch roundings, lubrication conditions and blank holder forces have been considered. Different examples of application to 2D and 3D sheet stamping problems are presented and compared with available experimental results.

The paper presents a heuristic method of node renumbering for wavefront reduction of the coefficient matrix of a linear system of equilibrium equations obtained in Finite Element (FEM) or in Finite Difference (FDM) methods for regular rectangular domains. From among all the node renumbering techniques for the Banachiewicz-Cholesky triangular decomposition of an assembled matrix with a compact (the least sparse possible) profile, the method presented herein assures the best reduction of matrix wavefront and time of decomposition

A rectangular specimen consists of two kinds of grains. Each kind has a different thermal expansion coefficient. The grains are randomly distributed in J rows and K columns of the specimen. The temperature of the whole specimen is increased and produces internal strains. It is assumed that each grain interacts with its four neighbours. The interaction force is proportional to the relative displacement. If the relative displacement equals the extension due to thermal expansion, the force equals zero. The relaxation method of calculating the equilibrium strains is used. The average maximum strains are calculated for a large number of numerical experiments. The standard deviations are calculated.

A solution to plane and axisymmetric elasto-plastic contact problem with linear hardening of contacting bodies, taking into account microstructural features of the contact zone is presented. A new quadratic-isoparametric contact element involving the irreversible nature of friction is developed. An incremental constitutive friction law, analogous to the classical theory of plasticity, is used. Several numerical examples are considered. The influence of parameters defining the contact stiffness interface on the distribution of displacements and stresses on the contact surface is discussed.

A new adaptive finite-element numerical method has been developed for the unsteady Navier-Stokes equations of incompressible flow in two dimensions. The momentum equations combined with a pressure correction equation are solved employing a non-staggered grid. The solution is advanced in time with an explicit/implicit marching scheme. An adaptive algorithm has been implemented, which refines the grid locally in order to resolve detected flow features. A combination of quadrilateral, as well as triangular cells provides a stable and accurate numerical treatment of grid interfaces that are located within regions of high gradients. Applications of the developed adaptive algorithm include both steady and unsteady flows, with low and high Reynolds numbers. Comparisons with analytical, as well as experimental data evaluate accuracy and robustness of the method.

The proposed algorithm is based on the fourth-order compact discretization schemes for the Navier-Stokes equations in streamfunction-vorticity-pressure formulation. The equations are expressed in terms of a general orthogonal curvilinear coordinate system which allows for modelling non-standard geometries. Two distinct parallelization strategies are considered. The first one relies on the domain decomposition approach, in which each subdomain is served by a different processor. In the second strategy, suitable for massively parallel computers, each processor serves a single grid point. The comparison of the performance of various computing platforms is presented, including a 2048-processor MasPar computer.

This paper presents a local mesh refinement (LMR) technique and its application to incompressible fluid flows with or without free surface boundaries. In the LMR method patches of fine grid are embedded in arbitrary regions of interest. Hence, more accurate solutions can be obtained with a lower number of computational cells. LMR is very suitable for the simulation of free surface movements because free surface flow problems generally require a finer computational grid to obtain adequate results. By means of this technique one can place finer grids only near surfaces and thus greatly reduce the total number of cells and computational costs. This paper introduces two LMR codes. Numerical examples calculated with the codes demonstrate well the advantages of the LMR method.

New methods of the neutron and photon transport Monte Carlo simulation suitable for vector computers have been investigated and general purpose multigroup and continuous energy codes have been developed. On vector supercomputers, the codes achieved high speed-up gains of an order of ten or more compared with the conventional scalar codes. To achieve more speed-up, the Monte Carlo codes are applied to three types of parallel processing environments; (1) a massively parallel computer, (2) a vector-parallel type supercomputer, and (3) a cluster of workstations connected to a network. On the massively parallel computer and the vector-parallel supercomputer, speed-ups almost proportional to the number of processors are achieved by simply assigning particles uniformly to each processor, and the speed-up with the vector-parallel supercomputer is enhanced by vector processing. On the other hand, in the workstation cluster, the computational power of each workstation may differ and the simple particle assignment may not be successful. By modifying particle assignment methods, effective parallel processings are made possible in such an environment.

The JAERI Monte Carlo Machine has been developed mainly to enhance the computational performance of numerical simulations with particle models such as Monte Carlo methods. The features of the JAERI Monte Carlo machine are i) vector processing capability for arithmetic operations, ii) special pipelines for fast vector processing in categorizations of particles, iii) enhanced load/store pipelines for indirectly addressed vector elements, iv) parallel processing capability for spatially and phenomenologically independent particles. This paper describes the design philosophy and architecture of the JAERI Monte Carlo machine and its effective performance through practical applications of the multi-group criticality safety code KENO-IV, the continuous-energy neutron/photon transport code MCNP and other codes for particle simulation.

Passive designs of several proposed light water reactors rely on containment cooling by condensation heat transfer in a high-concentration, noncondensable gas environment. To evaluate the safety of these plants, methods for analyzing the performance of the cooling systems must be developed. The current study discusses the physics of condensation in the presence of noncondensable gases and a method for predicting the accompanying heat transfer rates based on experimental data. The resulting experimental correlation for heat transfer coefficients has been implemented into the TRACG code, and a specific application has been made to the Simplified Boiling Water Reactor for conditions following a Design Basis Accident LOCA (Loss-of-Coolant Accident).

The paper presents selected results of the analysis of thermal and mass flow transient processes within the containments of the WWER-440 and the WWER-1000 nuclear reactors during Loss-of-Coolant Accidents based on the mathematical model and computer code for LOCA simulation. General assumptions of the mathematical model (with lumped parameters) are briefly presented. Changes of thermal variables (temperature, pressure etc.) are governed by the fundamental thermodynamic equations. All these equations have the nonlinear, integral form. The whole area of the containment is divided into several control volumes. Control volumes are joined in a given mode (orifices, valves, siphon closures etc.). The liquid phase (water) and the gaseous phase (air, steam and hydrogen) can appear in a control volume. Thermal equilibrium within an individual phase and a non-equilibrium state between phases is assumed. Heat accumulation in the walls and internal structures of the containment is taken into account and heat transfer between liquid and gaseous phases is also considered. The working mathematical model can be used for the analysis of different scenarios of LOCA within the containment of the PWR and BWR reactors. Later on the sample results of calculations of changes of pressure and temperature within the containment of the WWER-440 nuclear reactor and within the full containment of the WWER-1000 reactor are presented.

In the engineering processes it is important to simulate thermo-hydraulic phenomena numerically in the limited time before design of equipment. In thermo-hydraulic problem, as it may be time-consuming to solve elliptic equation numerically, a heavy burden is imposed on the computer. A SOR method is one of the effective methods to solve elliptic equation. As it is difficult to find the optimum relaxation factor, the value of this factor for the practical problems used to be estimated by the expertise. In this paper, the implications about the relaxation factor are translated into fuzzy control rules on the basis of the expertise of numerical analysts, and then the fuzzy controller is incorporated into the numerical algorithm. A Dirichlet problem of the Poisson's equation and the cavity flow problem are chosen to verify the feasibility of fuzzy controller for relaxation. Numerical experiments with the fuzzy controller resulted in generating a good performance.

First, an analytical asymptotic method to construct quasi-periodic solutions in autonomous dynamical systems governed by a nonlinear second order set of ordinary differential equations with delay is presented. The approach is based on the double asymptotic expansion of two independent perturbation parameters and is supported by symbolic computation using `Mathematica' package. Both resonance and non-resonance cases are successfully analyzed and the catastrophes of the torus solutions are classified and discussed. Second, a new method for numerical calculations of the quasi-periodic orbits, which is based on a concept of the general Poincare map, is addressed. In both cases considered examples support the introduced theory.

The paper presents the optimization of thin-walled structures such as vertical cylindrical reservoirs subject to pitting corrosion. The function of the structure utility is taken as an optimization criterion. The choice of an optimal thickness distribution of the reservoir shell along its height is determined from the conditions of its uniform reliability.

A computer method for elastic-plastic continuous beams with rotation constraints is proposed. Such structures belong to a particular class of slackened systems, i.e. systems with gaps at structural joints. The mathematical model of slackened structures represents a discrete form of the Kuhn-Tucker's conditions, and is equivalent to dual Quadratic Programming Problems (QPPs). The uniqueness of a solution to the problem of the beams under considerations is assured, excluding cases where the structure converts into a mechanism, and the solution corresponds to dual Linear Programming Problems (LPPs). In order to calculate both the structure and mechanism a concept of the finite element with elastic rotation supports is used in the computer program. The uniqueness of solutions makes it possible to use a pure elastic analysis with some additional constraints superimposed on state variables. It allows us to avoid the time-consuming mathematical programming methods. Several examples illustrate the behaviour of beams under multiparameter loads. Results relate the cyclic loading (shakedown) as well as elastic, sublimit and limit surfaces. The work presents the characteristic features of slackened structural systems.

An original idea of the Stochastic Finite Element Method (SFEM) application in numerical modelling of random fluctuations of elastic properties of fibre composites components has been presented in this paper. The displacement and the stress random fields have been analysed for various contents of a fibre periodicity cell of such a composite, and for different coefficients of variation of the Young modulus of both phases

Today the solution of mechanical problems in engineering practice is often routinely carried out by means of finite element packages. These packages are powerful and efficient and are able to solve many complicated problems of technical practice on a routine basis. The packages are more and more automated. In some cases, the user is even 'deprived' of solving meshing problems - the so called meshless finite element approach is being advocated. In other cases the packages take care of the correct determination of time step in transient problems. These packages offer a lot of options to choose from; the options themselves are described in particular manuals to a variable extent of details. As the Murphy law states, however, the manuals are as a rule read only if nothing else helps. It is thus worthwhile to recall some of the essentials from the finite element theory, show pitfalls which should be avoided and to present modern programming tools which help a lot in the derivation of necessary relations and in subsequent understanding of the matter. The behaviour of a rectangular membrane element and that of some finite element packages when solving simple problems will be shown in this paper with the intention to answer the question whether a modern engineer is supposed to know the theoretical details of the finite element theory and the essentials of programming.

The vapour explosion is a violent explosive phenomenon which may occur when two kinds of liquid of different temperature contact suddenly. Analysis of this phenomenon is needed in terms of safety evaluation of nuclear reactors, examination of volcanic eruptions and assurance of safety of various industrial processes. We have developed a simulation method applicable to coarse mixing of the vapour explosion. This process, including complex thermo-hydrodynamics, requires handling of multi-phase and multi-component. We employed CHAMPAGNE which is a general-purpose multi-phase flow code and modified it make it suitable for the analysis of the vapour explosion. Specifically, we improved interfacial heat transfer models and incorporated compensation for numerical dilution of the dispersed liquid. After some model calculations we simulated the MIXA experiment done at Winfrith. Details of the code modification and the simulation results are presented in this paper.

The operator splitting algorithm has been applied in FEM analysis of fluid flow and heat transfer to improve the computational efficiency through the use of the optimum FEM models and the optimum solvers independently for convection and diffusion. The need for decoupling convection and diffusion operators in FEM calculations comes from the behavioural error analysis, where conditions have been studied for a proper representation of major physical features of the convective-diffusive transport phenomenon on a coarse grid. The accuracy and efficiency of the algorithm have been verified by solving two pertinent benchmark problems of recirculating flow and free convection. The results obtained show that solutions of both equal- and unequal-order FEM interpolations are free from wiggles and spurious pressure modes and they fit fairly well the results reported elsewhere.

A new, original numerical method of free particles, for mechanics of continuous media, has been developed. The free particle hydrocodes (HEFP), based on this method, are the powerful tools that can be used to simulate, in the sense of computational physics, events with very high dynamic effects. In the paper, computational simulation of several attractive and practically important problems like: processes of the detonation, high velocity impacts and hypervelocity planetary impacts, shaped charge jet formation, explosive forming of projectiles, penetrating of the armour plate, is posed. All of them include shocks, very large deformations of solids, processes of cratering with impact jets generation and targets penetration. The method of free particles is a very useful for magnetohydrodynamical (MHD) simulation, too. It is possible to simulate ideal MHD and non-ideal MHD processes, and such exemplary results are also presented. In the paper, physical, mathematical and numerical models as well as results of some complex, unsteady, spatially two-dimensional simulations are presented.

A new type of the externally heated engine is the subject of the present paper. Air can be used as a working medium of the engine. Heat delivered to the working air may come from a combustion chamber or another heat generator of an arbitrary type. The engine construction and the thermodynamic cycle performed by the engine are original ones. The engine operation has been investigated basing on the presented computer simulation. As a result, the time-dependent pressures and temperatures in each part of the engine have been determined. The engine power and efficiency have also been calculated. When the lowest basic pressure of the engine cycle is equal to 1 MPa, the power of 30 kW per 1 liter of the cylinder volume and the efficiency 0.38 at 1500 rev/min can be achieved. The main aim of this paper is to present a numerical investigation of the engine operation for higher values of the basic cycle pressures. It has been shown that for the pressure equal to 3 MPa, the power of about 100 kW per 1 liter and the efficiency 0.40 at 1500 rev/min can be theoretically obtained. The mechanical losses of the engine are not taken into account during the power and efficiency calculations.

The problem of dislocation motion in monocrystals is faced in the framework of the continuum theory of dislocations. The presented approach is based on the defects balance law. A constitutive model is formulated which relates the driving forces with the dislocation velocity. The model makes use of the relations between the plastic deformation tensor and the tensor of dislocation density. Given a crystal under certain boundary and initial conditions, the evolution of both dislocation field and elastic-plastic deformations is obtained by solving the coupled system of equations resulting from the equilibrium equation and the dislocation balance for each time step. The set of equations is discretized by the finite element method. As an example the movement of an edge dislocation field inducing shear band deformation in a monocrystal is considered.

The paper presents the method of algebraic vorticity moments. It may be used to solve problems of viscous liquid motion in 2-D and 3-D cases. Its essence lies in the integration of a set of ordinary differential equations. The unknown functions of those equations defined as ${1 \over m!n!} \int_{E_2} {\omega{x^m}{y^n}\d x\d y}$ allow to find the vorticity field and next the velocity. We also show a number of 2D numerical examples.

The aim of the paper is to advocate the use of hybrid reasoning systems for computer-assisted analysis of physical systems. The paper starts from a critical assessment of classic numerical techniques, with the problem of sensitivity analysis of fuel rod support spring in a nuclear reactor used as an example. Then, the significance and some basic issues concerning qualitative physics methods of analysis of physical systems are discussed. Using the example of the so-called ``snap-through'' mechanism, the basic principles, advantages and limitations of qualitative simulation technique are shown. Certain future development possibilities are indicated, especially the necessity to formalise the order-of-magnitude reasoning. The recently developing techniques of diagrammatic reasoning are also introduced, with another mechanical example illustrating sources of their advantages for certain kinds of problems. The significant role of logical (expert-system-like) reasoning techniques and constraint-satisfaction systems is shown as well. Finally, the hybrid reasoning system concept is sketched. Such hybrid systems should integrate quantitative (numerical) (numerical) analysis, various methods of qualitative analysis as well as diagrammatic and logical reasoning techniques.

Natural frequencies of a vibrating hollow, elastic sphere are determined using both the 3-D elasticity and Kirchhoff shell theory.

The report is a continuation of the previous one. The closed-form solutions of the scattering problem by the 3-D elasticity and Kirchhoff shell theories are investigated.

The successful numerical analysis of plastic strain localization phenomena in ductile and brittle materials requires the fulfillment of several conditions in accordance with the formulation of the initial boundary value problem (IBVP). Sometimes it is necessary to use the regularization techniques which result in well-posedness of IBVPs. Then, there are several possibilities of introducing an internal length scale. If specific conditions are met, the results obtained in the numerical calculations are free of unexpected mesh sensitivity. In the paper the dynamical boundary values are studied. The rate-dependent regularized models of two materials are presented and used to solve practical engineering problems. The mathematical background which could be used to prove the well-posedness of IBVP as well as the physical arguments are discussed.

A general problem of parameter sensitivity of non-linear transient thermal systems is considered. The non-linear sensitivity path is followed by a weighted residual method employing the continuum description. The resulting finite element equations are derived. Both the direct differentiation and adjoint system methods are employed to evaluate sensitivity functional increments during the integration time step. Numerical results illustrate the method proposed.

The complexity of the physical engineering objects requires new technologies in software development able to simulate real-life cases. The huge number of such cases can be covered by object-oriented paradigm. This general idea and some advantages of using object-oriented language (Smalltalk) are exemplified by a presentation of a system for earth dam control. The system is an expert type program equipped with advanced monitoring and visualisation functions for existing dams. The software development process starting from the requirement description is presented. The structure of the dam model and of the inference engine as well as of the class hierarchy is shown as the examples. The re-usability of the system is proved by its implementation for different earth dams.

A tying algorithm for the linking of two originally geometrically incompatible finite element meshes with different degrees of refinement is proposed. It is characterized by the enforcement of geometric continuity between the two meshes at their common boundary and by specification of displacement constraints for the nodes located on this boundary. The two-dimensional as well as the three-dimensional case is considered. The proposed tying algorithm is applied to finite element analysis of the model of an automobile tire with a simplified tread profile. Consideration of this tread profile is restricted to the anticipated region of contact of the tire with the road surface and to its vicinity. For the remaining part of the analysis model a coarser finite element mesh is used. The tying algorithm is also applied to the generation of a finite element mesh with a realistic tread geometry in the aforementioned region.

Numerical solutions by means of the space-time finite element method to initial-boundary value problems for a hyperbolic model of heat conduction, are obtained. The heat conduction description is based on a concept a rigid conductor with a scalar internal state variable, that leads to a modified Fourier law. The obtained results are compared with existing experimental data know for semi-conductor crystals at low temperature.

The paper discusses the discrete optimization problem in structural space truss design. The optimal structure should satisfy limit state capacity and serviceability conditions. If the serviceability conditions are violated, the structure is not eliminated from considerations but it is modified by increasing structural stiffness. Many different ways to increase the stiffness of the structure are considered. The cross-sectional areas of truss bars A_k picked from a catalogue of circular hollow sections T and a number of elements in the catalogue t are taken as discrete design variables. The stress, local stability, displacement (design) constraints as well as technological and computational constraints are taken into account. The mass of truss bars including that of joints as well as exploitation and maintenance costs are chosen as optimization criteria. A labour consumption corresponding with a number of elements in the catalogue t is minimized, i.e., it is also regarded as an optimization criterion. Sets of non-dominated (efficient) and compromise (Pareto optimal) solutions, and the preferable solution for space truss are found. The results are presented in the form of diagrams and tables.

In this paper, the problem of parallelizing the finite element method for distributed memory computers using domain decomposition methods is addresed. We focus on direct domain decomposition methods because they are robust and well adapted to multi-level decompositions. Two important problems concerning these methods are studied: the condensation of subdomains and the resolution of the interface problem. Finally, the results are presented which show that, in sequential implementation, direct decomposition methods are more efficient than standard LDL^T-skyline solvers, and compare favorably with state-of-the-art LDL^T-sparse solvers.

The theoretical foundation and a numerical procedure of deriving stochastic effective properties of linear-elastic periodic fibre composite are presented. Using Monte-Carlo method, a Fortran program based on the deterministic rectangular plane strain element of the Finite Element Method has been worked out to evaluate probabilistic density functions of these properties. The expected values of elastic effective characteristics thus obtained are compared with deterministic results of COSAN modelling.

Some aspects of applying the external stabilization method to the treatment of selected cases of tibia fractures make the subject of this paper. ZESPOL, used as an external stabilizer, was selected from among many other methods. In order to define the state of deformations and stresses existing in a fractured tibia stabilized with ZESPOL, an unconventional quantitative model was prepared. Finite element analysis was applied to the strength analysis of the whole system. Some final results and computations are presented.

This paper describes a mathematical technique to calculate the model parameters for a classical Weibull statistic. This type of statistic can be applied in a number of life time expectancy problems. A typical example is the brittle behaviour of components produced from technical ceramics. A Nelder-Mead simplex algorithm is introduced to obtain the Weibull parameters using the maximum likelihood criterion. Program code for a Matlab for Windows environment is presented.

In the analysis of the problem the beam is modelled by hinge elements connected together by rigid bars while the foundation is replaced by spring elements supporting the hinges. The nonlinear behaviour of the beam and the foundation is described by specially formulated bilinear material models. The characteristics of these models are considered to be unknown but, on the other hand, the deflections of certain points of the beam are given. The goal of the investigation is to determine the best values of the material charcateristics by the use of a mixed variational principle based on the bilinear material model and by the application of the identification methods. The problem is stated in the form of constrained, nonsmooth, nonlinear mathematical programming problem, and the identification is equivalent to finding the minima of a non-linear, multivariable functional. The application is illustrated by the solution of an example.

In many engineering problems modelling of wave propagation in infinite or semi-infinite domains is of great importance. One of the main limitations of the usage of the finite element method in dynamic soil-structure interaction arises when it is used for the modelling of an infinite domain. If nothing is done to take care of artificial reflections at the mesh boundaries, errors are introduced into the results. To handle the reflections different artificial boundaries have been proposed in the literature and used. This paper deals with an improvement of one of the most widely used local absorbing boundary condition - the standard viscous boundary. Both analytical investigations of the efficiency of the boundary as well as numerical results are presented.

The paper concerns the application of an object-oriented approach to the development of FEM software. A brief introduction to basic concepts of object-oriented modelling is given, followed by a short overview of developed classes. Objects, classes, methods and inheritance are illustrated using a graphical representation. The design, implementation and maintenance of an object-oriented program is compared to that of an equivalent procedural program in order to identify advantages of the object-oriented approach. Some design problems of conventional finite element analysis software and their possible solutions offered by the object-oriented methodology are identified and discussed.

The initial-boundary value problem for quasi-linear parabolic equation with distribution coefficient modelling the nonlinear filtration is discussed. The presented results constitute extension of the earlier works of the authors concerning the filtration problem in the domains without sources to the case of filtration in the presence of sources.

A parameter identification problem for nonlinear parabolic equation describing the prelinear filtration phenomenon is considered. It is shown that the problem admits a non-empty solution set which is stable with respect to perturbations in the cost functional and the data. The numerical method for solving the inverse problem is given and the computational results are presented.

We examine S-continued fraction bounds on the effective dielectric constant epsilon_e of a two-phase composite for the case where the dielectric coefficients epsilon_1 and epsilon_2 are complex. The starting point for our study is a power series expansion of epsilon_e at z=0, z=epsilon_2/epsilon_1-1. The S-continued fractions to the expansions of epsilon_e(z) have an interesting mathematical structure. Its convergents represent the best bounds derived earlier by Milton, and independently by Bergman. Specific examples of calculation of complex S-continued fraction bounds on epsilon_e are provided.

The aim of this contribution is to present two-point Padé approximants method for the determination of upper and lower estimates on the effective transport coefficients of two-phase composite materials. The obtained formulae improve the corresponding one-point Padé approximants bounds. As an example, a set of narrowing bounds for the overall conductivity of a square array of cylinders has been evaluated.

Two topics are discussed. Firstly, exact formulae for the homogenized coefficients of a layered thermopiezoelectric composite are derived. Secondly, by applying the Ritz method, the local problems are solved approximately. Specific cases are also examined and illustrated.

The present paper further develops the boundary element technique to provide an efficient and accurate method of analysing the crack propagation processes in 2-D linear elastic structures. Based on both the direct boundary integral equations, for source points located on the external boundary of the plane elastic region, and the indirect boundary integral equations, for the resultant forces acting on one side of the crack surfaces, this technique allows to avoid problems associated with other numerical methods for fracture mechanics computation. In the first part of this paper, the proposed boundary element technique and also the strain energy density criterion, which determines the crack increment in a mixed-mode loading situations, are described. In the second part, two numerical examples are enclosed to demonstrate the capabilities of the boundary element technique as a tool for modelling an arbitrary crack, predicting its growth and updating the model geometry to simulate the next crack increment.

Distributed programming paradigm in key stages of CAD process is proposed, as an alternative to the conventional single-computer--single-user approach. Object-oriented technology is suggested for cooperative design and implementation of large scale engineering computations. Complex ideas concerning specification and design of the new system are presented. In addition, an example of the transformation of the old CAD system to the new environment is described.

Mathematical linguistics models that can be useful for controlling FE mesh generation are presented in the paper. The problems concerning an application of formal grammars for this purpose are outlined. Advantages and drawbacks related to the use of various types of Lindenmayer string/graph systems applied recently for FE mesh generation are discussed. An efficient (parsable) class of ETPL(k) graph grammars is proposed as a formal tool in this research area.

The paper deals with the optimization of regular space trusses with fixed external dimensions under uniform snow and dead-weight loading. Attempts are being made to find such a number of truss joints which minimise the material volume. The set of constraints imposed on a structure includes the effect of the loss of stability of the compressed bar. The statical problem of shallow domes including geometrical nonlinearity was solved by using the Newton-Raphson iteration procedure.

Interference effects in centers of "disk-like" solid cylinders of different photoelastic materials loaded by uniaxial forces acting along diameters was subject of study. An analysis of the intensity of light passing through the cylinder was carried out, and a few numerical models of the phenomenon were constructed and compared with the experimental results. The dispersive character of the "photoelastic constant" is shown and its consequence for the effect are emphasized. A computer aided spectrometer was specially constructed for the research as "the heart" of a semi-automatic measurement stand. The utilization of the effect for the construction of the optical force sensor is mentioned.

Rectangular cross-sections of reinforced concrete beams and columns with nonsymmetric reinforcement are considered in the paper. The~objective function represents the total cost of concrete, steel and formwork. Several dimensional and behavioral constraints (bearing capacity, cracking, deflection) are allowed for. The problem was formulated in general form so that introduction of specific regulations following from national codes is possible. The computer program for optimal design of beams and frames loaded in-plane has been developed. The numerical examples were computed taking into account the rules of Polish Design Code.

In the presented work a model of a layered, delaminated composite beam based on the finite elements method was introduced. In this model the beam was divided into finite elements, while the delamination was modelled using additional boundary conditions. One delaminated region in the cross-section of the beam was considered which extended to the full width of the beam. It was also assumed that the delamination was open. The influence of the delamination length and position on the changes of natural frequencies of flexural vibrations of the laminated composite cantilever beam were investigated.

A multi-disciplinary, numerical approach to shape optimization of notches is presented. The design of the optimal shape of notches in 2-D elastic machine (structural) components is formulated using the Fictitious Stress Method. The design objective is to minimize the maximum effective stress for a given load. Formulation is based on constant stress boundary element. A special concept of segmented Bezier interpolants is adopted for defining geometry of the machine component, and the Sequential Linear Programming is used as optimization procedure.

The flow formulation for metal forming analysis based on a rigid-viscoplastic material model is considered. Specifically, sensitivity evaluation techniques are discussed for different solution variables with respect to variations in parameters entering the constitutive (and other) equations such as material constants, imposed velocities or friction coefficient. A method to avoid spurious pressure modes is introduced which allows to use Q1/Q1 elements and thus to accurately calculate pressures, their sensitivities and friction forces. Also, not only spurious modes are eliminated but, in addition, one pressure unknown for each node is available in this method, thus yielding a finer discretisation for this variable.

Mechanical systems are quite often modelled as sets of stiff and flexible elements. If some conditions concerning connections of these elements are fulfilled, then we get a physical model having an interesting feature: it is quite easy to derive equations of motion from a diagram representing in a natural, intuitive manner the structure of the system. The algorithm for such derivation, including creation of a simple graphical user interface is presented in the paper. The algorithm takes advantage of the software package MATLAB/SIMULINK.

Generally, path-following algorithms are used for the history analysis of structures. Now, a new approach is presented for solving the problem by parametric optimization. The optimization problem is solved in a direct product of function spaces. The necessary conditions of the stationarity of a curve are examined. A method is presented for determining a piece of a continuous component of the Karush-Kuhn-Tucker stationary curve depending on one parameter which transforms the problem into the space L^2.

A generalized, space-time version of the $R$-function method has been presented. The general structure of the solution for the space-time problem and the algorithm for the determination of the unknown parameters of the structure have been given. The considerations are illustrated by two numerical examples: the first one concerns the cooling of a square plate, while in the second one more complex shape of domain is considered. The numerical solution of the first problem is compared with the solution obtained on the basis of FDM.

Application of the boundary element method for approximate solution of non-steady and nonlinear thermal diffusion problems is not possible in a direct way. The fundamental solutions (being a basis of the BEM algorithm) are known only for linear problems - in particular the linear form of the Fourier equation is required. On the other hand, the numerous advantages of the boundary element method are a sufficient justification for the examinations concerning the adaptation of the method in this direction. In the paper, the numerical procedures "linearizing" the typical mathematical model of heat conduction process will be discussed. Combining the basic BEM algorithm for linear Fourier equation with procedures correcting the temporary solutions for successive values of time, we obtain a simple tool which allows us to solve a large class of the practical problems concerning the heat conduction processes. In this paper we will discuss in turn the algorithms called the temperature field correction method (TFCM), the alternating phase truncation method (APTM) and the artificial heat source method (AHSM). In the final part of the paper, some examples of numerical solutions will be presented.

The Element-Free Trefftz method can solve the problem only by taking the collocation points on the boundary when the domain under consideration is governed by the linear and homogeneous differential equation. Only the coordinates and the boundary-specified values on the boundary collocation points are required as the input data and therefore, input data generation is much simpler than the other solution procedures. However, the computational accuracy is strongly dependent on the positions of the collocation points. For determining the positions with the desired accuracy, this paper presents h-adaptive scheme for the placement of the collocation points. Global and local error estimators are defined by the residuals of the boundary conditions. The refinement of the positions is performed so that new collocation points are placed in the center of the boundary segments with larger local error estimators than the global estimator. The present scheme is applied to the two-dimensional potential problem in order to confirm its validity.

The paper presents modelling of optimization process of thin-walled structures such as vertical cylindrical reservoirs subjected to pitting corrosion. The problem is formulated in terms of nonlinear mathematical programming. The function which is a product of its constituents is accepted as the optimization criterion. The choice of an optimal thickness of the reservoir shell along the height is determined from the conditions of its equal reliability.

This paper discusses the effect of deformation-sensitive loading devices. The nature of loading is generally not perfectly dead, namely, it is not perfectly independent of the occurring deflections. However, the surface tractions or body forces can show some variable characteristics, depending on the actual displacements and causing changes in the classical equilibrium and stability behaviour of the structure. The present analysis concerns the influence of deformation-sensitive loading devices on the structural tangent stiffness. The configuration-dependent loading devices can be characterized by some load-deflection functions, similarly to the material behaviour characterized by stress-strain functions. The effect of loading seems to be similar to that of the material and consequently, the nonlinear loading processes can be handled similarly to the nonlinear materials in the equilibrium analyses of structures. Thus, we can find that in the tangent stiffness of the structure, beside the tangent modulus of the material, the tangent modulus of the load.

We consider apriori and aposteriori error estimation for the FEM solution of Helmholtz problems that arise in acoustic scattering. Our focus is on the case of high wavenumber (highly oscillatory solutions) where existing asymptotic estimates had to be generalized to "preasymptotic" statements that are applicable in the range of engineering computations. We refer the key results of an 1D analytic study of error behavior (apriori estimates) and announce new results on aposteriori error estimation. Specifically, we show that the standard local aposteriori error indicators are not, in general, reliable for Helmholtz problems with high wave number, due to considerable numerical pollution in the error. We then discuss a methodology how to (aposteriori) estimate, in addition to the local error, the pollution error. Throughout, the theoretical results will be supplemented by numerical evaluation.

A sensitivity analysis method for elasto-plastic contact problems with large deformation is developed based on two contact constraint methods, i.e., the Lagrange multiplier and penalty methods. Throughout the formulation the importance of using consistent contact stiffness in the sensitivity analysis is emphasized, and is demonstrated in a simple contact problem. Also a heat-transfer tube and plate contact system of heat exchanger used in PWR is analyzed as a real numerical example. The obtained sensitivities of residual stress resulting from the tube expansion process are discussed so as to provide implications for design improvement and quality control.

The development of "DISDECO", the Delft Interactive Shell DEsign COde is described. The purpose of this project is to make the accumulated theoretical, numerical and practical knowledge of the last 25 years or so readily accessible to users interested in the analysis of buckling sensitive structures. With this open ended, hierarchical, interactive computer code the user can access from his workstation successively programs of increasing complexity. The computational modules currently operational in DISDECO provide the prospective user with facilities to calculate the critical buckling loads of stiffened anisotropic shells under combined loading, to investigate the effects the various types of boundary conditions will have on the critical load, and to get a complete picture of the degrading effects the different shapes of possible initial imperfections might cause, all in one interactive session. Once a design is finalized, its collapse load can be verified by running a large refined model remotely from behind the workstation with one of the current generation 2-dimensional codes, with advanced capabilities to handle both geometric and material nonlinearities.

Numerical simulations of the mechanical behaviour of structures composed of cohesive-frictional materials such as soils, concrete and rocks, still suffer from a lack of robustness. Too often an inability to continue the computation beyond a certain level of loading is encountered. Also, predictions of the structural behaviour can be quite inaccurate, with errors amounting up to 100%. Some typical causes for these observations are discussed and some remedies are suggested.

This paper presents an algorithm for parallel computers, which is suitable for the global (arbitrary displacements) computation of elastic bar structures subject to quasi-static loads. Our method is also capable to determine equilibria which are not connected to the initial, trivial configuration. The paper discusses the gains and the disadventages of the method, comparing it with other techniques.

In this paper two domain decomposition formulations are presented in conjunction with the preconditioned conjugate gradient method (PCG) for the solution of large-scale problems in solid and structural mechanics. In the first approach the PCG method is applied to the global coefficient matrix, while in the second approach it is applied to the interface problem after eliminating the internal d.o.f. For both implementations a Subdomain-by-Subdomain (SBS) polynomial preconditioner is employed based on local information of each subdomain. The approximate inverse of the global coefficient matrix or the Schur complement matrix, which acts as the preconditioner, is expressed by a truncated Neumann series resulting in an additive type local preconditioner. Block type preconditioning, where full elimination is performed inside each block, is also studied and compared with the proposed polynomial preconditioning.

Despite the long history of the theory of stability of deformable system, many basic notions, statements and theorems are applied, unfortunately, not rarely incorrectly. This situation is a result of the fineness, complexity, and diversity of the phenomena connected with diverse aspects of the loss of stability of equilibrium states of nonlinear deformable systems. The first part of the article is devoted to the attempt of elucidation of the use of a number of basic statements as the exchange of stabilities at singular points, or the effect of disappearance of bifurcation phenomena as result of geometrical imperfection of the system, and others. The second part of the present work deals with the method of investigation of the global picture of stability of nonlinear deformable systems subjected to multiparametrical loading. This method worked of by the author is based on the so-called ``deformation map'' which contains the whole information of the behaviour of the system subjected to three-parametrical loading. As a basic example taken the stability of geometrically nonlinear spherical shells subjected to transient pressure, contour external forces and temperature field. A number of new effects was revealed. The map can be applied for any nonlinear system (even non elastic) which is described by means of differential equations.

Walsh series and wavelets are nowadays widely applied in digital processes. Their use as approximation functions in a hybrid-mixed finite element formulation for elastic-plastic structural analysis is presented. This formulation is based on the direct approximation of the stress, displacement and plastic multiplier fields in the domain of the finite elements. The displacements on the boundary of the elements are also approximated independently. The essential characteristics and properties of the Walsh and wavelet approximation functions are reviewed. The performances achieved in the different solution phases of elastic and elastoplastic problems are illustrated with numerical applications.

In this paper the steady flow of a viscous incompressible fluid in a slightly asymmetrical channel is considered. The flow is considered for channel with a small aspect ratio. The solution is expanded into a Taylor series with respect to the Reynolds number. Using the D-T method (Drazin and Tourigny), a bifurcation study is performed. Parameter ranges for the Reynolds number, where no, one or two solutions of the given type exist, are computed.

Solving systems of algebraic equations is presented using the Gröbner Basis Package of the computer algebra system MAPLE V. The Gröbner basis computations allow exact conclusions on the solutions of sets of polynomial equations, such as to decide if the given set is solvable, if the set has (at most) finitely many solutions, to determine the exact number of solutions in case there are finitely many, and their actual computation with arbitrary precision. The Gröbner basis computations are illustrated by two examples: computing the global equilibrium paths of a propped cantilever and of a simple arch.

Model of longitudinal vibrations of mine hoist, treated as a discrete-continuous system is formulated. The model includes phenomena connected with variations of the load, carried by each rope and with sliding of the rope contacting with pulley. The effects of changes of length of both branches of rope, variations of their stiffness, internal damping, friction and diversification of parameters of individual ropes in multirope system are taken into account. General model equations, relations describing movement of elementary segments of ropes and of the whole system, and the method of solving the obtained equations are presented in the paper. Nonlinear system of partial and ordinary differential equations is solved numerically. Example results of numerical simulation, showing the possibilities of the formulated model and the program - are presented.

The paper presents numerical techniques useful in nonlinear analysis of structures. The main attention is focused on procedures for the determination of equilibrium paths and examination of critical points. Most of them are connected with the arc length method and can be treated as additional tools, that improve the effectiveness and reliability of computations. It was confirmed in a number of test examples, presented in authors' earlier papers. In this paper only one, but the most representative example including different types of critical points has been chosen. The conclusions are that even highly nonlinear problems can effectively be solved using relatively simple algorithms.

The algorithm for parametric sensitivity assessment for both materially and geometrically nonlinear static problems is presented. Similarly to its geometrically linear version presented elsewhere, the sensitivity analysis is shown to reduce to a linear problem with the same operator matrix that has been used in just completed equilibrium iteration, which makes the computations very efficient. Both total and updated Lagrangian approaches are analysed, including design differentiation of the configuration update transformation. Sensitivity with respect to constitutive parameters is discussed in detail. Possible extensions towards cross-sectional geometry or general shape parameters are pointed out.

By applying Padé approximants and continued fractions technique we investigate a composite material of the effective modulus consisting of two components of real moduli. Our estimations generalize the previous bounds reported in previous papers. The inequalities achieved are applied for the evaluation of the upper and lower bounds from the given experimental measurements.

Optimization of shape and size of foundation should consider the type of loading, numerous geotechnical and geological parameters as well as various safety and economic criteria. Dimensioning depends on various, often controversial, conditions and involves many uncertainties. Therefore we search compromise solutions using nondeterministic analysis based on mathematical logic. In our solution we use computer simulations and results of reliability theory.

Optimal remodelling for least-weight trusses under single as well as multi-load state and limits imposed on local strains is considered. The so called Virtual Distortion Method is applied to simulate process of structural remodelling through fictitious "virtual distortions". In effect, applying knowledge of strains induced by virtual distortions modelling material redistribution, analytical formulas for sensitivity analysis and remodelling simulation process can be obtained. Various algorithms for the VDM-based structural remodelling have been proposed and tested on examples of elastic and elasto-plastic trusses.

The paper shows the essential unity between the known approximation procedures to differential equations. The boundary type approximations associated with Trefftz are shown to be a particular form of the weighted residual approximation and can provide a very useful basis for generating hybrid `finite elements'. These can be used in combination with other finite element approaches.

Trefftz approximations are known to require very few degrees of freedom to give an order of magnitude of the solution. In this paper, we show that it is possible to take advantage of this situation in two ways: (i) we show that it is also possible to get accurate solutions (especially for the pressure) at a reasonable cost and (ii) we show that the low number of degrees of freedom needed for this accuracy allows an easy domain optimisation, which is illustrated here for the free boundary problem in extrusion. A construction of Trefftz polynomials associated with Stokes problem for plane strains is also given with some recurrence properties which is usefull for computing them at a low cost. Moreover a domain decomposition method which has shown to be efficient for compressible elastic material has been extended here to the case of incompressible linear viscous fluids.

In both boundary element methods and Trefftz-type finite element methods a discrete problem on the boundary of the domain and possibly the boundaries between subdomains. We consider a Trefftz element formulation which is based on the complementary energy functional, and we compare different regularizations of the interelement continuity conditions. Also starting from the complementary energy functional, mixed finite elements can be constructed such that the stresses satisfy equilibrium a priori. We describe a coupling of these elements with the by now classical symmetric Galerkin-BEM.

Two alternative models of the hybrid-Trefftz finite element formulation to solve linear elastodynamic problems are presented. In the displacement model, the displacements are approximated in the domain of the element and the tractions are approximated on its boundary. The fields selected for approximation in the complementary stress model are the stresses in the domain and the displacements on the boundary of the element. In both models the domain approximation functions are constrained to satisfy locally the governing wave equation. A Fourier time approximation is used to uncouple the solving system in the frequency domain. The formulations are derived from the fundamental relations of elastodynamics and the associated energy statements are obtained a posteriori. Sufficient conditions for the existence and uniqueness of statically and kinematically admissible solutions are presented. Numerical implementation is briefly discussed.

The author's algebraic theory of boundary value problems has permitted systematizing Trefftz method and expanding its scope. The concept of TH-completeness has played a key role for such developments. This paper is devoted to revise the present state of these matters. Starting from the basic concepts of the algebraic theory, Green-Herrera formulas are presented and Localized Adjoint Method (LAM) derived. Then the classical Trefftz method is shown to be a particular case of LAM. This leads to a natural generalization of Trefftz method and a special class of domain decomposition methods: Trefftz-Herrera domain decomposition.

This paper presents a method for a quick evaluation of stresses and displacements for elastostatic problems. A set of polynomial Trefftz functions and a variational formulation are introduced for solving elastostatic problems for simple star-shaped domains. It is shown, through examples, that this approximation allows the computation of the interior large wavelength effects. By a procedure for coupling separate domains, this method is extended to more complex structures, which is a natural extension of the above variational formulation. A discretization of the structure into large substructures, an easy to use and quick computation of the interior solution justify that this method can be termed `simplified'. Comparisons with other similar methods are also shown.

The numerical solution of Helmholtz' equation at large wavenumber is very expensive if attempted by "traditional" discretisation methods (FDM, standard Galerkin FEM). For reliable results, the mesh has to be very fine. The bad performance of the traditional FEM for Helmholtz problems can be related to the deterioration of stability of the Helmholtz differential operator at high wavenumber. As an alternative, several non-standard FEM have been proposed in the literature. In these methods, stabilisation is either attempted directly by modification of the differential operator or indirectly, via improvement of approximability by the incorporation of particular solutions into the trial space of the FEM. It can be shown that the increase in approximability can make up for the stability loss, thus improving significantly the convergence behavior of the knowledge based FEM compared to the standard approach. In our paper, we refer recent results on stability and convergence of h- and h-p-Galerkin (`standard') FEM for Helmholtz problems. We then review, under the label of `knowledge-based' FEM, several approaches of stabilised FEM as well as high-approximation methods like the Partition of Unity and the Trefftz method. The performance of the methods is compared on a two-dimensional model problem.

The thin plate p-elements considered in this paper are based on assumed displacement field chosen so as to a priori satisfy the governing Lagrange equation within the element. The required C1 conformity is then enforced in a weak sense trough an auxiliary displacement frame defined in terms of nodal and side mode parameters. While thus far the standard approach consisted in using three parameters (one displacement and two rotations) at corner nodes and an optional number of side mode parameters associated with mid-side nodes, other alternative formulations are also possible wherein the number of corner mode parameters is either inferior or superior to three. As compared to the standard frame, such alternative formulations may exhibit some advantages and some shortcomings with respect to accuracy, convergence rate, error distribution, computational efficiency and/or ease of use. The paper surveys and critically assesses some of such formulations and reports the results of extensive numerical studies involving regular and singular plate bending applications.

The reported research presents a finite element formulation for folded plate analysis based on the p-version of the hybrid-Trefftz finite element model. The internal displacement field of the elements consists of a suitably truncated T-complete set of in-plane (u,v) and out-of-plane (w) components which satisfy the respective governing differential plane elasticity and thin plate (Kirchhoff) equations. Conformity is enforced in a weak, weighted residual sense through an auxiliary displacement frame, independently defined at the boundary of the element and consisting of displacement components and normal rotation. The displacement frame parameters are the global Cartesian displacements at corner nodes and the hierarchical side-mode parameters for normal rotation and the global Cartesian displacement components, an optional number of which is allotted, formally, to mid-side nodes. The investigated approach is assessed on numerical examples.

This paper presents the boundary-type schemes of the first- and the second-order sensitivity analyses by Trefftz method. In the Trefftz method, physical quantities are approximated by the superposition of the T-complete functions satisfying the governing equations. Since the T-complete functions are regular, the approximate expressions of the quantities are also regular. Therefore, direct differentiation of them leads to the expressions of the sensitivities. Firstly, the Trefftz method for the two-dimensional potential problem is formulated by means of the collocation method. Then, the first- and the second-order sensitivity analysis schemes are explained with the simple numerical examples for their verification.

The paper propose two adaptive algorithms based on a Trefftz method for two-dimensional Laplace equation satisfying the maximal principle. First one for given the error tolerance and an initial number of terms in the solution expansion, the algorithm computes expansion coefficient by location of boundary conditions and evaluates the maximum absolute error on the boundary. If error exceeds the error the tolerance, additional expansion terms and boundary collocation points are added and process repeated until the tolerance is satisfied. The second one is based on Galerkin formulation of Trefftz method and utilizes the exact potential error norm for predict a new mesh and new solution expansion until the tolerance is satisfied.

The purpose of the paper is to propose of a way of constructing trial functions for the indirect Trefftz method as applied to harmonic problems possessing circular holes, circular inclusions, corners, slits, and symmetry. In the traditional indirect formulation of the Trefftz method, the solution of the boundary-volume problem is approximated by a linear combination of the T-complete functions and some coefficients. The T-complete Trefftz functions satisfy exactly the governing equations, while the unknown coefficients are determined so as to make the boundary conditions satisfied approximately. The trial functions, proposed and systematically constructed in this paper, fulfil exactly not only the differential equation, but also certain given boundary conditions for holes, inclusions, cracks and the conditions resulting from symmetry. A list of such trial functions, unavailable elsewhere, is presented. The efficiency is illustrated by examples in which three Trefftz-type procedures, namely the boundary collocation, least square, and Galerkin is used.

We introduce the hybrid-Trefftz FE formulations for linear statics of solids as well as for linear (slow velocity) steady fluid dynamics. Moving least square procedure is given to obtain continuous secondary fields (such as stresses for solids), which improves the results. For nonlinear problems the governing equations are satisfied in the discrete least square residual form. Also for such problems the hybrid FE formulation is shown.

A recent geometric presentation of a general and efficient methodology for recovering equilibrating tractions and stress fields from 2-D conforming displacement finite element models is reviewed, and further considered in the context of plate elements in 2-D and 3-D. This methodology requires the resolution of corner nodal forces/moments, and this presents localised problems which are solved in a simple way by exploiting Maxwell force diagrams. For more complex 3-D models including solid elements where higher degrees of element connectivity occur, the geometric procedure is adapted so as to retain the computational efficiency gained from recognising the topological and geometrical properties of a finite element model. Graph-theoretic and algebraic topological concepts are invoked in this context. The equilibrating tractions recovered for each element enable statically admissible stresses to be computed element by element, and local Trefftz fields may be exploited.

We describe a new Quasi Trefftz-type Spectral Method (QTSM) for solving boundary value and initial value problems. QTSM combines the properties of the Trefftz method with the spectral approach. The special feature of QTSM is that we use trial functions which satisfy the corresponding homogeneous equation only approximately. These trial functions are represented in the terms of a truncated series of eigenfunctions of some eigenvalue problem associated with the problem considered. The method has been found to work well for different elliptic problems with the Laplace, the Helmholtz and the biharmonic operators. We also consider some nonstationary parabolic problems including the problem in the domain with moving boundaries. The possibilities of further development of QTSM are also discussed.

Generally, two approaches have been used to study the nonlinear wave-structure interaction in the context of offshore engineering in recent years. One is based on the Stokes perturbation procedure in the frequency domain and has been applied to weak-nonlinear problems. The other is based on a full nonlinear solution to the resulting wave field by a time-stepping procedure with boundary conditions applied on the moving free and body surfaces. In the present work an alternative solution method for nonlinear wave-structure interaction problems is proposed. The method is based on the evolution equations for the free-surface elevation and the free-surface potential, which are solved by the time-stepping procedure. The field problem is solved at each time step by the perturbation method combined with Trefftz approach. The method is applied to the study of the evolution of three-dimensional waves generated by a vertical circular cylinder oscillating in water of constant depth.

A review is presented of a recent formulation of hybrid-equilibrium elements for modelling planar structural problems. The formulation is based on the use of polynomials of general degree to approximate internal stress fields and bounding side displacements. The existence of hyperstatic stress fields and spurious kinematic modes are considered algebraically for both primitive and macro-elements, the latter providing a means of controlling or removing the spurious modes in the former. Consideration is given to stress fields which are statically admissible, and to Trefftz stress fields which are both statically and kinematically admissible.

The aim of the paper is twofold. In the first part, we present an analysis of the approximation properties of `complete systems', that is, systems of functions which satisfy a given differential equation and are dense in the set of all solutions. We quantify the approximation properties of these complete systems in terms of Sobolev norms. As a first step of the analysis, we consider the approximation of harmonic functions by harmonic polynomials. By means of the theory of Bergman and Vekua, the approximation results for harmonic polynomials are then extended to the case of general elliptic equations with analytic coefficients if the harmonic polynomials are replaced with their analogs, `generalized harmonic polynomials'. In the second part of the paper, we present the Partition of Unity Method (PU). This method has the feature that it allows for the inclusion of a priori knowledge about the local behavior of the solution in the ansatz space. Therefore, the PU can lead to very effective and robust methods. We illustrate the PU with an application to Laplace's equation and the Helmholtz equation.

In this paper the possibility of applying the Trefftz-method to thick and thin shells is discussed. A mixed variational formulation is used in which the assumed strain and stress functions are derived from the three-dimensional solution representation for the displacement field. For the construction of the linearly independent Trefftz trial functions both the Neuber/Papkovich solution representation and a complex variable approach of the author are considered. The difficulty in constructing the solution functions for the displacement field consists of two problems: i) How can we choose the functions in order to have a symmetric structure in the displacement field and not to bias the solution in any direction? ii) How can we avoid to get linearly dependent terms for displacements, strains and stresses when seeking polynomial solution terms?

Modeling of elastic thin-walled beams, plates and shells as 1D and 2D boundary value problems is valid in undisturbed subdomains. Disturbances near supports and free edges, in the vicinity of concentrated loads and at thickness jumps cannot be described by 1D and 2D BVP's. In these disturbed subdomains dimensional (d)-adaptivity and possibly model (m)-adaptivity have to be performed and coupled with mixed h- and/or p-adaptivity by hierarchically expanded test spaces in order to guarantee a reliable and efficient overall solution. Using residual error estimators coupled with anisotropic error estimation and mesh refinement, an efficient adaptive calculation is possible. This residual estimator is based on stress jumps along the internal boundaries and residua of the field equation in L2 norms. In this paper, we introduce an equilibrium method for calculation of the internal tractions on local patches using orthogonality conditions. These tractions are equilibrated with respect to the global equilibrium condition of forces and bending moments. We derive a new error estimation based on jumps between the new tractions and the tractions calculated with the stresses of the current finite element solution solution. This posterior equilibrium method (PEM) is based on the local calculation of improved stress tractions along the internal boundaries of element patches with continuity condition in normal directions. The introduction of new tractions is a method which can be regarded as a stepwise hybrid displacement method or as Trefftz method for a Neumann problem of element patches. An additional and important advantage is the local numerical solution and the model error estimation based on the equilibrated tractions.

In this paper a block method is developed to use on uniform-graded mesh for the solution of Volterra integral equations of the second kind. This method permits the use of a variable step size when solving Volterra integral equations. Means of reducing the error. Extensive results are presented.

An efficient, accurate, and simple numerical method is necessary for analysis and design of an incompressible potential flow around multi-element airfoils. In this paper, which is the subject of the second part of the study, the mathematical model is built utilizing the local coordinate system, while in the first part of the study [1]. only the global coordinate system is used. Mathematical model, by the vortex panel method with the use of the stream function, is written for the analysis of potential flow over multi-element airfoils. The computational model is built for both uniform and linear vortex distributions with utilizing the constant stream function boundary condition. From the fact that any study which does not consider deeply and precisely, all the parameters relevant to the computational model, might make it fragmentary. Hence, the following parameters are tested to investigate their effect on the accuracy of the method. They are: both types of the vortex distribution, two types of panelling, different ways of applying the Kutta condition, and two ways of positioning the control points. For the purpose of easier comparison, the study cases performed using the present model are restricted only to single-element airfoils; NACA 0012 airfoil at an angle of attack alpha=8.3°, and a cusped trailing edge 15 percent thick Van de Vooren airfoil at alpha=5°. [1] M.M. Bahbah, B. Maruszewski. Effect of panelling and application of the numerical solution of panel methods. ECCS-1 Conference, Changsha, China, 1995.

In this paper a practical procedure for the solution of really sized mixed problems, generating a continuous stress field (where appropriate) and having both the stress and displacement boundary conditions exactly satisfied, is described. The system matrix for the present formulation can be subdivided into the blocks, if the field variables (stresses and displacements) are separated for computational purposes. In addition, the structure of these blocks is sparse, similarly as the structure of the stiffness matrix in classical finite element analysis. Block sparse solution procedure, accounting for the pattern of the resulting system matrix is proposed. Computer implementation confirmed feasibility of the described solution procedure. In addition, numerical tests show remarkably high accuracy and convergence rate of the present mixed scheme for both the stresses and displacements. Due to high accuracy of the scheme, it can be competitive in comparison with usual displacement approach, although the count of arithmetic operations for the same mesh density in mixed procedure can be an order of magnitude larger than in classical finite element analysis.

We investigate the performance of the Naghdi shell model using a family of hierarchic high order finite elements. We solve two cylindrical shell problems, representative of extremely discriminating situations: the membrane dominated Scordelis-Lo problem and a bending dominated problem already tested by Leino and Pitkäranta. As it is well known, these problems are hard tests for shell elements, especially when the thickness of the shell is approaching to zero, since the presence of hidden constraints can lead to numerical convergence problems, known as shear and membrane locking. The numerical results show the robustness of the finite elements developed, able to avoid the locking behavior.

The optimization of the nozzle shape was carried out using the finite element incompressible viscous flow solver, with discretization of total derivative, with the originally developed software. Optimization procedure used conjugate gradient method, with finite difference approximation of gradient of objective function. The mesh generator, specially adapted for chosen shape parametrization in the form of splines using Bezier cubic curve segments, has been used in optimal shape design of the nozzle. The examples of optimization with constraints, the nozzle shape optimization, and the unconstrained optimization of the confusor are presented. All test cases showed good convergence properties that qualifies the proposed methodology as appropriate for shape optimization in viscous flow problems.

In this paper we discuss the use of the singularity subtraction technique incorporated with the Tau Method for the numerical solution of singular partial differential equations which are relevant to the linear elastic fracture mechanics. To treat the singularity, we apply the singularity subtraction technique to the singular boundary value problems. The problems arising in this application are not in the standard form required by the Tau software. By introducing the pseudo-differential equations, lambda'_k = 0, k=1(1)m, to determine the stress intensity and higher order factors lambda_k results in the standard boundary value problems. We consider two model crack problems including Motz' anti-plane crack problem and a plane strain problem defined by the biharmonic equation. We obtain results of considerable accuracy which compare favorably with those published in the recent literature.

The paper presents some aspects of the formulation and numerical implementation of combined mathematical model "elastic body - Timoshenko plate". The variational problem is formulated. The existence of solution of combined model is considered. The numerical investigation of the problem is performed by coupling Direct Boundary Element and Finite Element Methods. Numerical example is presented supporting the analysis.

The paper presents some aspects of the sensitivity analysis within the multivariate distribution models. The presented procedures are provided for engineering problems based on the Nataf model. The Nataf model involves the marginal distributions of the random variables and the correlation between them. Sensitivities are considered through derivatives with respect to the correlation coefficients. The terms for the derivatives of the Nataf correlation coefficients with respect to the given correlation coefficients are presented. The derivatives of the transformations between the random variables are given next. The Cholesky decomposition and the spectral decomposition are applied. Derivatives of the Cholesky decomposition are obtained in the form of a recursive scheme. Derivatives of the eigenvalues and eigenvectors are obtained using perturbations. In addition, a comprehensive method for derivatives of distances and derivatives of angles between the directions is given. Finally, numerical examples are attached to illustrate the presented procedures.

Many numerical methods for studying chemical reaction problems require the computation of the eigenvalues of very large complex symmetric matrices. Recently, a new algorithm for this problem has been proposed by Bar-On and Ryaboy [1]. This algorithm is similar in concept and complexity to the Hermitian eigensolver and is based on application of complex orthogonal transformations to preserve symmetry and recovery transformations to preserve stability. We demonstrate the performance of the proposed algorithm on several high performance computers from Digital, SGI, and Cray. The results show that the new algorithm is much faster than the general eigensolver, the present method used for solving these problems. [1] I. Bar-On, V. Ryaboy. Fast diagonalization of large and dense complex symmetric matrices, with applications to quantum reaction dynamics. SIAM J. on Scientific Computing, 18: 1412--1435, 1997.

We discuss a global, iteration-free numerical scheme (based on the Piecewise Linear algorithm), with special respect to the computation of elasto-plastic frames. The plastic deformations are concentrated in plastic hinges which may appear at both ends of the bars, while the inner parts of the bars can have only elastic deformations but without limation on their magnitude. Our method is tested on a classical example and the results show very good match with those known from the literature. We discuss advantages and disadvantages and point out other, related applications.

New developments in structural analysis methods such as automatic error estimation, adaptive discretization control, and mesh generation are slowly becoming available in engineering practice. On the other hand, graphical interactive user environments and easy-to-use general purpose programs are prolific. Each of these new developments helps to ease the everyday work of the engineer, but only by joining them together in a unified framework and user environment, an entirely new class and generation of structural analysis tools on the computer can be generated. The present study suggests guidelines and principles how such a new generation of software can be brought about, and reports experiences with a prototype application that is already in practical use.

The solution procedure proposed by Vlasov based on the reduction of the basic two-dimensional boundary value problems into ordinary differential equations provides a good accuracy in the case of rectangular domains with small size ratios. The paper presents an extension of this method applied to rectangular Kirchhoff's plates in connection with the iterational scheme. The results are compared with analytical solutions available for rectangular plates with simplified boundary conditions and loading. The possibilities of application of the solutions for simple plate geometry to complex plate problems (e.g. complex geometry, boundary conditions) are discussed and illustrated by numerical examples.

An analysis of the ship stability requires computer simulations of the ship motions leading to its capsizing. The large amplitudes of roll motion of the ship are connected with phenomena of immersing of ship deck into water. These phenomena require to take into account additional moments connected with water on a deck. The paper presents a new method (1994) of calculating these additional moments. An approximate and simple calculation of the additional moments is based on the second principle of dynamics applied to an element of a water running off the deck. The additional moments applied in numerical simulations of the ship motions, change significantly the roll motion. The paper presents results obtained from computer simulations. Some of the results are compared with the results of an experiment done with the ship model.

We consider the numerical approximation of thin plate and shell structures. The plate model is described following the Reissner-Mindlin assumptions while the shell is described using the Naghdi formulation. It is well known that the numerical approximation with standard finite elements suffers of the so-called locking phenomenon, i.e., the numerical solution degenerates as the thickness of the structure becomes smaller. Plates exhibit shear locking and shells show both shear and membrane locking. Several techniques to avoid the numerical locking have been proposed. Here we solve the problems using a family of high order hierarchic finite elements. We present several numerical results that show the robustness of the finite elements, able to avoid in many circumstances the locking behavior.

This paper presents a numerical algorithm for the study of the absolute instability of a vortex street with external axial velocities and finite length vortices. The aim is that this will be of relevance to the study of the flow over slender bodies at yaw. The algorithm is based on the vortex dynamics momentum equation. Special core treatments have been implemented to tackle the problem of infinite self-induced velocity. A small perturbation method is then used to formulate the eigenvalue problem.

In this paper we discuss sparse matrix computational methods, and their parallel implementations, for evaluating matrix-vector products in iterative solution of coupled, nonlinear equations encountered in finite element flow simulations. Based on sparse computation schemes, we introduce globally-defined preconditioners by mixing clustered element-by-element preconditioning concept with incomplete factorization methods. These preconditioners are implemented on a CRAY T3D parallel supercomputer. In addition to being tested in a number of benchmarking studies, the sparse schemes discussed here are applied to 3D simulation of incompressible flow past a circular cylinder.

This paper introduces a simple and approximate method of calculating the elastic driving force acting on the interface in two-phase materials. The method is based on considerations of the elastic energy connected with the change in the shape of the interface. The two phases are considered to be elastically isotropic media with different elastic constants. The procedure is developed in the framework of the finite element method and is applied to the estimation of the local driving force in the case of the edge of aa interface with a singular distribution of stress. The application of T-stress to the problem is suggested.

Local approach in fracture mechanics is based on the application of appropriate failure micromechanistic models to make predictions of fracture behaviour. The FEA of crack-tip and an associated post-processing routine is usually applied. Here should be noted the distinction between the cells of material, having characteristic microstructural dimensions, which constitute the cleavage process zone, and the corresponding finite elements used to represent their behaviour. Predictions of brittle fracture are based on the Beremin local approach model, where the Weibull location parameter sigma_u and shape parameter m have been calculated using FEM for Charpy type specimen. These parameters are considered to be transferable material properties, independent of temperature, specimen geometry or loading mode and can be used for prediction of the stress intensity factor K.

This paper presents an optimal design method of continuum structures by genetic algorithm. Profiles of the objects under consideration are represented by the spline functions and tnen, the chromosomes for the profiles are defined by the coordinates of the control points of the functions and the material code of the structures. The profiles and the material code are optimized by the genetic operations in order to determine the object satisfying the design objectives. The minimum weight design of the plate is considered as a typical example. The present method is applied to the problem in which the profile and the material of the objects are unknown.
Keywords: genetic algorithms (GAs), boundary element methods (BEMs), shape optimization, material selection, Riesenfeld spline functions.

Analysis of fracture processes in structures of quasi-brittle concrete-like materials is here discussed on the basis of discrete cohesive crack models and of a nontraditional boundary element method. This method, called 'symmetric Galerkin BEM', is characterized by the combined use of static and kinematic sources (i.e. traction and displacement discontinuities) to generate a symmetric integral operator by its space discretization in the Galerkin weighted-residual sense. Consistently, the discrete crack model is enforced in a weak sense and expressed in terms of Prager's generalized variables. On this basis, some of the main aspects of a computational theory of quasi-brittle fracture mechanics are presented and discussed.

The behaviour of planar Newtonian and non-Newtonian polymeric jets is investigated in the context of injection mould filling. The incompressible Stokes flow model consistent with the application of injection mould filling is described together with the shear rate dependent fluid viscosity for a typical polymeric melt. The numerical procedure for the solution of the nonlinear system is briefly discussed as well as the mesh generation and the melt front tracking algorithms employed. In the analysis, the buckling behaviour of Newtonian and non-Newtonian jets are firstly compared. Thereafter the behaviour of Newtonian jets are analysed for various values of the aspect ratio in an attempt to study the validity of the Cruikshank buckling conditions for planar Newtonian jets. It is argued that the Reynolds number of highly viscous polymeric melts is relatively low and the aspect ratio condition is the critical condition dictating the buckling behaviour. Finally, an aspect ratio design criteria is established for buckling-free and folding-free flow of polymeric jets.
Keywords: injection moulding, free surface flows, unsteady non-Newtonian flow.

The paper presents the axiomatic approach for solving the multicriteria optimization of thin-walled structure such as vertical cylindrical reservoirs subject to pitting corrosion. The probabilities of derivation of the compromise optimal project based on MaxMin principle are investigated. The analytic dependencies for estimation of the partial criteria weighting coefficients are obtained. The project consists of the optimal thickness of reservoir shell along its height

This paper presents a practical algorithm for on-line parameter identification of squeeze-film bearing of multi-mode rotor-bearing system. The identification procedure is based on modeling each of the bearing pedestal by applying a multi-frequency excitation force on, the rotor and frequency transfer function data are used. It suggested that accurate identification coefficients with reduced standard errors can be achieved without resource to full or reduced-order rotor system measurements. The approach can be applied to rotor-bearing system with any degree of complexity and other types of bearing. Simulation and experimental investigation show that the identification algorithm developed in the paper will considerably simplify the measurement and calculation task for testing work in laboratory and industrial environment without any lost of identification accuracy. The experimental results of stiffness and damping characteristics of the squeeze-film bearings for different rotating speed are also presented.

The paper presents a space-time discrete modeling of the dynamic rail-wheel contaet problem and an analysis of the induced corrugations. First, the space-time approach to simple contact problems is presented: Then, the resulting differential equation of motion is solved by discrete time integration. An arbitrary mesh modification, both in time and space, enables an easy modeling of rapidly varying contact zone. The velocity formulation is used and the discontinuity of the velocity in the contact is removed by a special algorithm. Finally the discussed technique is used to simulate interaction of the elastic wheel and rigid rail. It is shown that the contact force oscillates and the material of the wheel rotates oscillatory.

The paper describes an implementation of the variant of the speed method in shape optimization for plane elastic structures, based on harmonic transformations. It is coupled with special method for solving the singular elliptic problems resulting from geometric features like e.g. reentrant corners. Both approaches are based on the works of the author. The interactive system has been built, based on MATLAB environment, and the examples showing the robustness of the algorithms were solved.

The aim of this paper is the discussion on the applicability of some rectangular elements to plane strain boundary value problems. Four different elements were considered: 4-node, 5-node, Serendipity 8-node and Lagrangian 9-node. Two cases: the material layer loaded by a concentrated vertical force and the same layer loaded by a symmetrical rigid punch were discussed. An elastic material was used to avoid the influence of the constitutive model on solutions. To model interface behaviour on the contact surface a Coulomb friction condition was applied. The use of the 4- and 5-node elements resulted in the prediction of the `island' pattern of stress and strain tensors distributions and their non-applicability was proved independently from the boundary condition. The 8-node element predicted erroneous distributions of nodal forces and should be avoided in the case of contact problems. Among the discussed group of elements only the 9-node element turned out to be applicable for boundary value problems under plane strain condition.

This paper provides an analysis of the results of a comparison exercise on the numerical 2D solution of melting from a vertical wall, dominated by natural convection in the liquid phase. The thirteen contributions to this exercise cover the great variety of mathematical models and numerical procedures most commonly used in this field. The main conclusions presented at the AMIF Workshop (PCC99) held in Warsaw in June 1999 and at the Moving Boundaries Seminar in Ljubljana are summarized in the paper. They emphasize the need for the definition of such reference validation tests.

The paper concerns shape functions formulations in the scope of the recent methods generalizing finite elements and whose common feature is the absence of a mesh. These methods may also be interpreted as a generalization of the finite difference approach for irregular grids. The shape functions obtained by the Moving Least Squares and by the GFDM (Generalized Finite Difference Method) approach exhibit a number of interesting properties, the most interesting being a local character of the approximation, high degree of continuity and the satisfaction of consistencu contraints neccesary for exact reproduction of polynomials. In the present work we formulate the shape functions directly as solutions of the minimization of a weighted quadratic form subjected to the consistency contraints explicitly introduced by Lagrange multipliers. This approach gives similar results as the standard moving least squares algorithm applied to the Taylor series expansion where the consistency is automatically satisfied but is more general in the sense, that an explicit specification of wished properties permits an introduction of additional arbitrary constraints other than consistency. It also leads to faster and more robust algorithms by avoiding matrix inversion. On the other hand, the consistency based formulations naturally lead to diffuse (or incomplete) derivatives of the shape functions. They are obtained at a significantly lower cost than full derivatives and their convergence to extact derivatives is demonstrated.

One of the simplest ways of representation of uncertain or inexact data, as well as inexact computations with them, is based on interval arithmetic. In this approach, an uncertain (real) number is represented by an interval (a continuous bounded subset) of real numbers which presumably contains the unknown exact value of the number in question. Despite its simplicity, it conforms very well to many practical situations, like tolerance handling or managing rounding errors in numerical computations. Also, the so-called alpha-cut method of handling fuzzy sets membership functions is based on replacing a fuzzy set problem with a set of interval problems. The purpose of this paper is to investigate possibilities of and problems with application of interval methods in (qualitative) analysis of linear mechanical systems with parameter uncertainties, in particular truss structures and frames. The paper starts with an introduction to interval arithmetic and systems of linear interval equations, including an overview of basic methods for finding interval estimates for the set of solutions of such systems. The methods are further illustrated by several examples of practical problems, solved by our hybrid system of analysis of mechanical structures. Finally, several general problems with using interval methods for analysis of such linear systems are identified, with promising avenues for further research indicated as a result. The problems discussed include estimation inaccuracy of the algorithms (especially the fundamental problem of matrix coefficient dependence), their computational complexity, as well as inadequate development of methods for analysis of interval systems with singular matrices.

A hybrid system of coordinates and a relatively general Lagrangian formulation for studying the dynamics and control of spacecraft with flexible members is developed. Versatility of the formulation is illustrated through a dynamical study of the satellite with two symmetrical flexible solar panels, where the finite element method is used to describe elastic deformations of solar panels modelled as flat plate structures in bending. The performance of the satellite undergoing roll maneuver is simulated. Results indicate that, under an unshaped input, the maneuvers induce undesirable roll motion of the satellite as well as vibration of the solar panels. A zero vibration input shaper is then applied to reduce the largest magnitude of residual oscillation of roll motion. Once the shaped roll torque input is applied to the satellite, the performance improves significantly. When the longest distance of impulsing time sequences in the input shaper is close enough to the period of large amplitude vibration of flexible members, its maximum deflection during attitude maneuver will also be close enough to the amplitude of vibration with this period under the bang-bang input.

In certain problems of loading of elastic-perfectly plastic thin sheets a continuous displacement solution may not exist. The evolution of plastic zone is then connected with the evolution of discontinuity lines in both velocity and displacement fields. In the present paper it is assumed that in the presence of discontinuity lines the localized plastic zones start to proceed. A numerical study of decohesion within thin elastic-plastic sheets is conducted to total collapse. It is shown, that the localized plastic flow may develop simultaneously with the diffuse plastic zones. The structural softening caused by decohesive cracks is coupled with a complex elasto-plastic deformation process, where the previously developed diffuse plastic zones are subjected to unloading. The post-critical analysis is performed using a new reliable algorithm of a continuation method. The algorithm is based on a rank analysis of the rectangular matrix of the homogeneous set of incremental equations.

The axisymmetric flow of a viscous fluid and heat transfer in a pipe filled with porous media driven by suction at the pipe wall is examined. For low suction Reynolds number flow, asymptotic solutions are developed. Using MAPLE, the solution series is extended and a bifurcation study is performed. Our results show that a decrease in the permeability of porous media may reduce the magnitude of heat transfer across the wall. The absence of real solutions of the given type between two turning points is also noticed and this gap of no solution disappears as the permeability of the porous media decreases.

Preface

Meshfree methods have been developed based on Galerkin type weak formulation and strong formulation with collocation. Galerkin type formulation in conjunction with the compactly supported approximation functions and polynomial reproducibility yields algebraic convergence, while strong form collocation method with nonlocal approximation such as radial basis functions offers exponential convergence. In this work, we discuss rank instability resulting from the nodal integration of Galerkin type meshfree method as well as the ill-conditioning type instability in the radial basis collocation method. We present the recent advances in resolving these difficulties in meshfree methods, and demonstrate how meshfree methods can be applied to problems difficult to be modeled by the conventional finite element methods due to their intrinsic regularity constraints.


Keywords: meshfree methods, stabilization method, collocation method, reproducing kernel, radial basis function.

The expressions of vibration power flow (VPF) in beam-plate structures (BPS) have been derived in the Part I of this paper. Based on those results got in Part I, Part II presents the expressions of VPF in BPS under the following three cases as shown Figs. 1, 2 and 3 below. (1) the isolating component 1 (ICl) being added at the free end of the beam; (2) isolating component 2 (IC2) being embedded between the beam and the plate; and (3) IC1 and IC2 being in BPS simultaneously (IC1 and IC2). According to these expressions, the corresponding numerical calculations are completed. The influence of parameter of the isolating components on VPF is also considered in this part. And then numerical calculations of VPF are verified by the measurements of VPF. Some valuable conclusions have been applied to vibration control of tracked vehicles mentioned in Part I.
Keywords: vibrational power flow (VPF), beam-plate structures (BPS), isolation.

This paper presents the expressions of Vibrational Power Flow (VPF) in Beam-Plate Structures (BPS). These expressions are derived based on structural dynamics. BPS is composed of a constant cross-section beam and a thin flat rectangular plate. In expressions the plate is four-edge simply suppored and four-edge fixedly supported, respectively. The numerical calculation of these expressions is implemented. IţIeanwhile, the different parameters of beam and plate are also considered in the calculation. Finally, the numerical solutions of VPF in BPS are compared with the corresponding the measured VPF. The numerical VPFs have a good agreement with the measured VPF: The results of VPF provide a tool for analyzing vibra- tional energy transmission between the support roller and the armored plate of tracked vehicles.
Keywords: vibrational power flow (VPF), mechanical mobilities, beam-plate structures (BPS).

A description of the play, that may be applied to many other problems, is the basis of the model of a beam system presented in this paper. Equations describing the motion of the system of spring elements under dynamic load have been derived taking into consideration the play occurring between the elements. The equations have been derived according to the Hamilton's variational prineiple. The play has been treated as a force interacting between the elements whose value depends non-linearly on the mutual distance of the contact places. The function that defines the elements' interacting force may be easily enriched with elements responsible for the energy dissipation, eg. friction. The value of the method presented was proved by the carried out comparative analysis. The equation obtained has been used for an example which the finite elements method (modal technique) has been applied too for comparison. In order to make the comparison more complete, the calculations have been performed not only for the beam model but for a full spatial model as well (basing on the shell model).

An approach for modeling finite-rate chemistry effects such as local extinction and reignition in piloted diffusion fiames of CO/H₂/N₂ or CH₄ and air is presented. A partial equilibrium/two-scalar exponential PDF combustion model is combined with a 2D Large Eddy Simulation procedure employing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of the PDF scalars is avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is accounted for by comparing the local Damkohler number against a `critical' local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is modelled via a Lagrangian transport equation for a reactedness progress variable that follows a linear deterministic relaxation to its mean value (IEM). Comparisons between simulations and measurements suggested the ability of the method to calculate adequately the partial extinction and reignition phenomena observed in the experiments.
Keywords: CO/H₂/N₂ or CH4₄ flames, extinction and reignition, partial equilibrium model, Large Eddy Simulations, Lagrangian models.

An analytical study of stability is made for a hydromechanical servomechanism used in copying systems. In the framework of a nonlinear system of ODE mathematically modelling the servomechanism, we prove that for a ramp input the steady-state solution bifurcates into a stable limit cycle for a certain value of the underlap spool valve.

The paper is concerned with the mathematical modelling and numerical solution of unilateral problems for viscoelastic-plastic structural systems. A new material model is proposed in which the viscoelastic and plastic strains are governed by different constitutive laws. The model is restricted to isothermal quasistatic deformation processes under conditions of geometric linearity. The mechanical problem is posed in the format of piecewise linear plasticity and the unilateral contact conditions are described by means of the clearance function. The linear viscoelastic laws are integrated by a creep approach method, which allows for jump-discontinuities in the history of stress. For the evolution of plastic strains an implicit method is used. The problem is formulated and solved as a sequence of nested (mixed) linear complementarity problems. The question of existence and uniqueness of a solution to the problem is discussed. A numerical algorithm based on the pivotal transformations is devised and its stability is shown numerically. Results of numerical experiments for several illustrative examples of a beam/foundation system subjected to nonproportional loading histories are presented. The results clearly demonstrate the impact of the history of loading and the unilateral constraints upon the current state of the structural system.
Keywords: viscoelasto-plasticity; creep approach; unilateral constraints; finite element method; linear complementarity problem.

The single-mode equation of motion of a class of buckled beams is considered, and the attention is focused on the phenomena of irregular, unpredictable transient oscillations which are observed in the region of the nonlinear resonance hysteresis. This type of transient motion may be dangerous in engineering dynamics, because it may last very long and is defined neither by the coefficient of damping nor by the magnitude of perturbation. While the steady-state chaotic motion has been studied extensively in the recent literature, little attention was paid to the chaotic transients. In the paper the criteria for transient chaos, i.e. the domain of the system control parameter values, where the chaotic transient motion can occur, are determined. The criteria are based on the theoretical concept of global bifurcations, and are estimated numerically.

Recent advances in reliability methods, optimization as well as design sensitivity analysis have resulted in development of computational systems supporting RBDO processes for medium/large structures. For RBDO the efficiency problems are critical and in order to get the optimum design a number of fast approximate methods have been recently proposed. These methods, tested for rather small problems, show acceptable accuracy and speed up computations considerably. However, when applied in the automated way to medium/large scale problems they may cause severe convergence problems or lead to a poor local minimum after expensive computations. Instead of an automated optimization procedure, an interactive approach is proposed. Implemented in the POLSAP-RBO system it allows to combine effective interactive design methods with visual capabilities to efficiently generate optimum design. Benchmark studies of an offshore jacket structure show efficiency of the interactive approach which employs integration, approximation and reduction techniques for maximizing efficiency of RBDO.

The authors developed a calculation module into a commercial finite element analysis (FEA) program, which is capable of calculating foundation rafts quickly, with correct results for the engineering practice. The calculation method is based on the so-called `uncoupled iterative method', wherein the structure and the soil continuum are analysed separately. The results of one analysis form the boundary conditions for the subsequent analysis as part of an iterative process. The connection between the raft and the soil is considered to be represented by the bedding modulus of the raft and by the soil stresses. The method provides the same displacements for the raft as for the soil surface, provided sufficient convergence can be reached if the raft is not elevated from the soil.

Paper presents a numerical method for solving the initial boundary-value problem for a certain quasilinear parabolic equation describing the low velocity filtration problem. The convergence of the method is proven.

The single mode equation of motion of a suspended elastic cable under planar excitation is considered, and numerical exploration is focused on the chaotic oscillations which occur in a certain domain of system control parameters. Bifurcations of the subharmonic resonance oscillation and their evolution into chaotic attractor are studied. Then the global bifurcation theory is applied to determine the critical system parameters for which the chaotic attractor undergoes the subduction destruction in the "boundary crisis'' scenario. The post-crisis transient motion, which in this case becomes the generic long-lasting chaotic system response, is also studied.

This paper presents a strategy to analyze the accuracy of measurements obtained in the calibration process of a Coordinate Measuring Machine (CMM). Thereafter, the operator will be able to find the most appropriate placement region for a part to be analyzed in order to reduce the error and take into account the shape of each part. Such strategy was developed through the visualization of error contours in the measurement space. Five different error indexes were developed for this analysis, associating different values to each point of the measurement space, allowing the user to choose the aspect he wants to take into consideration in the measurement process: centering of samples, dispersion, average errors, and others. Finally, the results are transformed into images, analysed and compared.

The problem of sensitivity of viscoelastic response with respect to material parameters is studied in the paper. The direct differentiation method is employed. The FEM-related implementation issues are discussed. A number of numerical examples illustrates the theory.

The back-propagation neural network was trained off line in order to simulate operation of the return mapping algorithm. Selection of patterns and the neural network training as well as testing processes are discussed in detail. The network was incorporated into the FE computer code ANKA as a neural procedure. The hybrid neural-network/finite-element-method program ANKA-H was used for the analysis of two elastoplastic plane stress examples: i) perforated tension strip, ii) notched beam. The results of computations point out quite good accuracy of the hybrid analysis. Some prospects of development of hybrid NN/FEM programs are given at the end of paper.

The paper deals with a comprehensive methodology concerning knowledge acquisition on machinery for the purpose of expert systems suitable for aiding of diagnostic inference. The methodology includes selected methods of diagnostic knowledge representation, methods of knowledge acquisition from domain experts and from preclassified examples, methods of assessment of previously acquired knowledge and a scenario of knowledge acquisition process. All the methods have been implemented in a Knowledge Acquisition System. Moreover, some examples of applications of the elaborated methodology have been given.
Keywords: machinery diagnostics, knowledge acquisition, domain experts, machine learning, assessment of knowledge.

The paper deals with application of the ortho-diagonal (O-D) method of finding the nondominated sets of solutions and evaluations for discrete polyoptimization problems. First, the (O-D) method was modified for finding minimum of a scalar function. The monotonicity property of a vector objective function is used by the (O-D) method for consecutive finding of j-th-criteria partial nondominated sets, j \in {1,2,...,J}. To find the nondominated evaluations sets the discrete neighbourhoods S of the point x_i are investigated starting from the solution x*_1 which minimizes the first objective function. In this way the consecutive nondominated solutions x*_{ND} are determined. An accuracy of solution and CPU computing time depend on the way the discrete neighbourhoods S of the point x_i in the design space are defined. The algorithm of the (O-D) method is applied to solve the discrete polyoptimization of a hall with spatial grid structure.

The main results of numerical analyses of a possible design configuration of a submerged structure subjected to impulsive loading due to explosion, performed for various material models assumed for a plain concrete are presented and discussed. Three different models were considered - the modified Drucker-Prager plasticity model, brittle cracking model and the elastoplastic model with damage. The present study suggests problems and possible solutions to be applied into numerical analysis of such structures by means of available finite element computer codes.

Paper summarizes the first results of two-dimensional (2D) numerically modelled expansion and flow of compressible and non-viscous gas in typical parts of air jet weaving system; namely in main nozzle designed as an ejector with various shapes of the mixing zone, in relay (auxiliary) nozzle with substantial flow separation in the rash flow bend directly before the nozzle outlet, and the influence of the reed dent edges shape on the free stream reflection and penetration through reed gaps along a real ``porous'' wall. The used Euler's equations are solved by a Finite Volumes Method (FVM) with automatic mesh generation and optimization of unstructured triangle mesh. Graphical results show 2D isolines of all gas state values, further Mach number, entropy and velocity vectors. 1D profiles of all quantities along chosen cross-sections or surfaces can be obtained, too. They give to the designer a large and quick review about the problem. The coincidence with experiment, measuring and real weaving tests is very good. The advantage of numerical modelling consists in the very quick, simple and user-friendly operation.

This paper presents a finite-difference solution of the two-dimensional, time dependent incompressible Navier-Stokes equations for laminar flow about fixed and oscillating cylinders placed in an otherwise uniform flow. Using boundary fitted coordinates, the equations are transformed to a non-inertial reference frame fixed to the cylinder. The primitive variable formulation is used for the solution of the problem. A special transformation provides a fine grid scale near the cylinder walls and a coarse grid in the far field. Forward difference is used in time, fourth order central difference in space except for convective terms for which a modified third-order upwind scheme is used. Velocity values are obtained explicitly, and the successive over-relaxation (SOR) method yields the pressure distribution. Computed drag coefficients and dimensionless vortex shedding values were compared with experimental results for rigid cylinders and a very good agreement has been obtained. Amplitude bounds of locked-in vortex shedding due to forced crossflow oscillation of a circular cylinder are also determined for Re=180.
Keywords: incompressible flow, Navier-Stokes equations, unsteady flow, laminar flow, bluff body, lock-in.

A general solution of the diffusion problems which concern the R.C. structures, may be deduced by the limit analysis, by means of truss schemes suitable to model the load transfer mechanism. In particular such schemes allow us to share the carrying functions between concrete and steel reinforcement. Latest developments call this kind a solution Strut-and-Tie (S&T) modellization. In this paper a procedure for the automatic search for optimal S&T models in R.C. elements is proposed. A highly indeterminate pin-jointed framework of a given layout is generated within the assigned geometry of the concrete element and an optimum truss is found by the minimization of a suitable objective function. Such a function allows us to search for the optimum truss according to a reference behaviour (the principal stress field) deduced through a F.E.A. and assumed as representative of the given continuum. After having explained the theoretical principles and the mathematical formulation, some examples show the pratical application of the procedure and its capability in handling complex stress paths, through schemes which result rational and suitable for a consistent design.

The ability to model the different regimes of a physical event using different numerical techniques has a number of advantages. Instead of applying the same general solver to all domains of a problem, a solver optimized for a particular regime of material behavior may be used. Thus, in a single analysis, one type of solver may be used for fluid behavior while another type is used for solid/structural response. The various domains in the problem are then coupled together in space and time to provide an efficient and accurate solution. Examples in the use of Eulerian, Lagrangian, Arbitrary Lagrange Eulerian (ALE), Structural, and Smooth Particle Hydrodynamic (SPH) techniques, in various combinations, will be applied to general problems in fluid-structure interaction and impact problems. The relative advantages and limitations of such coupled approaches will be discussed. Examples include the following: fluid dynamics, blast, impact/penetration (Euler); hypervelocity impact onto spacecraft shields (Lagrange-Lagrange); buckling of a thin walled structure (Structural); impact and penetration of a projectile onto concrete (SPH-Lagrange, Lagrange-Lagrange, Euler-Lagrange). Numerical results are presented with comparison against experiment where available.

In this paper, we introduce a new branch-and-bound type method, for discrete minimal weight design of geometrically nonlinear truss structure subject to constraints on member stresses and nodal displacements when the member cross-sectional areas are available from a discrete set of a given catalogue. The discrete optimization problem can be formulated as a tree search procedure. The initial - unfeasible - node of the searching tree is obtained by decreasing the relaxed cross-sectional areas to the closest discrete catalogue value. Each node of the branch-and-bound searching tree is characterized by the weight of the structure, the actual value of the infeasibility penalty function, and the minimal relaxed additional weight, that is needed to obtain a feasible structure from the given state. The proposed method involves an exterior point method to determine the relaxed solution of the minimum weight design problem. The algorithm seems computationally attractive and has been tested on a large number of examples. Numerical results are presented for a well-known test problem.

The aim of this paper is to present a numerical method to determine a field of constrain forces which hydrodynamically represents the effect of the blading of the impeller of a radial-flow pump. The field of constrain forces are perpendicular to the stream surfaces of the relative velocity field and congruent to the blade surface of the impeller. The calculation of the constrain force field is based on the solution of the inverse problem of the hydrodynamic cascade theory. In the determination of the constrain force it is supposed that the frictionless and incompressible fluid flow is completely attached to the blade surfaces. The constrain force field can be calculated by the change of the moment of momentum in the absolute inviscid fluid flow which depends on the state of the pump. Knowing the constrain force field it is possible to calculate the distributions of the relative velocity, pressure and energy loss on the mean stream surface (F) of the impeller by solving the governing equations of the viscous relative flow. By calculating the energy loss belonging to different volume rates an approximate real head-discharge characteristic of the impeller also can be computed.

Bolker and Crapo gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. Using this model there are very fast methods for connected planar square grid frameworks to determine their (infinitesimal) rigidity when we can use diagonal rods, diagonal cables or struts, long rods, long cables or struts. But what about square grids containing some kind of holes? We will show that the model can be extended to the problem of holes too.
Keywords: grids, rigidity, frameworks, graphs.

We consider the optimal design of a machine frame under several stress constraints. The included shape optimization is based on a Quasi-Newton Method and requires the solving of the plain stress state equations in a complex domain for each evaluation of the objective therein. The complexity and robustness of the optimization depends strongly on the solver for the pde. Therefore, solving the direct problem requires an iterative and adaptive multilevel solver which detects automatically the regions of interest in the changed geometry. Although we started with a perfected type frame we achieved another 10% reduction in mass.

In order to avoid a fully nonlinear prebuckling analysis by the finite element method for the mere purpose of obtaining the stability limit in the form of a bifurcation or a snap-through point, this limit may be estimated by means of the solution of a suitable linear eigenvalue problem. What seems to be most suitable in this context, is a consistent linearization of the mathematical formulation of the static stability condition. It can be interpreted as the stability criterion for the tangent to the load-displacement diagram at a known equilibrium state in the prebuckling domain. Based on this linearization, higher-order estimates of the stability limit can be obtained from scalar postcalculations. Unfortunately, the order of such an estimate is only defined in an asymptotic sense. Nevertheless, for many engineering structures the geometric nonlinearity in the prebuckling domain is moderate. In this case, the general information from asymptotic analysis is frequently relevant for the entire prebuckling domain. This allows good ab initio estimates of stability limits based on nonlinear load-displacement paths. The nucleus of this article is the discussion of the potential and the limitations of determination of stability limits based on ab initio estimates of nonlinear load-displacement paths. The theoretical findings are corroborated by the results from a comprehensive numerical study.

In the paper a general purpose finite element software for the simulation of piezoelectric materials and structronic (structure and electronic) systems is presented. The equations of coupled electromechanical problems are given in a weak form, which are the basis of the development of 1D, 2D, 3D as well as multilayered composite shell elements. The smart structures finite element code includes static and dynamic analysis, where also controlled problems can be simulated. Two test examples are presented to compare the numerical results with measurements.

We have considered a linearly elastic body loaded by tractions inward normal to the instantaneous surface. Due to the increment of the surface element vector there is a contribution to the tangent stiffness matrix referred to as load correction stiffness matrix. The goal of the numerical experiments is to determine the bifurcation point on the fundamental equilibrium path. Linear eigenvalue problems with follower loads are also analysed.
Keywords: follower loads, finite element method, limit of elastic stability, eigenvalue problem.

We present a two-dimensional discrete model of solids that allows us to follow the behavior of the solid body and of the fragments well beyond the formation of simple cracks. The model, consisting of polygonal cells connected via beams, is an extension of discrete models used to study granular flows. This modeling is particularly suited for the simulation of fracture and fragmentation processes. After calculating the macroscopic elastic moduli from the cell and beam parameters, we present a detailed study of an uniaxial compression test of a rectangular block, and of the dynamic fragmentation processes of solids in various experimental situations. The model proved to be successful in reproducing the experimentally observed subtleties of fragmenting solids.

An efficient numerical method which can calculate the eigenproblem for the large structural system with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method to the transformed problem. The method can calculate the natural frequencies and mode shapes without any numerical instability which may be encountered in the well-known methods such as the subspace iteration method or the determinant search method which has been widely used for solving eigenvalue problem. The efficiency of the method is verified by comparing convergence and solution time for numerical examples with those of the subspace iteration method and the determinant search method.
Keywords: free vibration analysis, accelerated Newton-Raphson method, multiple or close natural frequencies.

An efficient solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonproportionally damped structural systems with close or multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem format through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even if the shift value is an eigenvalue of the system, the proposed method guarantees nonsingularity, which is analytically proved. The initial values of the proposed method can be taken as the intermediate results of iteration methods or results of approximate methods. Two numerical examples are also presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.
Keywords: quadratic eigenproblem, eigenvalue, non-proportional damped system.

In this paper the optimum design of bent cylindrical shells with welded ring or stringer stiffeners are treated. The objective function is the cost of the structure and the constraints are related to overall and local stability. The problem is solved by MathCad 7.plus software and presented also graphically for ring stiffened cylinders and by CFSQP optimization software for stringer stiffened cylinders.

The thermal processes proceeding within a perfused tissue in the presence of a vessel are considered. The Pennes bio-heat transfer equation determines the steady state temperature field in tissue sub-domain, while the ordinary differential equation resulting from the energy balance describes the change of blood temperature along the vessel. The coupling of above equations results from the boundary condition given on the blood vessel wall. The problem is solved using the combined numerical algorithm, in particular the boundary element method (for the tissue sub-domain) and the finite differences method (for blood vessel sub-domain).

The paper presents the application of Artificial Neural Networks for the identification of the load causing a partial yielding in the cross-section of a simple supported beam. The identification of the load was based on a change of the dynamic parameters (eigenfrequencies) of the partially yielding structure. On this basis and using neural networks a tool for the location and evaluation of the load causing the deformation was built. The optimum network architecture, learning algorithm, number of epochs, and the minimum number of eigenfrequencies have been found. In order to come to the final conclusions, a wide variety of network architectures (from simple networks with four neurons in one hidden layer to complex networks consisting of two or three simple networks), learning algorithms and different numbers of learning epochs have been tested.

Generalized exponential penalty functions are constructed for the multiplier methods in solving nonlinear programming problems. The non-smooth extreme constraint Gext is replaced by a single smooth constraint Gs by using the generalized exponential function (base a>1). The well-known K.S. function is found to be a special case of our proposed formulation. Parallel processing for Golden block line search algorithm is then summarized, which can also be integrated into our formulation. Both small and large-scale nonlinear programming problems (up to 2000 variables and 2000 nonlinear constraints) have been solved to validate the proposed algorithms.

Symbolic computation has been applied to Runge-Kutta technique in order to solve two-point boundary value problem. The unknown initial values are considered as symbolic variables, therefore they will appear in a system of algebraic equations, after the integration of the ordinary differential equations. Then this algebraic equation system can be solved for the unknown initial values and substituted into the solution. Consequently, only one integration pass is enough to solve the problem instead of using iteration technique like shooting-method. This procedure is illustrated by solving the boundary value problem of the mechanical analysis of a liquid storage tank. Computation was carried out by MAPLE V. Power Edition package.

In this paper the dynamic behaviour of a continuum inextensible pipe containing fluid flow is investigated. The fluid is considered to be incompressible, frictionless and its velocity relative to the pipe has the same but time-periodic magnitude along the pipe at a certain time instant. The equations of motion are derived via Lagrangian equations and Hamilton's principle. The system is non-conservative, and the amount of energy carried in and out by the flow appears in the model. It is well-known, that intricate stability problems arise when the flow pulsates and the corresponding mathematical model, a system of ordinary or partial differential equations, becomes time-periodic. The method which constructs the state transition matrix used in Floquet theory in terms of Chebyshev polynomials is especially effective for stability analysis of systems with multi-degree-of-freedom. The stability charts are created w.r.t. the forcing frequency omega, the perturbation amplitude nu and the average flow velocity U.
Keywords: pulsatile flow, Floquet theory, Chebyshev polynomials.

Controlling time periodic systems is a significant engineering challenge. One innovative approach that seems to be especially promising involves application of the Lyapunov Floquet (LF) transformation to eliminate time periodic terms from the system state matrices. Traditional control design techniques are then applied and the resulting gains transformed back to the original domain. Typically, the controller design process involves the use of an auxiliary control matrix and (assuming that the actual control matrix is time-varying and non-invertable) a pseudo inverse (which introduces approximations into the procedure). The degree to which the desired control results are achieved depends very strongly upon the impact of these approximations on the actual system dynamics. The research effort described below is concerned with investigating the performance of this LF control strategy and the existence of situations in which application of the procedure may produce undesirable behaviors.

The paper deals with a special inverse boundary problem, when the boundary of the domain is completely unknown and a singular integral equation for the velocity angle is obtained. For the model of free plane symmetric incompressible jet forked by an airfoil, the boundary equations and airfoil shape are ``a posteriori'' determined, while the velocity along them is ``a priori'' prescribed. With the aim to obtain minimum drag, in the present paper there is solved the optimization problem for airfoils, using the penalty method and the golden section method. In the case of optimum, numerical computations are performed and the airfoil design together with the drag coefficient are obtained.
Keywords: inviscid jets, inverse problems, singular integral equation, optimum airfoil, optimization.

In this paper some results of the computer simulation of mixing of non-Newtonian fluid are presented. Numerical calculations were done for dimensionless form of the equations of motion for the Carreau fluid in incompressible and viscous flow in a two-dimensional semi-cylindrical cavity. The full Navier-Stokes equations for the Carreau fluid were written in velocity-vorticity, and next in finite difference form. The solutions were accomplished by finite time-step advancement. The mixing process was studied by tracking the motion of particles in the mixing region. The particles were represented by marked points. The mixing efficiency was quantified in terms of the average distance between the tracer particles and the centroid of the particle distribution.

A three-dimensional rest-to-rest attitude maneuver of a satellite with flexible solar panels equipped by on-off reaction jets is studied. Results indicate that, under an unshaped input, the maneuver induces an undesirable motion of the satellite as well as vibration of the solar panels. Fuel-efficient input shapers are then applied to reduce the residual oscillation of its attitude. By reducing vibrations at several large-amplitude natural frequencies, the expected pointing precision of the satellite can be satisfied.

This paper describes the phenomena that occur when a simplified model of train interacts with the tunnel at three locations - before, entering and leaving the tunnel. The Navier-Stokes equation is solved by introducing the artificial compressibility to change the governing equation type from the elliptic to hyperbolic. The Baldwin-Lomax turbulence modeling is employed to simulate the flow field with a Reynolds number of 10^6, and the computation domain is divided into three blocks considering the train and tunnel geometries. The grid is algebraically adapted determining the maximum solution change plane and solution weighting factors. The pressure in the adapted solution is not changed much, however, the skin friction is severely varied comparing with those of the non-adapted solutions. When the train enters into the tunnel, there are large increase in the surface pressure and skin friction distribution on the train surface.

In the paper some results of investigations of two intelligent information systems: a feedforward neural network and an adaptive fuzzy expert system, are presented. The systems can be used for example in approximation and control problems or in diagnostics. The adaptive fuzzy expert system is constructed as a hybrid in which a fuzzy inference system is combined with a neural network. In the learning process for given set of training points an optimal value of the so-called generalized weight vector is searched. The Lapunov theory is used to examine the non-sensitivity of the optimal value of a generalized weight vector to initial conditions and training data. Some necessary and sufficient conditions are formulated in terms of the Hessian matrix of the error function.

The analysis of multi-leaf structures should be performed taking friction into account. The objectivity of friction law should be preserved because large deformation generally occurs. By use of the convected coordinate system, the objectivity can be preserved naturally. Therefore, in finite element analysis, the element local coordinate system can be used. However, when a contact point slides over the element boundary, a problem arises due to the discontinuity of the local coordinates between elements. In this work, an algorithm is proposed, i.e., the formulation is essentially based on the convected coordinate system while the sliding term is redefined as a spatial vector and is calculated in the reference configuration. Thus, the finite sliding due to large deformation can be treated without paying special attention to the limit of the local coordinate system. Two numerical examples including a simplified model of a leaf spring structure used in nuclear power plants are given.

Although there is a need for sensitivity analysis for frictional contact problems in many engineering fields, research work on it has rarely been reported due to the complexity of the problems. In this paper, a sensitivity analysis procedure based on a semi-analytical method for frictional contact problems is presented. The unbalance force due to the variation of design parameters is evaluated numerically, thus the related routine of an existing FEM code can be utilized regardless of the friction law employed. The continuum-mechanics-based formulation is carried out first and then a discretized form is derived. The stick state is modeled by introducing a penalty-type constraint. A couple of numerical examples, including a realistic leaf spring structure used in nuclear power plants, are given to demonstrate the effectiveness of the proposed approach.

A numerical method based on compliance approach is presented for analyzing an isotropic homogeneous sheet enclosing a crack. The method calculates the strain energy release rate and determines the stress intensity factors K_{I} and K_{II}. This method is suitable for any load combination in pure mode I, pure mode II and mix mode loading. A simple and efficient solution approach is developed in which the strain energy release rate is calculated by combining the finite element method with the fundamental relationships in fracture mechanics. The solution technique converges to accurate results for a small crack extension of the finite element mesh. The solution approach is also shown to be suited for separating the mode I and mode II stress intensity factors for a mixed mode loading. Numerical examples are presented to demonstrate the accuracy of the proposed approach.

The main objective of this study is to design three-dimensional geometrical and mechanical finite element model of the intervertebral disc between L2-L3 vertebras in the lumbar and C5-C6 cervical spinal segment. The model was directed toward understanding the work and the role of the intervertebral disc that performs in the human spinal segment body. The three-dimensional finite element motion segment was developed and its response to different loads was performed. The model accounted for the solid component of the nucleus pulposus while anulus fibrosus was modeled as a matrix of homogeneous ground substance reinforced by anulus fibers. End plates similarly to the nucleus pulposus were simulated using volumic elements. Simultaneously the vertebral bodies have been modeled as a complex construction of a cancellous core covered by a cortical shell of the orthotropic material properties. Isotropic material has been used to model posterior elements. To simulate ligament like behavior, tension only elements have been used. Numerical studies of the lumbar segment have been consequently compared with the experimental investigation performed on the porcine model by authors and other in vitro experiments on human lumbar spine accomplished by other scientists. In cervical spinal segment numerically two surgical techniques (Cloward and Robinson-Smith) have been tested. Two types of loads have been applied to three models - to an intact C5-C6 spinal segment and then to the vertebras after performing those two surgical techniques. All numerical analysis have been undertaken using ANSYS 5.4 commercial application.

The purpose of this polyoptimization was to find optimal tubular cross section catalogues for the specified spatial trusses. Five different spans of trusses have been analyzed, starting from 24x24 m ending at 72x72 m, trusses supported at every other perimeter node, with loading conditions typical for roofs. Four decision variables were taken under consideration, i.e. the catalogue size t, its arrangement T in a metallurgical catalogue T_M, minimal and maximal diameters of tubular elements D_{min} and D_{max}. Two objective functions: truss mass and manufacturability of particular solutions were evaluated. For that purpose, some design, technological, and computational constraints were taken into account. For the specified spans L, different catalogues of cross sections were defined by TOPSIS method.

The main objective of the paper is the investigation of localization phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings. Recent experimental observations for cycle fatigue damage mechanics at high temperature and dynamic loadings of metals suggest that the intrinsic microdamage process does very much dependent on the strain rate and the wave shape effects and is mostly developed in the regions where the plastic deformation is localized. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms (nucleation, growth and coalescence of microcracks); (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity; (vi) plastic spin. To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elastic-plastic response can be obtained. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. The Lax-Richtmyer equivalence theorem is formulated and conditions under which this theory is valid are examined. Utilizing the finite difference method for regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented. Particular examples have been considered, namely dynamic, adiabatic and isothermal, cyclic loading processes for a thin steel plate with small rectangular hole located in the centre. To the upper edge of the plate the normal and parallel displacements are applied while the lower edge is supported rigidly. Both these displacements change in time cyclically. Small two asymmetric regions which undergo significant deformations and temperature rise have been determined. Their evolution until occurrence of final fracture has been simulated. The accumulation of damage and equivalent plastic deformation on each considered cycle has been obtained. It has been found that this accumulation distinctly depends on the wave shape of the assumed loading cycle.

The work is devoted to the practical application of dual grids in the boundary element method (BEM). Definitions of dual grids on the plane are given and algorithm constructing dual grid for a given triangulation is described. The problem of utilizing two numerical solutions of one problem defined on the couple of dual grids is considered and the results of this technique are demonstrated. The examples from geomechanics modelling the contact interaction of shallow foundations and elastic bases are presented.

The phenomenal development and popularisation of Object Oriented Programming (OOP) in recent years has created a new dimension in the innovation and implementation of powerful panel method techniques. Although many scientists and engineers are already employing OOP languages such as C++, some of them are still using the languages in a procedural and non-hierarchical manner, leaving a large proportion of these languages' capability unexplored. This paper presents the idea and implementation of OOP in the panel method, which is widely used in ground vehicle aerodynamics. Program examples will show that OOP enables the writing of highly modularised, reusable, readable and debuggable panel method programs.
Keywords: object oriented programming, panel method, BEM, ground vehicle aerodynamics.

An analysis of the influence of the manner of dividing the structure on the numerical solution of the static problems of the concrete and of the reinforced concrete deep beams, using a constitutive model of the concrete that demonstrates the material softening, is given. Detailed results of the numerical solutions are presented in the paper. The results indicate that taking into account the scale parameters makes it possible to increase the objectivity of the numerical results of modelling of the behaviour of concrete and reinforced concrete structures when the material softening is considered. The numerical analysis for the reinforced concrete deep beams indicates the differentiation of the obtained results according to the fracture energy values.

High demands for dynamic thermal insulating protection of machine parts lead to the development of thermal barriers. The mathematical and simulation model has been developed to simulate thermomechanical processes during thermal shock on the surface of different thermal barrier structures. The finite element method has been applied to the heterogeneous thin layer structure of the thermal barrier. Temperature, temperature gradient, heat flux, thermally induced stress and strain have been chosen as the characteristics describing the dynamic behaviour of the thermal barrier during the thermal shock. Results of the simulation for several alternatives of thermal barrier are discussed to summarize the effect of characteristic parameters of the thermal barrier to its dynamic behaviour.
Keywords: computer simulation, FEM, thermomechanical processes, thermal barrier, special industrial application.

In the paper a new approach for the computation of slightly damped elastic structural vibrations over the medium frequency range is proposed. The effective quantities (deformation energy, vibrational intensity, etc...) are evaluated after resolution of a small system of equations that does not in any way result from a fine ``finite element'' discretisation of the structure.

Dynamic optimization problem for a machine rigid block foundation on an inhomogeneous soil is considered. The soil deposit under the base of block corresponds to a layer with linearly varying properties overlying a uniform half space. Furthermore, the block may be surrounded by a backfill. The optimal designs of a vertically excited rectangular block foundation are found by iterative application of a sequential linear programming for a number of rationally inhomogeneous supporting media as well as for a uniform half space. It illustrates the problem of adequate modelling of the nature of the soil profile and provides an insight into the action of the soil-foundation-machine system from the point of view of the long-term satisfactory performance and safety.

The paper discusses the physical basis of the process of filtration of water in a case of very low velocities and presents the mathematical model of the process, based on a new constitutive formula. The existence and uniqueness of a weak solution to the resulting nonhomogeneous initial boundary-value problem is then proven.

The eigenvalue optimization problem for anisotropic plates has been dealt with. The variable thickness of a plate plays the role of a design variable. The state problem arises considering free vibrations of a plate. The demand of the lowest first eigenfrequency means the maximal first eigenvalue of the elliptic eigenvalue problem. The continuity and differentiability properties of the first eigenvalue have been examined. The existence theorem for the optimization problem has been stated and verified. The finite elements approximation has been analyzed. The shifted penalization and the method of nonsmooth optimization can be used in order to obtain numerical results.

We study a phase-field model for the isothermal solidification of a binary alloy which involves the relative concentration and the order parameter. We prove the existence of weak solutions as well as regularity and uniqueness results under Lipschitz and boundeness assumptions for the nonlinearities. A maximum principle holds that justifies these assumptions. A numerical approximation and some numerical results are also presented.

A finite element model has been developed for the computation of melting/solidifying process under the combined action of buoyancy and surface tension forces. Validated on the square cavity benchmark of Gobin and Le Quéré (Bertrand et al. [1], Gobin and Le Quéré [2]), the numerical model is used to extend this previous analysis to the free surface case where surface tension can drive the flow (capillary flow). A comparison of the results obtained for three types of boundary conditions applied at the top of the melting pool is performed. It shows that in the studied case of tin where the thermal Bond number is moderated (Bo=200), the flow is still mainly dominated by buoyancy effect as long as the melted pool is deep enough like in the square cavity case of the above mentioned benchmark. [1] O. Bertrand et al.: Melting driven by natural convection. A comparison exercise. Int. J. of Therm. Sci., 38: 5-26, 1999 [2] D. Gobin, P. Le Quéré: Melting in enclosures: Coupled heat transfer and natural convection. In: T.A. Kowalewski et al., eds., ESF-AMIF Workshop on Phase Change with Convection, Modeling and Validation, 13-18, 1999.
Keywords: phase change (melting, freezing), natural convection (buoyancy, thermocapillary flows), incompressible Navier-Stokes equations, finite element method.

A numerical and experimental study is presented of unsteady natural convection during freezing of water in a differentially heated cube shaped cavity. A boundary fitted grid as well as the enthalpy-porosity fixed grid numerical models are used in this study. Both numerical models show very good agreement with the experimental data only for pure convection and initial time of freezing process. As time passes the discrepancies between numerical predictions and the experiment became more significant. To elucidate these differences several numerical tests are performed, verifying assumptions made in the models.

Finite Element Method (FEM) calculations have been performed to address the problem of the influence of anisotropy of permeability and of thermal conductivity of a mushy region on a temporary flow pattern and temperature during solidification of binary mixtures. Computationally effective FEM algorithm is based on the combination of the projection method, the semi-implicit time marching scheme and the enthalpy-porosity model of the two-phase region. Example calculations are given for two different dilute solutions of ammonium chloride and water. The effect of permeability anisotropy considerably changes the shape of the mushy zone. Three different models of thermal conductivity, the first - based on a mixture theory, the second - fully anisotropic one and the third - the model of isotropic effective conductivity, have been analyzed and mutually compared. It has been found that the impact of the thermal conductivity anisotropy is visible only in the case when this property differs significantly in both phases.

Frontal polymerization has been studied for many years experimentally and theoretically. This technique can exhibit a phase change between a liquid monomer and a solid polymer and many studies, both theoretical and experimental, have been devoted to the stability of the front which separates the two phases in the presence of thermal convection. We present here a new technique for the numerical simulation of this process which takes account of the chemical reaction, the phase transition and the hydrodynamics; it is based on the method of characteristics and a fictitious domain method. These two methods are known, but the coupling of them and the application to this problem is new. We also present and discuss some results of simulations.

Numerical computations of the yttrium distribution in the BaO-CuO melt were performed for the single crystal growth of yttrium barium copper oxide superconductor (YBa_2Cu_3O_(7-x)) with the Czochralski method. The finite volume method was used to calculate the fluid flow, heat transfer and yttrium distribution in the melt with staggered numerical grid. The flow in the melt was assumed to be axisymmetric and was modelled as an incompressible Newtonian, Boussinesque fluid. Mass transfer was due to both convection and diffusion. Calculations were presented for a buoyancy/crystal-rotation driven combined convective flow.

The macroscopic equations describing the process of solidification in binary systems are usually introduced via the volume averaging technique. A different approach to obtain these equations, based on the ensemble averaging technique, is proposed in the paper. This technique was used to derive energy and solute conservation equations and the basic constitutive relations appearing in the macroscopic description of the solidification phenomena occurring in the mushy region. In general these relations are non-local and account for non-equilibrium processes. Problem of thermodynamic equilibrium (thermal and chemical) is also discussed. Formulae for enthalpy and porosity of the mushy zone, in the latter case, are given.

A modified Allen-Cahn equation is combined with the compressible Navier-Stokes system. After a physically motivated modification of the stress tensor, for the resulting equations the second law of thermodynamics is valid. The model can be used to describe the forming of gas phases in a flowing liquid.

A mathematical model of diffusion of vaporized interacting metal molecules in a fireproof material is considered. The model is based on microscopic kinetic equations describing the process under condition of a strongly non-homogeneous temperature field. A two-dimensional structure is examined, where the inner hot surface acts as the source of metal vapour and the outer surface - as a cooler. Due to interaction between metal molecules, a phase transition (condensation) proceeds near the outer surface. A conservative, monotonous, and absolutely stable difference scheme is developed on the basis of a special exponential substitution for the concentration of molecules. Results of 2D numerical experiments in non-steady state are presented.

In this paper the multiphase diffusion-convection problem is solved numerically by using upwind and characteristic schemes. Discretization for the schemes are performed by finite difference method. For solving the algebraic equations on every time level the modified S.O.R. method is used. In the numerical results computing time, number of iterations and accuracy of the schemes are analysed.

The paper presents a general numerical model for the analysis of prestressed concrete with the application to beam, thin shell and volume type of prestressed structures. Discrete, embedded approach is used to model curved, bonded or unbonded tendons. Also a partial bond may be introduced by the friction between the tendon and the surrounding body. In the finite element model, two types of elements are obtained. One is a typical finite element for the kind of structure modeled, and the other is an embedded, three noded, subparametric tendon element. Equations of the finite element method have been obtained from the incremental form of the principle of virtual work providing geometrical linearity and possibility of nonlinear physical relations. Numerical examples illustrate application to modeling of beam, thin shell and volume type of prestressed structures as well as the impact of the friction on the axial force distribution in prestressing tendon.

On the basis of a recently developed method which allows the use of linear elements for metal forming simulation within the flow approach, sensitivity analysis is carried out. Aiming at large, industrial problems, attention is focused on the explicit version, which is considered more effective for such problems, although implicit time integration is possible as well. By time step splitting a stabilization sub-matrix is obtained, which allows the use of equal interpolation for velocity and pressure. Specifically, linear triangles and tetrahedra have been used, which are easily generated by automatic meshers. Sensitivity analysis is carried out by the Direct Differentiation Method, with which similar analyses have been performed by the author for the flow approach within a direct solution scheme.
Keywords: sensitivity analysis, metal forming, explicit time integration, split algorithm, flow approach.

In most cases a safety of optimal construction may be limited by the violation of stress, buckling or displacement constraints. An unexpected exceed of these constraints may be caused by manufacturing tolerances of structural elements (differences between assumed and obtained dimensions). This requires an incorporation of tolerance problem in optimum design. One may deal with two different tolerances - the first case is when it's related to the members' cross-section variations, whereas the second notion represents the variation of elements' lengths. Considering operation conditions and manufacturing techniques the second case of tolerance seems to be more important. This approach states the problem of minimum weight design of a structure with initial distortions. A standard solution algorithm with the Kuhn-Tucker theorem was used with the adjoint variable method. Necessary optimality conditions have the form of equations and inequalities. The equality constraints were put forward for the average values of design variables l, while tolerances t_j were introduced into inequality equations i.e. the limit values of stresses and displacements were diminished by the positive products of appropriate sensitivities and tolerances. The method was next illustrated by an example of a ten bar bench-mark problem - a typical one for testing algorithms in structural optimization. The idea presented in this paper may be used not only for truss structures but it can be easily extended to other kinds of structures like frames, composites etc.
Keywords: structural optimization, manufacturing tolerances, nonlinear optimization.

We consider the nonlinear eigenvalue problem of a nonlinear partial differential equation under Dirichlet boundary condition in a two-dimensional space. The classical solutions are given for rectangular domains. We give numerical solutions obtained by finite element method for the first eigenvalue and eigenfunctions and we analyze the error in the approximate finite element solutions.

The objective of the work was an efficient, numerical implementation of one of the unified, internal-state-variable constitutive models. Such models are general and convenient in numerical applications since they describe elastic, plastic, viscous, damage phenomena and they do not require neither yielding condition nor loading/unloading criterion. However, they result in so called stiff initial-boundary value problems. Therefore, an efficient numerical implementation demand adaptive techniques, both in space and in time. The paper presents application of such an adaptation approach. It uses an improved version of the semi-implicit Euler method with automatic time step control and the h refinement of the FEM meshes based on the interpolation error estimate and on the reliable, selfequilibrated, implicit, a posteriorii estimate. Selected problems were solved and both the efficiency and reliability of the unified model were confirmed.

In this paper the performance of four solvers for systems of nonlinear algebraic equations applied to a number of test problems with up to 250 equations is discussed. These problems have been collected from research papers and from the Internet and are often recognized as "standard'' tests. Solver quality is assessed by studying their convergence and sensitivity to simple starting vectors. Experimental data is also used to categorize the test problems themselves. Future research directions are summarized.

The subject of this paper is a movable antiaircraft short-range rocket set. The control algorithm for a target homing short-range rocket missile by means of the proportional approach method is performed by an executive system comprising the co-ordinator and automatic pilot devices. The co-ordinator is equipped with a gyro-device and a system determining working out of the ideal, desirable signal. The automatic pilot device has a pair of double-position external vanes and internal gas control engine. A missile control, in accordance with the implemented algorithm, is achieved by using a rocket rotating motion around its longitudinal axis.

The analytical formulation of an iterative procedure applied for structure-subsoil systems is presented in the paper. A physical and engineering interpretation has been given for the presented algorithm.

The article presents the high-performance Ritz-gradient method for the finite element (FE) dynamic response analysis. It is based on the generation of the orthogonal system of the basis vectors. The gradient approach with two-level aggregation preconditioning on the base of element-by-element technique is applied to minimize the Rayleigh quotient for the preparation of each basis vector. It ensures the evolution of the regular basis vector toward the lowest eigenmode without aggregating and decomposing the large-scale stiffness matrix. Such method often happens to be more effective for dynamic response analysis, when compared to the classical modal superposition method, especially for seismic response analysis of the large-scale sparse eigenproblems. The proposed method allows one to apply arbitrary types of finite elements due to aggregation approach, and ensures fast problem solution without considerable exigencies concerning the disk storage space required, which is due to the use of EBE technique. This solver is implemented in commercial programs RobotV6 and Robot97 (software firm RoboBAT) for the seismic analysis of large-scale sparse problems and it is particularly effective when the consistent mass matrix is used.

The spreading of fluid under gravity occurs in both nature and man-made situations and has been the subject of many previous studies. Considerably less attention has been paid to cases in which there is a strong thermal coupling influencing the flow. In this paper, simple models of the spreading of materials with temperature-dependent viscosity are presented and features that are commonly seen in experiments, such as plateauing and fingering, are shown to result. A model which includes latent heat effects is also briefly outlined.

Recently formulated shakedown theorems for materials with temperature-dependent yield stress [1] are applied to evaluation of the elastic shakedown boundary. In order to simulate actual shakedown behavior of elastic-thermo-plastic structures resulting from experimental investigations, the material model of the German mild steel St 37 is considered. It is found that the obtained elastic shakedown boundaries are within the corresponding boundaries based on the classical shakedown theory. Two examples are compared with the well-known solutions obtained for the neglected yield stress dependence on temperature.

In this paper, an algorithm of calculation of extreme values of temperature based on interval arithmetic is presented. Many mechanical systems with uncertain parameters lambda in Lambda can be described by a parameter dependent system of linear equations K(lambda)T=B(lambda). Using natural interval extension of a real function, one can transform the system of linear equations into the system of linear interval equations K(lambda)T=B(lambda). Solution of the system of linear interval equations always contains the exact solution of the parameter dependent system of equations. A new method of computation of extreme values of mechanical quantities based on the monotonicity test is introduced. This method can give exact solution of a parameter dependent system of equations.

In the paper some a-priori hp--adaptive error estimates, applied to the problem of acoustic wave scattering on an elastic body in the 2D space, solved by the Boundary Element Method, are presented. The estimate includes both the function- and boundary approximation errors.
Keywords: Boundary Element Method, acoustic scattering, hp- adaptive method, a-priori error estimate.

This paper concerns modelling of surfaces resulting from measurements or from digital simulation of surfaces e.g., tooth flanks, based on the theory of gearing, with intentionally introduced modification usually defined in discrete form. Computational methods of modelling of curves and surfaces are briefly reviewed. Problems of stability of geometric modelling and related problems of parametric estimation of mathematical models, representing curves and surfaces are discussed. An analysis of multicollinearity of the measurement matrix is performed. A method of regularization of matrix, containing coordinates of nodes from considered surface, is proposed. This method allows to improve the robustness of parametric estimation and is specially helpful for on-line parametric estimation of surface models utilized during measurements.

The study presents a class of effort of brittle media problems. The model of human tooth with non-carious cervical lesion was analysed. Regions of the most disadvantageous loads was determined.

In the paper are derived the equations of motion of a gyroscope on elastic suspension, mounted on a movable base. An algorithm for the selection of the optimum construction parameters and the matrices of amplifications of the gyroscope regulator is presented. The latter is aimed at the quickest transitory process damping and also at the minimisation of errors resulting from the friction in frame bearings, base angular motion and non-linearity of the impact.

The paper presents an algorithm of coverage 2-D multiconnected domain by trianlges and quadrilaterals. The zone covered with quadrilaterals is structured, thus the zone covered with triangles is unstructured. The density of the structured grid is controlled only on one of the surrounding loop, on which the points are generated with mesh density function. Unstructured zone is triangulated by using Delaunay advancing front technique triangulation of points previously generated.

An algorithm of remeshing based on graded meshes generator is presented. The algorithm starts with an initial grid, which is iteratively improved taking into account error estimate. Mesh density functions are used to generate grid over domain on which boundary value problem is solved. It is observed, that succussive meshes are convergent and especially they become denser near singularities. For unstructured grid generation the advancing front technique combined with Delaunay triangulation is used. The boundary of 2-D domain may be represented by B-spline curves. It may be multiconnected.

The paper discusses various classes of solution sets for linear interval systems of equations, and their properties. Interval methods constitute an important mathematical and computational tool for modelling real-world systems (especially mechanical) with (bounded) uncertainties of parameters, and for controlling rounding errors in computations. They are in principle much simpler than general probabilistic or fuzzy set formulation, while in the same time they conform very well with many practical situations. Linear interval systems constitute an important subclass of such interval models, still in the process of continuous development. Two important problems in this area are discussed in more detail - the classification of so-called united solution sets, and the problem of overestimation of interval enclosures (in the context of linear systems of equations called also a matrix coefficient dependence problem).

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The aim of the present paper is a synthesis of both realistic modelling of the structural behavior of reinforced concrete (RC) shells and an adaptive finite element (FE) calculation tool suitable for the solution of nonlinear problems involving strain-hardening and softening plasticity. In the context of incremental-iterative analysis, an incremental error estimator is introduced. It is based on the rate of work. The reference solution required for error estimation is obtained by means of a recovery scheme applied to stress resultants. If the estimated error exceeds a prespecified threshold value, a new mesh is designed. Mesh generation is performed in the 2D parametric space of the shell. After mesh refinement, the state variables are transferred from the old to the new mesh and the calculation is restarted at the load level which was attained by the old mesh. The usefulness of the developed adaptive analysis scheme is demonstrated by a numerical analysis of an RC cooling tower.

The boundary element method is applied for numerical simulation of the freezing process proceeding in biological tissue under the influence of cylindrical cryoprobe. From the mathematical point of view the problem discussed belongs to the group of moving boundaries ones for which the mushy zone sub-region (intermediate phase) is considered. In this paper the mathematical model of the process is formulated using the fixed domain approach and a parameter called the substitute thermal capacity determines the evolution of latent heat. On a stage of numerical computations the generalized variant of the alternating phase truncation method (APTM) is applied and the basic mathematical model is rebuilt by the introduction of the enthalpy function. The boundary element method together with APTM leads to the simple and effective numerical algorithm because the difficulties connected with the non-linear problem modelling can be omitted. In the final part of the paper the results of computations are shown.

The results of computations of forces and moments in induction motor made with OPERA 2D program and possibilities of application of FEA methods to consider the failure states during the calculations of induction machine dynamics are discussed in this paper. A mathematics model of an induction motor makes it possible to perform the calculations and analysis of stator currents and electromagnetic torque when the rotor rotates eccentrically, as well as when a bar or rotor ring is broken. A tool has been created which enables to predict preliminarily the results of the defects, which might be introduced at the motor manufacturing stage. To calculate 3D free vibration frequencies of the rotor system of the motor under consideration the PATRAN package has been used. It allowed us to examine the resonance frequencies of the rotor. For the diagnostic measurements the MotorMonitor(TM) program has been applied. It was possible to attain high computational effectiveness due to parallel programming on CONVEX computers of ACC ``CYFRONET''.

The problem of optimal design consists in finding the optimum parameters according to a specified optimality criterion. Existing optimization methods [1,2] usually are not reliable or cannot use the nondifferentiable, not continuous objective functions or constraints. An interval global optimization method is very stable and robust, universally applicable and fully reliable. The interval algorithm guarantees that all stationary global solutions have been found. In this paper the algorithm is applied to optimization of mechanical systems, calculation of extreme values of mechanical quantities and to optimization of structures with uncertain parameters. [1] http://solon.cma.univie.ac.at/~neum/glopt.html [2] http://plato.la.asu.edu/guide.html

The purpose of this paper is to create an efficient finite element for the static analysis of 3D arch structures. It is the circural in-plane element with possibility of out-of-plane action. In the element the influences of shear and axial forces on arch displacements are taken into account. The base is the set of exact shape functions, which fulfil the differential equilibrium equation of 3D arch. These shape functions allow us to obtain the exact element stiffness matrix. The element was tested in several numerical examples, results were compared with available analytical solutions and other numerical results. A very good agreement of the results was obtained.

The paper deals with the numerical modelling of solidification of two-component metal alloys. The numerical model was worked out using the enthalpy formulation of solidification and the finite element method. The work concentrated on one enthalpy formulation, namely the basic enthalpy formulation [1].The models of solid phase growth as well as implementation details are shown in the paper [2].A comparison of the results of the numerical simulation of solidification was made for three approaches to enthalpy approximation as a function of temperature. The three approaches were called: complete, incomplete and linear. The results of simulation, for incomplete enthalpy approximation were almost identical to the results of complete approximation. The computing time for incomplete approximation was substantially lower than the computing time for complete approximation, and comparable to the computing time for linear approximation. [1] Ph. Thevoz, J.L. Desbiolles, M. Rappaz. Modeling of equiaxed microstructure formation in casting.Metall. Trans. A, 20A: 311-322, 1989. [2] N. Sczygiol. Object-oriented analysis of the numerical modelling of castings solidification. CAMES, 8: 79-98, 2001.

By introducing a variable coding technique, a parallel optimization method based on a combination of GAs and ESs is presented. The advantages of both GAs and ESs, like coding of genetic information and adaptation of optimization parameters, are enhanced by this new method.

In nonlinear dissipative mechanical systems, bifurcations of chaotic attractors called boundary crises appear to be the cause of most sudden changes in chaotic dynamics. They result in a sudden loss of stability of chaotic attractor, together with destruction of its basin of attraction and its disappearance from the phase portrait. Chaotic attractor is destroyed in the collision with an unstable orbit (destroyer saddle) sitting on its basin boundary, and the structure of the saddle defines the type of the crisis - regular or chaotic one. In the paper we exemplify both types of the boundary crisis by using a mathematical model of the symmetric twin-well Duffing oscillator; we consider the regular boundary crisis of the cross-well chaotic attractor, and the chaotic boundary crisis of the single-well chaotic attractor. Our numerical analysis makes use of the underlying topological structure of the phase space, namely the geometry of relevant invariant manifolds, as well as the structure of basins of attraction of the coexisting attractors. The study allows us to establish some relevant relations between the properties of the regular and chaotic boundary crisis, and to outline the differences that result mainly in the post-crisis system behavior.

On the base of Hopfield-Tank neural network the Panagiotopoulos approach is briefly discussed. The approach is associated with the analysis of quadratic programming problem with unilateral constraints. Then modifications of this approach are proposed. The original Panagiotopoulos approach is illustrated by the analysis of crack detachment in an elastic body [1]. Efficiency of the proposed modifications is shown on a numerical example of an angular plate. Finally some special conclusions are expressed. [1] P.S. Theocaris, P.D. Panagiotopoulos. Neural networks for computing in fracture mechanics - methods and prospects of applications. Comp. Meth. Appl. Mech. Eng., 106: 213-228, 1993.

The incorporation of displacement discontinuities in finite elements is examined. The incorporation of displacement discontinuities allows the use of discrete constitutive models in a continuum framework in order to avoid the mesh sensitivity of classical continuum models when strain softening is introduced. The procedure for building discontinuities into finite elements is examined, as well as two classes of constitutive models for mode-I and mode-II failure analysis. The performance of the model is illustrated with three-dimensional examples.

The paper presents an application of Artificial Neural Networks for updating a mathematical model of the structure based on dynamic parameters. Neural networks which predict the value of selected stiffness or concentrated masses on the basis of Frequency Response Function (FRF) have been built. Two types of neural networks have been used for this task: multi-layer feed-forward (MLFF) networks with different learning algorithms and networks with radial basis function (RBF). Preceding the update, the FRF is compressed in order to reduce the number of input values necessary for updating the model.

In this work, the application of an indirect Trefftz collocation method to the analysis of bending of thin plates (Kirchhoff's theory) is described. The deflection field approximation is obtained with the use of a set of functions satisfying a a priori the homogeneous part of the differential equation of the problem. Each of the approximating functions is derived from a known thick plate solution. The boundary conditions are imposed by means of continuous (integral) and discrete (collocation) least squares methods. Numerical examples are presented and the accuracy of the proposed technique is assessed.
Keywords: Trefftz method, thin plates, point collocation, complex trial functions, least squares.

The paper contains a review of problems connected with numerical analysis of elastic-plastic surface structures. Given is detailed information about finite elements as well as about the algorithm of physically non-linear analysis using the incremental-iterative Newton-Raphson method with the consistent modular matrix. The main goal of the paper is to compare numerical results obtained with elements based on either the volume or area approach to the formulation of physical relations. The presented examples are obtained with the use of computer code MANKA. They illustrate some numerical problems induced by elastic-plastic deformation of chosen types of plates.
Keywords: material non-linearity, FEM, volume/area approach

The shape optimization of machine elements or structures consists in searching the optimal form satisfying the imposed mechanical, technological and geometrical criteria. In this paper two methods, developed for shape optimization of uni and bidimensional mechanical structures are offered. The first one, known as the adjoint variables method, is based upon the evaluation of the sensitivity or the derivatives of the functional with respect to the evolution of the structure shape. It requires the use of a mathematical optimization code in order to converge towards the solution. The second method deals with Genetic Algorithms whose principle rises from the evolution of individuals living in nature. Within the framework of structures optimization, a new Genetic Algorithm has been developed. The analysis is carried out by the finite element method. The first part of this article is devoted to optimal shape research of unidimensional structures such as beams while the second treats the shape optimization of bidimensional parts. To show the effectiveness of each of the two methods, examples are presented, and the numerical results obtained show that a good convergence was obtained in each case.

The paper concerns a method of implementation for the numerical modelling of the solidification process in which the finite element method was used. Modern techniques of software engineering were applied to reach the aim. The decomposition of the problem domain, for the needs of object-oriented analysis, was carried out. The relationships between parts of the analysed problem were discussed. At first, the object-oriented analysis was investigated in general for the wide range of problems solved by the finite element method, e.g. thermomechanic problems of castings, and then it was investigated in detail for the solidification process. The most important specialisation of classes for object implementation of the solidification model were also discussed. The enthalpy solidification formulations were used in the numerical modelling. The three models of solid phase growth, used for solidification modelling of two-component alloys, were described. The method for determining the dependence of enthalpy in relation to temperature and the formula for calculating the solid fraction were shown for each of the three models.

The paper deals with a numerical modelling of solidification in which enthalpy formulations were used. The finite element method (FEM) was applied for computer simulation of solidification. This is the most common numerical method used in the simulation of physical processes. The enthalpy formulations are more convenient to use than temperature formulations in the multidimensional problems in which FEM is applied. The paper concentrated on two enthalpy formulations: the apparent heat capacity formulation and the basic enthalpy formulation. The time integration schemes and the numerical realisation of boundary conditions were discussed. The models of solid phase growth and the implementation details used in this paper were shown in the first author's paper right above. The presented results of computer simulations contain: temperature fields, solidification kinetics, cooling velocities and calculated distributions of equiaxed grain size.

Previously known multi-time step integration methods for finite element computations in structural dynamics have been shown to be unstable due to interpolation error propagation. New algorithms of multi-time step integration based on constant velocity during subcycling are investigated. The assumption of constant velocity gives linear variation of displacements so the errors connected to interpolation at the interface between different time step partitions are eliminated. As a consequence, the new constant velocity algorithms give bounded solutions and have been shown to be conditionally stable by their authors. However, numerical investigation demonstrates that if time steps close to the stability limit are used, the errors for higher natural modes are so huge that the obtained solutions can only be considered as incorrect. The main reason for this behaviour is that the constant velocity time integration algorithms are inconsistent. Displacements can be calculated either by direct integration or from the equation of motion leading to different solutions. Based on the numerical results it is concluded that use of time steps below stability limit is insufficient to assure proper solutions. Therefore, significant time step reductions are often required to assure acceptable error levels. As a consequence, the new subcycling algorithms can be more expensive than ordinary time integration. Because they also lead to larger errors the constant velocity subcycling algorithms are useless from practical point of view. Since subcycling is available as an option in LS-DYNA a serious warning is issued to potential users.

The most frequent motivation for the use of mixed methods is their robustness in the presence of certain limiting and extreme situations. At variance, the main goal of the present paper is to reconsider the use of mixed formulation as a tool for wider application, i.e., to study the stability of the proposed procedure treating problems in elasticity otherwise well suited for the solution by the usual displacement method. Computational procedure for the inf-sup test is outlined, and the results are given.

The problem of the stability "in the large'' and the unsafe disturbances of the equilibrium position is studied for the structures whose dynamics is governed by the equation of motion of the pendulum with parametric excitation. The system displays a variety of nonlinear and chaotic phenomena, so that the study requires the use of theoretical concepts of the mathematics of chaos. Detailed explorations are performed by the aid of the nonlinear software package Dynamics.

Physicochemical studies of the organic-water mixtures show that their properties are not linear functions of their concentration but depend on the mixture composition in various ways. The evaluation of the measurement results requires an interpolation of the experimental data and the derivatives of a mixture property with respect to concentration should be known as well. The results of measurements are disturbed by experimental error which causes the scatter of the approximated function values and oscillations of the approximating function derivatives. In the paper an application of the 3rd degree splines for the calculation of derivative and the interpolation for a non-uniform mesh are considered. Smoothing methods of an approximating function by means of splines are proposed. Some numerical examples illustrating the efficiency of the smoothing method and its applications are presented.
Keywords: splines, approximation, smoothing.

The problem of instability and strain localization in a hardening non-associative Drucker-Prager plasticity theory is analyzed. The classical and gradient-enhanced versions of the theory are reviewed and instability indicators are summarized. The regularizing properties of the gradient-enhancement are shown. The classical plane strain biaxial compression test is analyzed in terms of the analytical prediction of ellipticity loss and numerical simulation of the process of shear band formation and evolution. The influence of material model parameters, especially of the degree of non-associativity and the gradient influence, on the instability properties is demonstrated.

Variational formulations that can be employed in the approximation of boundary value problems involving essential and natural boundary conditions are presented in this paper. They are based on trial functions so chosen as to satisfy a priori the governing differential equations of the problem. The essential boundary conditions are used to construct the displacement approximation basis at finite element level. The natural boundary conditions are enforced on average and their integral forms constitute the variational expression of the finite element approach. The shape functions contain both homogeneous and particular terms, which are related through the interpolation technique used. The application in the framework of the finite element method of the approach proposed here is not trouble free, particularly in what concerns the inter-element continuity condition. The Gauss divergence theorem is used to enforce the essential boundary conditions and the continuity conditions at the element boundary. An alternative but equivalent boundary technique developed for the same purpose is presented also. It is shown that the variational statement of the Trefftz approach is recovered when the Trefftz trial functions are so chosen as to satisfy the essential boundary conditions of the problem.

The limiting analysis problem for dielectrics in nonhomogeneous powerful electrical fields is considered. In the framework of this problem the external charges for which the appropriate electrostatical variational problem has no solution are calculated, that solution is treated as a beginning of the electrical puncture of dielectric. From the mathematical point of view the limiting analysis problem is non-correct and needs a relaxation. This is achieved using a partial relaxation based on a special discontinuous finite-element approximation.

The stress model of the hybrid-Trefftz finite element formulation is applied to the elastoplastic analysis of solids. The stresses and the plastic multipliers in the domain of the element and the displacements on its boundary are approximated. Harmonic and orthogonal hierarchical polynomials are used to approximate the stresses, constrained to solve locally the Beltrami governing differential equation. They are derived from the associated Papkovitch-Neuber elastic displacement solution. The plastic multipliers are approximated by Dirac functions defined at Gauss points. The finite element equations are derived directly from the structural conditions of equilibrium, compatibility and elastoplasticity. The non-linear governing system is solved by the Newton method. The resulting Hessian matrices are symmetric and highly sparse. All the intervening arrays are defined by boundary integral expressions or by direct collocation. Numerical applications are presented to illustrate the performance of the model.

The work presents the application of heat polynomials for solving an inverse problem. The heat polynomials form the Trefftz Method for non-stationary heat conduction problem. They have been used as base functions in Finite Element Method. Application of heat polynomials permits to reduce the order of numerical integration as compared to the classical Finite Element Method with formulation of the matrix of system of equations.

The errors of finite element approximations are analysed in a general frame, which is completely independent from the way through which the approximate solution was obtained. It is found that the error always admits decomposition in two terms, namely the equilibrium error and the compatibility error, which are orthogonal. Each of these admits upper and lower bounds that can be computed in a post-processing scheme.

A new prediction technique, based on the indirect Trefftz method, has been developed for the steady-state dynamic analysis of coupled vibro-acoustic systems. In contrast with the finite element method, in which the dynamic field variables within each element are expanded in terms of local, non-exact shape functions, the dynamic field variables are expressed as global wave function expansions, which exactly satisfy the governing dynamic equations. The contributions of the wave functions to the coupled vibro-acoustic response result from a weighted residual formulation of the boundary conditions. This paper discusses the basic principles and convergence properties of the new prediction technique and illustrates its performance for some two-dimensional validation examples. A comparison with the finite element method indicates that the new prediction method has a substantially higher convergence rate. This makes the method suitable for accurate coupled vibro-acoustic predictions up to much higher frequencies than the finite element method.

The paper reports on the work on hybrid-Trefftz finite elements developed by the Structural Analysis Research Group, ICIST, Technical University of Lisbon. A dynamic elastoplastic problem is used to describe the technique used to establish the alternative stress and displacement models of the hybrid-Trefftz finite element formulations. They are derived using independent time, space and finite element bases, so that the resulting solving systems are symmetric, sparse, naturally p-adaptive and particularly well suited to parallel processing. The performance of the hybrid-Trefftz stress and displacement models is illustrated with a number of representative static and dynamic applications of elastic and elastoplastic structural problems.
Keywords: Hybrid-Trefftz elements, elasticity, elastoplasticity, dynamics.

A unified approach for the treatment of the non-linear dynamics of multibody systems (MBS) composed of both rigid and elastic bodies is proposed. Large displacements and rotations, large strains and non-linear elastic material response are considered for the elastic bodies. The proposed formulation exploits three key ingredients: the use of a dependent set of inertial coordinates of selected points of the system; the use of a basic constraint library enforced through the penalty method; the use of the energy-momentum method to integrate the equations. The proposed algorithm is set in the framework of a non-conventional finite element formulation, which combine naturally the displacement-based discretisation of the deformable bodies with rigid body mechanics. Two key performance features are achieved. The exact conservation of total momentum and total energy in conservative systems is ensured. The major drawback of the penalty method, namely numerical ill-conditioning that leads to stiff equation systems, is overcome.

Professor Jirousek has been a very important driving force in the modern development of Trefftz method, contributing to its application in many different fields such as elasticity, shells and plates theory, Poisson equation and transient heat analysis. This article is dedicated to him. The focus of the paper is to incorporate Jirousek method into a very general framework of Trefftz method which has been introduced by Herrera. Usually finite element methods are developed using splines, but a more general point of view is obtained when they are formulated in spaces of fully discontinuous functions - i.e., spaces in which the functions together with their derivatives may have jump discontinuities - and in the general context of boundary value problems with prescribed jumps. Two broad classes of Trefftz methods are obtained: direct (Trefftz-Jirousek) and indirect (Trefftz-Herrera) methods. In turn, each one of them can be divided into overlapping and non-overlapping.

This paper presents a hybrid-Trefftz finite element algorithm designated as fictitious load approach. Its originality resides in the formulation and practical application of concepts which make it possible to account for the unilateral contact conditions of a plate without modification of the finite element mesh. To reach this aim, the approach allows the movable interface between the contact and non-contact parts of the plate to travers any finite element subdomain. The adjustments are confined to fictitious load dependent terms, while the element stiffness matrices remain unchanged during the whole iterative process. Several numerical examples are analysed to assess the effectivity of the T-element algorithm and to compare it with some of the existing solutions of the same problem.
Keywords: finite elements, Trefftz method, contact problem.

The purpose of the paper is to propose of a way of constructing trial functions for the indirect Trefftz method as applied to 2-D creeping (Stokes) flow problems. The considered cases refer to the problems of flow around fixed and rotating circular cylinders, in corners with two walls fixed, or one wall moving, and flow possessing particular symmetry. The trial functions, proposed and systematically constructed fulfil exactly not only the governing equation, like T-complete Herrera functions, but also certain given boundary conditions and conditions resulting from assumed symmetry. A list of such trial functions, unavailable elsewhere, is presented. The derived functions can be treated as a subset of T-complete Herrera functions, which can be used for solving typical boundary-value problems.

The paper contains a general procedure for obtaining of Trefftz polynomials of arbitrary order for 2D or 3D problems by numerical or analytical way. Using Trefftz polynomials for displacement and tractions the unknown displacements and tractions are related by non-singular boundary integral equations. For a multi-domain (element) formulation we suppose the displacements to be continuous between the sub-domains and the tractions are connected in a weak (integral) sense by a variational formulation of inter-element equilibrium. The stiffness matrix defined in this way is nonsymmetric and positive semi-definite. The finite elements can be combined with other well known elements. The form of the elements can be, however, more general (the multiply connected form of the element is possible, transition elements which can be connected to more elements along one side are available). It is also very easy and simply possible to assess the local errors of the solution from the traction incompatibilities (the inter-element equilibrium, which is satisfied in a weak sense only, is the only incompatibility in the solution of the linear problem). The stress smoothing is a very useful tool in the post-processing stage. It can improve the accuracy of the stress field by even one order or more comparing to the simple averaging, if the stress gradients in the element are large. Also the convergence of the so obtained stress field increases. The examples with high order gradient field and crack modelling document the efficiency of this FEM formulation. The extension to the solution of other field problems is very simple.

The purpose of this work is to compare and assess, more in terms of computational efficiency than in terms of accuracy, three alternative implementations of a boundary formulation based on the Trefftz method for linear elastostatics, namely a collocation-based and two Galerkin-based approaches. A finite element approach is used in the derivation of the formulation for the Galerkin-based alternative implementations. The coefficients of the structural matrices and vectors are defined either by regular boundary integral expressions or determined by direct collocation of the trial functions. Numerical tests are performed to assess the relative performance of the different alternative implementations.

A method is proposed for smoothing approximate fields of stress-resultants in patches of finite elements. The method is based on combining Trefftz fields of stress-resultants in a p-version so as to obtain a closest fit using the strain energy norm as a measure. The local systems of equations are formulated from boundary integrals. The method is applied to a problem of a square plate modelled by hybrid equilibrium plate elements using Reissner--Mindlin theory. Results for the problem indicate that the smooth solution for stresses can be in close agreement with the analytic solution in the interior of a patch. Proposals are also included to aid the visualization of tensor and vector continuous fields as stress trajectories.

In this paper a guaranteed upper bound of the global discretization error in linear elastic finite element approximations is presented, based on a generalized Trefftz functional. Therefore, the general concept of complementary energy functionals and the corresponding approximation methods of Ritz, Trefftz, the method of orthogonal projection and the hypercircle method are briefly outlined. Furthermore, it is shown how to use a generalized Trefftz functional to solve a Neumann problem in linear elasticity. Based on an implicit a posteriori error estimator within the finite element method, using equilibrated local Neumann problems, the generalized Trefftz functional yields a computable guaranteed upper bound of the discretization error without multiplicative constants.

Equilibrated solutions, locally satisfying all the equilibrium conditions, may be obtained by using a special case of the hybrid finite element formulation. Equilibrium finite element solutions will normally present compatibility defaults, which may be directly used to estimate the error of the solution, a posteriori. Another approach is to construct a compatible solution using the stresses and displacements available from the hybrid solution. From this dual solution, an upper bound for the global error is obtained. In this paper, the hybrid equilibrium element formulation, the occurrence of spurious kinematic modes and the use of super-elements, in 2D and 3D, are briefly reviewed. Compatibility defaults for 2D and 3D are presented, together with an expression for an element error indicator explicitly based on such defaults. A local procedure for recovering conforming displacements from the equilibrium finite element solution is also presented. The h-refinement procedure is adapted to prevent irregular refinement patterns.

It is well known today that the standard finite element method (FEM) is unreliable to compute approximate solutions of the Helmholtz equation for high wavenumbers due to the pollution effect, consisting mainly of the dispersion, i.e. the numerical wavelength is longer than the exact one. Unless highly refined meshes are used, FEM solutions lead to unacceptable solutions in terms of precision. The paper presents an application of the Element-Free Galerkin Method (EFGM) leading to extremely accurate results in comparison with the FEM. Moreover, the present meshless formulation is not restricted to regular distribution of nodes as some stabilisation methods and a simple but real-life problem is investigated in order to show the improvement in the accuracy of the numerical results, as compared with FEM results.

The paper deals with a strategy of reliable application of the Trefftz elements in the linear analysis of complex engineering structures with stress concentrators. The standard p-adaptivity is suggested in the low gradient areas. For selected large-gradient local zones certain specific T-element substructures are proposed. The h-p adaptive procedures for optimization of parameters of the substructures are numerically investigated.

In a large class of linear, mathematically modelled engineering problems the Trefftz algorithms give accurate solutions in a relatively short computational time. Moreover, the Trefftz functions, fulfilling the governing differential equations, can be used as shape functions of finite elements (T-elements), also with openings and notches. This suggested the authors to investigate the advantages and limitations of the method in optimization of structures with the stress concentrators, e.g. perforated plates. Certain auxiliary object functions, which included simultaneously the objective of the optimization and the constraints, were introduced and investigated. Different optimization strategies were also taken into consideration. To improve the optimization task in case of a large number of variables the authors suggested an algorithm, which used the engineering sensitivity analysis to eliminate less important variables in the particular stages of the procedure.

In this paper, we construct a nonlinear Extended State Observer (ESO) to estimate the dynamics of linear or nonlinear systems with parameter uncertainties and unknown external disturbances. We then apply ESO to the high-precision attitude control of a flexible satellite whose dynamics are unknown. Simulation results demonstrate the usefulness of the proposed control method.
Keywords: attitude control, extended state observer, flexible satellites.

The problem of blood flow in arteries induced by peristaltic waves has been investigated. The methodology of modelling global circulation system has been outlined. Medical measurements required for problem formulation have been presented. Numerical solutions of blood flow in artery based on finite element method have been worked out. The paper presents local model of pulsatile blood flow in the human artery. Modelling of pulsatile flow in cardiovascular system could improve understanding and interpretation of flow measurements in arteries locally as well as ventricular-vascular interaction in healthy patients at rest and while exercising. Results achieved on local models could be generalized to formulate a global model of haemodynamics of cardiovascular system in man. This approach could help identifying physiology of optimal heart work at rest, physical activity and also in pathological conditions as hypertension, cardiac insufficiency, heart defects, coronary heart disease and origin and progression of artherosclerosis as well.

An approximate solution for the problem of unsteady flow and heat transfer caused by a suddenly stopped continuous moving surface and its gradual cooling has been obtained by solving the non-linear governing equations with the implicit finite difference scheme. Stability and convergence of the scheme are first verified. Then, the influence of the plate velocity, Prandtl number, time of stopping of the plate t_1 and the cooling constant on the flow pattern, temperature, wall shear stress and heat flux is analyzed. It is found that velocity, temperature, wall shear stress and heat flux decrease in time. When the plate moves faster, fluid velocity, wall shear stress and heat transfer intensity are augmented whereas temperature goes down. The Prandtl number increases and the cooling constant reduces temperature and heat flux.

In the paper a new meshless FEM method is proposed. The method is physically based and the defined element ensures agreement with equilibrium equations. A special functional is defined which consist of a smoothing term, a boundary term and eventually an experimental one. In one calculation both theoretical and experimental data are used to establish proper solution. The method may be used even in the case when constitutive equation is unknown, what is especially important for residual stress problems.

In the paper a crack growth analysis in quasi brittle materials in plane stress state coupling the Fictitious Crack model to meshless Element-Free Galerkin method is presented. The FC model has been generalized and as a result a uniform algorithm of the analysis of crack propagation, which is a combination of elementary states mode I and mode II has been prepared. The problem is nonlinear because the traction forces contain, besides external loads, cohesive forces on the boundaries of the crack which depend on the actual state of the displacement field. The efficiency of the method has been tested on two standard examples.

In this study, a recursive method for generating the equations of motion of a system of rigid bodies with all common types of kinematic joints in plane motion is presented. The method rests upon the idea of replacing the rigid body by a dynamically equivalent system of particles with added geometric constraints that fix the distance between the particles. Some kinematic constraints due to common types of kinematic joints are automatically eliminated. The concepts of linear and angular momentums are used to generate the rigid body equations of motion without either introducing any rotational coordinates or distributing the external forces and moments over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.

Comparison of the classical methods and the tools of the catastrophe theory is presented through the imperfection-sensitivity analysis of the classical stable-symmetric bifurcation problem. Generally, classical global methods are related to a large interval, while catastrophe theory concerns the neighborhood of the critical point only, being a local method. Unfortunately, in most cases of practical problems, by using classical global methods, there can hardly be obtained analytical solutions for the multivalued imperfection-sensitivity functions and the associated highly folded imperfection-sensitivity surfaces. In this paper, an approximate solution based on the catastrophe theory is presented, in comparison with the exact solution obtained in graphical way. It will be shown that by considering the problem as an imperfect version (at a fixed imperfection) of a higher order catastrophe, a topologically good solution can be obtained in a considerably large, quasi in a nonlocal domain.

A phenomenon called the Critical Impact Velocity (CIV), which is directly related to material behavior under dynamic loads, is of special interest in this paper. Deformation trapping due to thermoplastic instability caused by the propagation of plastic waves is the main physical reasons for the CIV. This critical value of shear velocity should be considered as a material constant, but it is difficult to estimate due to complicated material response. Analytical approaches may only provide some preliminary estimates, because they are based on simple constitutive relations. On the other hand, experimental techniques are more reliable, but then there exist problems in specimen design. Numerical techniques such as FE method offer a possibility to treat the problem in a more general aspect. Numerical results obtained in the environment of ABAQUS code demonstrate the role to be played by computer simulations as compared to the analytical and experimental findings. The CIV in shear is studied for the case of martensitic steel VAR4340, and the FE models are based on geometry of the Modified Double Shear specimen (MDS). Thus, the principal questions are formulated as follows: to which extent the analytical approach approximate the CIV, what is the role of experimental results and what information can be obtained after numerical simulations.

In this paper the sensitivity based optimization problem is considered. The shape of the first of two contacting bodies is optimized on the basis of sensitivities calculated for the second body i.e. workpiece. The finite element simulation of sheet metal forming process and direct differentiation method of sensitivity analysis is used. Some energy measure of deforming sheet metal is chosen as a cost functional. Its gradients with respect to the tool (punch) shape parameters are evaluated. Tool shape optimization based on `exact' sensitivity results is performed. Calculated sensitivities with respect to the tool shape parameters are the input for the optimization algorithm. The cost functional is minimized, yielding the optimal shape of the tool. The theory is illustrated by numerical example. Shape optimization of the compressor cover produced in one of sheet stamping factories is performed.
Keywords: sheet metal forming, sensitivity, optimization, tools design.

Different friction models: the classic one proposed by Amontons-Coulomb (AC) with a constant friction coefficient, a three-parameter model proposed by Wriggers et al. [1], and a model based on the concept of `work-hardening' proposed by de Souza Neto et al. [2], are applied to the 3-D square-cup drawing and S-rail stamping FE simulations. The benchmark problems used during NUMISHEET'93 for a cup drawing and NUMISHEET'96 for S-rail stamping were simulated here. The results obtained for these three models are presented to illustrate the influence of the friction model on the drawing process. [1] P. Wriggers, T. vu Van, E. Stein. Finite element formulation of large deformation impact-contact problems with friction. Computers and Structures, 37: 319-331, 1990. [2] E.A. de Souza Neto, K. Hashimoto, D. Peric, D.R.J. Owen. A phenomenological model for frictional contact accounting for wear effects. Phil. Trans. R. Soc. London, A354: 819-843, 1996.

A new numerical method for 2D linear elliptic partial differential equations in an arbitrary geometry is presented. The special feature of the method presented is that the trial functions, which are used to approximate a solution, satisfy the PDE only approximately. This reduction of the requirement to the trial functions extends the field of application of the Trefftz method. The method is tested on several one- and two-dimensional problems.

The aim of the paper is to present the application of the evolutionary algorithms to selected optimization and identification problems of mechanical systems. The coupling of evolutionary algorithms with the finite element method and the boundary element method creates a new artificial intelligence technique that is very suitable in computer aided optimal design and defect detection. Several numerical examples for optimization and identification are presented.
Keywords: evolutionary algorithms, finite element method, boundary element method, optimization, identification.

The aim of the paper is to point out the most important factors that should be taken into account during the designing of expert systems for technical diagnostics and advanced condition monitoring. The first such factor is the proper design of unified databases. It was assumed that discussed system consists of a network of coexisting and related nodes containing active statements looking for an equilibrium state. Such network represents a diagnostic model. Diagnostic models describe the relations between observed symptoms and their causes, i.e. the technical states of the object. Direct specification of such models is difficult due to the complex nature of state-symptom relations. An interesting idea is connected with example based inverse diagnostic models. Suggested solutions simplify the development and reduce maintenance costs for the whole system. A very important benefit for industrial application is the opportunity to arrange an incremental development of the final diagnostic expert system.
Keywords: expert systems, blackboard, reasoning strategy, inverse models.

The methods of nuclear power plant safety assessment and accident management used in Sweden and selected computerized decision support systems are briefly described. The defense-in-depth strategy, which comprises three elements, namely prevention, protection and mitigation, is essential for keeping the fission product barriers intact. The safety assessment program, which focuses on prevention of incidents and accidents, has three main components: periodic safety reviews, probabilistic safety analysis and analysis of postulated disturbances and accident progression sequences. Even if prevention of accidents is the first priority, it is recognized that accidents involving severe core damage, including core melt, may nevertheless occur. Therefore, measures are required to achieve reasonable capability to manage such accidents. Emergency Operating Procedures and Severe Accident Management Guidelines are the vital components of the Accident Management System. Computerized decision support systems, to be used during normal, disturbed and accident states of a plant are expected to play increasingly important role in safety assessment and accident management, including support in rapid evaluation of possible radioactive releases in the event of a severe accident.

The paper focuses on using of artificial neural networks in model-based fault detection and isolation. Modelling of a system both at its normal operation conditions and in faulty states is considered and a comparative study of three different methods of system modelling that use a linear model, neural network nonlinear autoregressive with exogenous input model, and neural network Wiener model is presented. Application of these models is illustrated with an example of approximation of a dependence of the juice steam pressure in the stage two on the juice steam pressures in the stages one and three of a five stage sugar evaporator. Parameters of the linear model are estimated with the recursive pseudolinear regression method, whilst the backpropagation and truncated backpropagation through time algorithms are employed for training the neural network models. All the considered models are derived based on the experimental data recorded at the Lublin Sugar Factory.
Keywords: fault detection and isolation, neural network models, parametric models, evaporation stations.

The paper deals with selected problems of knowledge acquisition for intelligent information systems that may be applied for aiding technical diagnostics of machinery and equipment. Two main kinds of knowledge are discussed, i.e. declarative and procedural knowledge. Some methods of declarative knowledge acquisition from domain experts and from databases are presented, the latter being divided into machine learning methods and knowledge discovery ones. Examples of declarative knowledge acquisition and discovery from databases are shown. Moreover, an example of procedural knowledge acquisition from a domain expert is presented. The paper concludes with new issues of knowledge acquisition methodology.
Keywords: intelligent information systems, knowledge base, procedural knowledge, declarative knowledge, knowledge acquisition, knowledge discovery.

In this study, we develop an idea of knowledge elicitation realized over a collection of databases. The essence of such elicitation deals with a determination of common structure in databases. Depending upon a way in which databases are accessible abd can collaborate, we distinguish between a vertical and horizontal collaboration. In the first case, the databases deal with objects defined in the same attribute (feature) space. The horizontal collaboration takes place when dealing with the same objects but being defined in different attribute spaces and therefore forming separate databases. We develop a new clustering architecture supporting the mechanisms of collaboration. It is based on a standard FCM (Fuzzy C-Means) method. When it comes to the horizontal collaboration, the clustering algorithms interact by exchanging information about local partition matrices. In this sense, the required communication links are established at the level of information granules (more specifically, fuzzy sets forming the partition matrices) rather than patterns directly available in the databases. We discuss how this form of collaboration helps meet requirements of data confidentiality. In case of the horizontal collaboration, the method operates at the level of the prototypes formed for each individual database. Numeric examples are used to illustrate the method.
Keywords: fuzzy clustering, collaboration, data confidentiality and security, data interaction, cluster (partition) interaction, vertical (data-based) and horizontal (feature-based) collaboration.

The paper presents a concept of knowledge based software supporting a long period machine design analysis - intelligent personal assistant. The concept of intelligent personal assistant is based on the maze model and optimisation model of the design process. The functional structure of the whole system is shown.

The paper discusses some methods of commonsense reasoning applicable to analysis of truss structures. The proposed method, based on qualitative representation of trusses, allows to reach conclusions in the case of highly incomplete knowledge about the system. Two cases are considered. First, when only the general geometry of the structure is known, without the quantitative knowledge of stiffness coefficients of bars. Second, with additional assumption that all stiffness coefficients of bars are roughly equal.

The paper tries to show the role that can be played by genetic optimization strategies in solving huge global optimization problems in computational mechanics and other branches of high technology. Genetic algorithms are especially recommended as the first phase in two-phase stochastic optimization. The self-adaptability of genetic search is shown on the basis of the mathematical model introduced by M. Vose. Main goals of adaptation are used as leading criteria in the simple taxonomy of genetic strategies.
Keywords: genetic algorithms, stochastic search, two-phase strategies.

This paper presents possibility of identification of loads in mechanical systems based on response measurements during operation. Information of loads is very useful in diagnostic process, if usage of structure is under investigation. State of the art in the field of loads identification is presented. The problem of load identification is defined, and some methods are presented. The paper is focused on the problem of loads identification based on measurements of process parameters or movement parameters for vehicles or airplanes. Two methods are applied to show applicability of this approach in industrial practice; neural network based method and regression model based method. A case study of identification of load of helicopter structure during flight is presented.
Keywords: loads identification, neural networks application for loads identification, helicopter loads identification, regression model for load identification.

We investigate the evolution of Tollmien-Schlichting waves in boundary layers in the presence of moderate buoyancy arising from the heating or cooling of a compliant wall. We exploit the multi-deck structure of the flow in the limit of large Reynolds numbers to make an asymptotic analysis of the pertubed flow, along the upper-branch of the neutral stability curve, to derive linear neutral results. These results are discussed and are compared to rigid wall results. Also, a brief parametric study, based on the linear neutral results, is presented and the results are discussed.
Keywords: linear stability, heating and cooling, compliant surface.

In the paper, the layout optimization of rigid-plastic disks is presented. The method is based on a model where a disk is subdivided into rectangular elements interconnected by normal and shear forces along their edges. Using this model statically admissible stress fields are constructed and the static theorem of limit analysis is applied. Following the concept of porous materials the design variables are the unknown densities of the elements with variable yield stress expressed in terms of the densities. Two complementary optimum design problems are presented. The load intensity is maximized at given intensity of the load and the total amount of material is minimized at prescribed amount of material, respectively. Both problems are expressed in the forms of nonlinear mathematical programming. The application is illustrated by two examples.

This paper describes the topology and the shape optimization scheme of the continuum structures using the cellular automata simulation. The design domain is divided into small square cells. By considering the cells as the elements, the stress analysis of the structure is carried out by finite element method. Then, the design variables are updated according to the local rule and the stress distribution. The rule is defined as the simple relationship between a cell whose design variable is updated and its neighborhood cells. In this paper, we will discuss the formulation to analytically derive the rules from the optimization problems. The special constraint condition named as ``CA-constraint condition'' is introduced first and then, the global optimization problem for the whole structure is divided into the local problem for some neighboring cells. The derived rules are applied to the same numerical example in order to discuss the theoretical validity of the formulation and the feature of the rules.
Keywords: topology and shape optimization, cellular automata (CA), local rule, 2D elastic problem, finite element method (FEM).

The aim of this paper is to present an application of the global optimization method of Boender et al. to a material function identification in a mechanical problem. These material functions are found in the evolution equation for a volume void fraction parameter describing nucleation and growth of microvoids in the flow of porous ductile solids and they play an important role in proper constitutive modelling of postcritical behaviour and fracture. In the evolution equation a plastic strain controlled nucleation process is simulated and uniaxial tension deformation history is considered. In nonlinear regression the minimization of the mean squares functional is assumed. The problem is treated directly as a global optimization one. The necessity of the use of a global optimization approach follows from the hypothesis that there can exist many local minima in the considered problem. The possibility of the existence of many local minima is not usually taken into account. The global optimization method of Boender et al. was applied to minimize the least squares functional. We determine the material functions parameters on the basis of the given Fischer's experimental data set. This data set has been obtained for axisymmetric tension of steel specimens. The results of numerical calculations presented in the paper proved the validity of the hypothesis about the existence of many local minima.
Keywords: plastic flow of voided media, material functions identification, global optimization, nonlinear regression, nonlinear programming.

This paper is intended to summarise the actual work in the area of large deformations of tension systems. The previously conducted research adds significant contributions to the understanding of the response characteristics of pneumatics and suspended membranes with wrinkling allowed. Here the attention will be focused on the applications of the one-dimensional tensioned cable systems. Two- and three-dimensional tensile structures, will be forced to work with compressed members. Since cables can not transmit any compressive forces a verified numerical algorithm, based on the monitoring of the load displacement path is proposed. The special computer code NAFDEM (Nonlinear Analysis by Finite Difference and Element Methods) was adapted to solve undertaken highly nonlinear problems. Calculated results were verified numerically and compared with the solutions obtained by the numerical integration technique.

The paper presents application of the Trefftz method for analysis a case of heat conduction problem across two coupled regions - fouling layer of complex form deposited onto the tube wall at its outer periphery. Taken into considerations modes of heat transfer from a hot gas to the outer surface of the fouling layer are: either by pure convection or radiation, and by both the modes combined. A fluid flowing inside the tube exchanges heat by only convection at constant transfer coeffcient. Based on the variational principle and Trefftz method the boundary weighted residual approach has been developed providing in turn an equation system for analysis of the problem under study. Then, results of series of systematic numerical experiments illustrating convergence and accuracy of the approach when applied to the case in point have been shown for a specific input data set assumed. To emphasise practical significance of the method, a calculated temperature distribution 3D chart and thermal resistance of 2D fouling deposits conclude the paper.

A monotone predictor-corrector finite difference scheme solving the advection equation has been proposed. A geometrical interpretation of the Burstein scheme forms a basis for construction of the new scheme. The main idea consists in defining a proper limitation algorithm in the predictor step preventing formation of new extremes of the solution profile. Various variants of the scheme have been tested for the linear advection equation and an optimum version has been chosen for further developments. Extensions to the nonlinear case and inhomogenous, solution independent velocity field have been made. Application of the time splitting procedure enables the scheme to be applied for multidimensional advection problems. For chosen test problems the scheme behaves better than schemes proposed in the literature.
Keywords: finite difference schemes, monotone schemes, advection equation.

The circular ring is linearly elastic and its cross-section is rectangular. Two deformation dependent distributed loads, that is follower loads, are applied simultaneously on the outer surface of the ring. The first load is a uniform pressure on the whole outer surface. The second load is uniform normal traction exerted on two surface parts situated in axially symmetric positions. Both loads are selfequilibrated independently from each other. A nonlinear FE program with 3D elements is used for the numerical analysis of a geometrically perfect and two imperfect rings. Displacement control is used in the equilibrium iterations. Equilibrium surfaces are determined in the space of three parameters such as one characteristic displacement coordinate, and two load factors. The stability analysis is performed in the knowledge of the equilibrium surfaces.
Keywords: deformation dependent loads, two-parameter loads, geometric imperfection, displacement control, equilibrium surface, limit point, bifurcation point, unstable region.

We present a new methodology for the integration of general non-linear multibody systems within a finite-element framework, with special attention to numerical robustness. The outcome is a non-linearly unconditionally stable algorithm with dissipation properties. This algorithm exactly preserves the total linear and angular momenta of holonomically constrained multibody systems, which implies the satisfaction of Newton's Third law of Action and Reaction. Furthermore, the scheme strictly dissipates the total mechanical energy of the system. This is accomplished by selective damping of the unresolved high-frequency components of the response. We derive the governing equations relying on the 6-D compact representation of motion and we employ a parameterization based on the Cayley transform which ensures geometric invariance of the resulting numerical schemes. We present some numerical tests in order to illustrate the main features of the methodology, and to demonstrate the properties predicted in the analysis.

The initial-boundary value problem in the weak form is formulated for the general six-field non-linear theory of branched shell structures. The extended time-stepping algorithm of the Newmark type is worked out for the non-linear dynamic analysis on the configuration space containing the rotation group SO(3). Within the finite element approximation, an accurate indirect C0 interpolation procedure on SO(3) with a transport of approximation domain is developed. Numerical simulations by the finite element method of 2D and 3D large overall motions of several flexible elastic shell structures are presented. It is shown that values of potential and kinetic energies may oscillate in time, but the total energy remains conserved during the free motion of the structures in space.

The quality of spraying chemicals in a field depends on the distance between the boom of the sprayer and the canopy. Keeping that distance relatively constant enables even distribution of chemicals over the field. However, because the boom has a significant moment of inertia due to its length, (commonly 30 [m] and above) the vehicle has a tendency to roll. The excessive rolling significantly decreases the quality of spraying and can even cause damage to the boom if the tip of the boom hits the ground. The boom itself deflects significantly due to its flexibility and can increase the total amplitude of the boom tip point movement during spraying operation. In this study the effect of the boom flexibility on vehicle rolling, boom rolling and boom reaction forces is evaluated. Also the effect of number of modes selected to represent flexible model, on the boom tip point deflection is analyzed. The simulation model of the sprayer is developed in DADS multibody code and mode shapes of the boom are obtained from I-DEAS code. The simulation model of the sprayer is driven over a ramp and a numerical representation of the NATC (Nevada Automotive Test Center) track.

When new formulations for the description of flexible multibody systems are proposed, often they imply the use of new sets of generalized coordinates, even if the finite element method is used to describe the system flexibility. The adoption of such formulations implies that an additional effort must be made to describe the kinematic constraints that involve flexible bodies. The commercial multibody codes generally have good kinematic joint libraries for rigid bodies, but they are limited in the type of joints available in what flexible bodies are concerned. This work proposes and demonstrates that such limitations can be overcome by using virtual rigid bodies. The idea is to develop a single kinematic joint that restricts all relative degrees of freedom between one or more nodes of the flexible body and a rigid body. The designation of virtual body derives from assuming that it is a massless rigid body. In this form any of the kinematic joints between rigid bodies available in the multibody code libraries, can be used. In the process it is shown that the interaction of the user with the multibody code is much simpler. The numerical problems resulting from ill-conditioned mass matrix, due to the null inertias of the virtual bodies, are avoided by using a sparse matrix solver for the solution of the equations of motion. The proposed formulation is applied to a complex flexible multibody system, represented by the model of a road vehicle with flexible chassis, the results are presented and the discussion on the relative virtues and drawbacks of the current methodologies is made with emphasis on the models and algorithms used.

A Nordsieck form of multirate integration scheme has been proposed for flexible multibody dynamic systems of which motions are represented by large gross motion coupled with small vibration. Based on the conventional flexible multibody dynamics formulation, vibrational modal coordinates with floating reference frame and relative joint coordinates are employed to describe the motion in this research. In the multirate integration, the fast variables of the flexible multibody system are integrated with smaller stepsize, whereas the slow variables are integrated with larger stepsize. It is assumed that vibrational modal coordinates are treated as fast variables, whereas the relative joint coordinates are treated as slow variables to apply multirate integration method. A method that decomposes the equations of motion for flexible multibody systems into a fast system with flexible coordinates and a slow system with joint relative coordinates has been also proposed. The proposed multirate integration method is based on the Adams-Bashforth-Moulton predictor-corrector method and implemented in the Nordsieck vector form. The Nordsieck form of multirate integration method provides effective step-size control and at the same time, inherits the efficiency from the Adams integration method. Simulations of a flexible gun and turret system of a military tank have been carried out to show the effectiveness and efficiency of the proposed method.

A finite element formulation for a transition element between shells and beam structures is described in this paper. The elements should allow changes between models in an `optimal' way without or with little disturbances which decrease rapidly due to the principle of Saint-Venant. Thus, the constraints are formulated in such a way that a transverse contraction within the coupling range is possible. The implementation of the coupling conditions is done with the Penalty Method or the Augmented Lagrange Method. The element formulation is derived for finite rotations. Same rotational formulations are used in beam and shell elements. Rotational increments up to an angle of 2pi are possible without singularities based on a multiplicative update procedure. It can be shown that the transition to rigid bodies can be derived with some modifications. Examples prove the reliability of the transition formulation. Here simple element tests and practical applications are shown.

The paper presents a semi-analytical method for the study of a linear differential system with variable coefficients. The solution is given in terms of real positive integer powers; it is obtained in terms of independent functions which are computed numerically. The paper extended the semi-analytical method from [1] (for one differential equation only), to the study of a linear differential system. The differential system became a system with recurrent expressions between the coefficients of the power series in a matrix form. The strength of this method is shown by application to the dynamic analysis of typical rotor blades. The frequencies and mode shapes are calculated. The results are compared with theoretical results for the degenerate cases and with results obtained through other methods. [1] V. Giurgiutiu, R.O. Stafford. Semi-analytic methods for frequencies and mode shape of rotor blades. Vertica, 1(4): 291-306, 1977.

An antiplane mixed boundary problem of electroelasticity for a hollow piezoelectric cylinder with an arbitrary system of active surface electrodes exciting its oscillations is considered. The solution is carried out on the basis of the approach developed in [1] for investigation of the oscillations of a solid piezoceramic cylinder with a given system of active surface electrodes. Results of numerical realization of the obtained algorithm characterizing amplitude-frequency features of the cylinder and also the behaviour of electroelastic quantities in the cylinder area and on the boundary are given. [1] M.L. Filshtinsky, D. Bardzokas. Boundary integral equation method in diffraction problems of electroelastic waves (in Russian). Proceedings of University of Sumy, p. 194. Sumy, 1999.

We shall be dealing with the eigenvalue optimization problem for an anisotropic plate. The plate is partly unilaterally supported on its boundary and subjected to longitudinal forces causing its buckling. The state problem has then the form of an eigenvalue variational inequality expressing the deflection of the plate and the maximal possible value of the acting forces keeping its stability which corresponds to the first eigenvalue. The demand of the maximal first eigenvalue with respect to variable thicknesses of the plate means to solve the optimal design problem with eigenvalue variational inequality as the state problem. The existence of a solution in the framework of the general theory will be examined. The necessary optimality conditions will be derived. The convergence of the finite elements approximation will be verified.

This paper presents a simple method for evaluating the threshold value for fatigue cracks that emanate from a V-notch. The proposed method is based on the similarities between the elastic-stress fields around the tip of a crack and the tip of a V-notch. Threshold values for fatigue cracks that emanate from a V-notch are expressed by means of the threshold value for the propagation of a high-cycle-fatigue crack and the opening angle of the V-notch. The corresponding calculations were performed by the finite-element method.

In this paper, Trefftz polynomials are used for the development of FEM based on the reciprocity relations. Such reciprocity principles are known from the Boundary Element formulations, however, using the Trefftz polynomials in the reciprocity relations instead of the fundamental solutions yields the non-singular integral equations for the evaluation of corresponding sub-domain (element) relations. A weak form satisfaction of the equilibrium is used for the inter-domain connectivity relations. For linear problems, the element stiffness matrices are defined in the boundary integral equation form. In non-linear problems the total Lagrangian formulation leads to the evaluation of the boundary integrals over the original (related) domain evaluated only once during the solution and to the volume integrals containing the non-linear terms. Also, Trefftz polynomials can be used in the post-processing phase of the FEM computations for small strain problems. By using the Trefftz polynomials as local interpolators, smooth fields of the secondary variables (strains, stresses, etc.) can be found in the whole domain (if it is homogeneous). This approach considerably increases the accuracy of the evaluated fields while maintaining the same rate of convergence as that of the primary fields. Stress smoothing for large displacements will be the aim of further research. Considering the examples of simple tension, pure bending and tension of fully clamped rectangular plate (2D stress/strain problems) for large strain-large rotation problems, the use of the initial stiffness, the Newton-Raphson procedure, and the incremental Newton-Raphson procedure will be discussed.

The presented work shows one of possibilities of numerical modelling of castings. The simulation is a base of modern design. The finite difference simulation program enables computer aided calculations of a form filling and solidification. It is possible to analyse thermal behaviour of the casting, cooling, or heating system with the simulation. The optimisation of the process can be handled easily by a user of the software.

In the case of a Hypothetical Core Disruptive Accident (HCDA) in a Liquid Metal Fast Breeder Reactor, it is assumed that the core of the nuclear reactor has melted partially and that the chemical interaction between molten fuel and liquid sodium creates a high pressure gas bubble in the core. The violent expansion of this bubble loads and deforms the reactor vessel, thus endangering the safety of the nuclear plant. The experimental test MARA 8 simulates the explosive phenomenon in a mock-up enclosed in a flexible vessel with a flexible roof. This paper presents a numerical simulation of the test and a comparison of the computed results with the experimental results and previous numerical ones.

The paper deals with the problem of material identification for smooth muscle tissue in activated, or passive states. In [1] a composite type mathematical model has been proposed describing the complexity of the tissue reduced to the networks of muscle and collagen fibres. The computational model is based on the total Lagrangian formulation with incompressibility of the bulk material. The problem of inflating vessels is considered in order to allow simulation of real experimental conditions and, thus, to determine constitutive parameters of muscle in active state. These parameters are identified also from hysteresis, or relaxation curves. The direct differentiation, or the adjoint systems techniques are applied to the sensitivity analysis. Results of numerical tests are given. [1] E. Rohan, R. Cimrman. Numerical simulation of activated smooth muscle behaviour using finite elements. In: Proceedings of UWB, 143-155. University of West Bohemia, Plzen, 2000.

A variant of the method of characteristics for hyperbolic conservation laws is proposed in this paper. It is based on the time interpolation instead of space interpolation as in the standard method of characteristics. A new method for calculating the propagation velocity is proposed as well. The numerical results of some presented typical tests indicate that algorithm is very accurate.

The paper concerns the theoretical derivation of a new formulation for solution of the initial-boundary value problems for the diffusion equation. The global and local integral equations are derived by using the fundamental solution for the Laplace differential operator. Assuming certain approximations with respect to spatial variable, we obtain a set of the ordinary differential equations (ODE) with continuous time variable. Standard methods for the time integration can be applied to these ODEs. Besides a review of the one step theta-method we propose a new integral equation method for solution of a set of linear ODEs. The paper deals also with the numerical implementation of the global and local integral equations yielding the ODEs.

For some combinations of rotor speed and radial load, the pressure field of bearing fluid can perturb the pure rotational motion and disturb the normal operation of a rotating machine. Classical approach to the stability analysis of Jeffcott rotor in fluid-film bearings is modelling bearings as spring-damper elements and disregarding the external rotor damping [1,2]. Nonlinear models are used to verify results obtained from a linearized model. This paper deals with the influence of external rotor damping on the size of stability regions. Stability analysis of the Jeffcott rotor in fluid-film bearings is performed by using both the linear model based on the linearization of bearing force around the static equilibrium position and the nonlinear model of the velocity linearization [3,4]. [1] D. Childs. Turbomachinery Rotordynamics. John Wiley, New York...Singapore, 1993. [2] E. Krämer. Dynamics of Rotors and Foundations. Springer-Verlag, Berlin...Budapest, 1993. [3] S.H. Crandall. The instability mechanism responsible for oil whirl and oil whip. In: Proceedings of Greek National Congress on Mechanics, 659-672. Democritus University of Thrace, Xanthi, 1995. [4] S.H. Crandall. Velocity linearisation of the dynamic response of fluid-film bearings. In: L. Pust, ed., Proceedings of European Nonlinear Oscillation Conference, 119-124. Institute of Thermomechanics, Prague, 1996.

A modification of the Fourier transform method, which makes feasible transforming products of two functions and/or their derivatives, is described. By application of this method, some kinds of nonlinear differential equations can be transformed and solved. In this paper, the solution of the problem of bending a beam with fixed supports, under continuous transversal loading is given. Equations of the large deformations theory are used. The mutual influence between the deflection and the axial force is taken into account. The problem is mathematically described by a system of three nonlinear differential equations, with the appropriate boundary conditions. The solution is obtained by making use of an iterative procedure, based on the modified Fourier transform method.

A coupled three-phase soil model, consisting of a deformable soil skeleton and the fluid phases water and compressed air, applicable for tunnelling below the ground-water table by means of compressed air, is presented. In this model interactions of the flow of the fluids in the soil with the deformations of the soil skeleton are taken into account in a physically consistent manner. The theoretical background and the implementation of the model into a finite element code are briefly addressed. Several applications dealing with the numerical simulation of laboratory tests and a full-scale in-situ experiment are discussed. These experiments focus on the flow of (compressed) air in dry as well as semi-saturated soil.

In this paper, we investigate the bio-mechanics of atherosclerosis development in human physiology. Blood is modelled as an incompressible fluid of variable viscosity flowing in a slightly diverging channel (i.e. large artery) of small aspect ratio [1]. The hypothetical viewpoint in this work is the existence of relationship between the atherosclerosis development, blood viscosity, flow separation and turning points in the flow field. The problem is tackled by asymptotic approximation and the graphical results are discussed quantitatively. [1] O.D. Makinde. Effect of variable viscosity on arterial blood flow. Far East J. Appl. Math., 4(1): 43-58, 2000
Keywords: aorta, blood viscosity, bifurcation study, atherosclerosis development.

The aim of this paper is to establish the bounds of applicability of the single-domain numerical approach for computations of convection in composite porous/fluid domains. The large number of papers that have utilized this numerical approach motivates this research. The popularity of this approach is due to the simplicity of its numerical formulation. Since the utilization of the single-domain numerical approach does not require the explicit imposing of any boundary conditions at the porous/fluid interface, the aim of the this research is to investigate whether this method always produces accurate numerical solutions.

The purpose of this paper is to analyze the bar rolling process by means of various roll's shapes under the reduction zone of a three-roll planetary mill. The problems were solved with the aid of the finite element program MARC adopting the large deformation-large strain theory and the updated Lagrangian formulation (ULF) and a mesh rezoning procedure was adopted to improve the unexpected error of element turning inside out. The mesh system of the whole bar billet was established by using three-dimensional brick elements, and the three-dimensional elastic-plastic finite element model in MARC was chosen to perform the simulation of the three-roll planetary rolling processes. Totally five different roll's shapes were used to simulate the rolling process. The numerical results; such as the equivalent von Mises stress and plastic strain distributions, rolling force, rolling moment, billet speeds at the entrance and exit planes of the roll gap, etc., are useful in the design of three-roll planetary rolling processes.
Keywords: three-roll planetary rolling process, mesh rezoning, roll's shape design.

The aim of this paper is to simulate numerically the two-dimensional steady state double diffusive flow in a composite fluid-porous layer, submitted to a transverse magnetic field. Both the temperature and solute gradients are imposed horizontally, and the two-buoyancy effects can either augment or counteract each other. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively is used for the momentum equation, and the SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: tic field. Both the temperature and solute gradients are imposed horizontally, and the two-buoyancy effects can either augment or counteract each other. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively is used for the momentum equation, and the SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: Ra=1e5, 1e-8<=Da<=1, N=1, Le=10 and Ha<=100. This study is limited to Pr=7 for the binary solution of (Na2Co3). This choice is motivated by the experimental work on phase change realized in laboratory. It is shown that the main effect of the porous layer is to reduce the heat and mass transfer when the permeability is reduced. Isotherms and streamlines are plotted for several values of Hartman (Ha), Darcy number (Da) and porous layer thickness (Xp). The effect of the magnetic field is found to be rather significant on the flow pattern, heat and mass transfer.
Keywords: double diffusion, porous media, magneto-hydrodynamics, finite volume method.

A new finite element to analyze problems of anisotropic hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative - instead of additive - decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models.
Keywords: finite element method, logarithmic strain measure, elastic material, anisotropic material, constitutive behaviour.

The main objective of the paper is the investigation of the interaction and reflection of elastic-viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic-viscoplastic material with thermomechanical coupling is used. An adiabatic inelastic flow process is considered. Discussion of some features of rate dependent plastic medium is presented. This medium has dissipative and dispersive properties. In the evolution problem considered in such dissipative and dispersive medium the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections. Numerical examples are presented for a 2D specimens subjected to tension, with the controlled displacements imposed at one side with different velocities. The initial-boundary conditions which are considered reflect the asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation. The influence of the constitutive parameter (relaxation time of mechanical perturbances) is also studied in the examples. The attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformations.

This paper deals with computer-aided design of layouts of buildings. The methodology based upon graph grammars and graph transformations allows the designer to distract itself from details and to consider the functionality of the designed object, the constraints and the requirements to be met and the possible ways of selecting optimum alternatives. The specification of building is made in the UML with the aid of the FUJABA system. After this has been accomplished, a proper graph grammar is generated automatically. Such a grammar defines a class of objects that fulfill prescribed requirements and deliver required functionality. The user of the proposed system can browse members of that class, i.e. compare alternative plausible designs, using any commercially available visualization tool.

The paper discusses the problem of designing the stiffest truss with a given and fixed number of joints and element connections. The design variables are the cross sectional areas of the bars or/and the nodal points locations. In each case a maximal volume of a truss, constituting an isoperimetric unilateral condition is prescribed. The nodal force vector is assumed to be independent of the design variables, hence fixed during the optimization process. The equilibrium problems of the trusses are modeled by the conventional linear as well as nonlinear finite element analyses taking into account large nodal displacements and small deformations of members. New optimal layouts of plane and space trusses are presented. These new layouts are found by using the moving asymptotes algorithm, the simplex method and the optimality criteria method.

The paper is concerned with a class of generalized structural optimization problems for which not only stiffness, damping and mass parameters but also loading and support parameters are unspecified and subject to sensitivity analysis and optimization. Both, viscous and complex modulus damping models are used. Single concentrated force and coupling of a force with a concentrated moment, which lags by pi/2, are considered. The latter case corresponds to an excitation induced by a rotational machine with eccentricity. Steady-state periodic vibrations are studied. Response functionals in the form of displacement amplitudes are discussed. Numerical examples of beam and plate structures illustrate the theory and demonstrate the accuracy of the derived formulae for sensitivity operators.
Keywords: sensitivity analysis, optimal design, structural dynamics, vibrations.

Numerical aspects of a level set based algorithm for state constrained linear-quadratic optimal control problems for elliptic partial differential equations are discussed. The speed function needed in the level set equation is derived from shape sensitivity analysis. The discretization operates on a fixed grid and additional boundary points representing the discrete interface between the coincidence set and the set where the bound to the state is not active. The discretization of the hyperbolic level set equation, the shape gradient of an appropriate penalty functional and an useful extension of this gradient (naturally defined only on the interface) to the whole computational domain are discussed.

The topological derivative of an arbitrary shape functional is introduced in [1] for 2D elasticity. The optimality conditions for general shape optimization problems are established in [2] using the shape variations including boundary and topology variations. The topology variations result in the presence of topological derivatives in the necessary conditions for optimality. In the present paper we derive the necessary optimality conditions for a class of shape optimization problems. The topological variations of shape functionals are used for the numerical solution of inverse problems. The numerical method uses neural networks. The results of computations confirm the convergence of the method. [1] J. Sokolowski, A. Zochowski. On topological derivative in shape optimisation. INRIA-Lorraine, Rapport de Recherche No. 3170, 1997. [2] J. Sokolowski, A. Zochowski. Optimality conditions for simultaneous topology and shape design, to appear in SIAM Journal on Control and Optimization, 2003.
Keywords: topological derivative, shape optimization, optimality conditions, artificial neural network, shape inverse problem, nucleation of openings.

The paper deals with optimal design of thin plates. The plate thickness assumes two possible values: h1 and h2 and the plate volume is given. The problem of minimizing the plate compliance needs relaxation. The relaxed formulation was found by Gibiansky and Cherkaev in 1984 [1]. In the present paper a finite element approximation of this problem is presented in the framework of rotationally symmetric bending of circular and annular plates. The problem is composed of a nonlinear equilibrium problem coupled with a minimum compliance problem. The aim of the present paper is to analyze the forms of the optimal solutions, in particular, to look into the underlying microstructures. It is proved that in some solutions a ribbed microstructure occurs with ribs non-coinciding with both the radial and circumferential directions. Due to non-uniqueness of the sign of an angle of inclination of ribs the appearance of this microstructure does not contrasts with the radial symmetry of the problem. In the degenerated problem when the smallest thickness h1 vanishes the above interpretation of the inclined ribbed microstructure becomes incorrect; in these regions one can assume that the plate is solid but with a varying thickness. The degenerated case of h1=0 was considered in the papers by Rozvany et al. [2] and Ong et al. [3] but there such a microstructure was not taken into account. One of the aims of the paper is to re-examine these classical and frequently cited results. [1] L.V. Gibiansky, A.V. Cherkaev. Designing composite plates of extremal rigidity In: A.V. Cherkaev, R.V. Kohn, eds., Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, Boston 1997. [2] G.I.N. Rozvany, N. Olhoff, M.P. Bendsoe, T.G. Ong, R. Sandler, W.T. Szeto. Least-weight design of perforated elastic plates. I,II. Int. J. Solids. Struct., 23: 521-536, 537-550, 1987. [3] T.G. Ong, G.I.N. Rozvany, W.T. Szeto. Least-weight design of perforated plates for given compliance: non-zero Poisson's ratio. Comp. Meth. Appl. Mech. Eng., 66: 301-322, 1988.

We would like to show how to perform shape optimization and state control at a cost comparable to the one of analysis. To this end, we propose to only use informations available for cost function evaluation and incomplete sensitivities not requiring the solution of the linearized state equation. The application of the method is presented for microfluidic MEMs design and control.

The work presents a process of analytical identification via a standard steel frame example. Some experimental tests are made to verify the identification process. Under controlled external loadings the values of displacements and strains are recorded and an approximate FEM-based model is formulated. The polyoptimization approach is employed to analyze that model. The compatibility criteria for comparison of theoretical and experimental models are assumed as square sums of differences between displacements and strains. The whole problem is proceeded in three cycles of evolution suggested by the authors.

In this paper the constitutive model of thermoviscoelastic model is presented. To obtain the parameter sensitivity equations the direct differentiation method is applied. The paper also deals with the finite element for equilibrium and sensitivity analysis problems. Consistent tangent operator for the model is derived. To integrate the creep evolution equation the backward-Euler scheme is efficiently applied. The thermoviscoelastic model with parameter sensitivity analysis is implemented in object-oriented finite element system. Many advantages of the object-oriented approach in FE programming are described in the paper. Two numerical examples are solved. Very good agreement between the FE and analytical results is observed.
Keywords: viscoelasticity, transient heat transfer, sensitivity analysis, object-oriented approach.

In this paper a numerical design algorithm is described which enables the minimization of the stress intensity factor in a machine component by introducing the defense notch system into the component (weakening of the component) or/and by introducing stiffeners into the component (stiffening of the component) and selection of the shape of its boundary. The paper starts with the extensive review of literature devoted to the optimal design of machine parts with fracture constraints. The design procedure used is the combination of mathematical methods of computer graphics, the Boundary Element Method or the Finite Element Method used for the analysis of the stress field, the sensitivity analysis for the response gradient computations assisted by the Sequential Linear Programming. Also the concept of stop holes drilled at the crack tip, to crack arrest, is discussed. That means replacement of singular stress filed problem (cracks) by quasi-singular one (notches) and optimal design of stop holes becomes notch shape optimization problem.
Keywords: stress intensity factor, optimization, BEM, FEM, SLP, defense notch system, stop holes.

The variational theory is the theoretical basis of the finite element method, meshfree particle methods and other modern numerical techniques. The present paper establishes a family of variational principles for nonlinear piezoelectricity. A new constitutive relation is suggested, which is deduced as a stationary condition of a generalized variational principle.
Keywords: variational theory, piezoelectricity, constitutive equations.

This paper presents a mechanical model of the partitioned-pipe mixer (PPM) in case where pipe of the static mixer rotates with angular periodic velocity. Mixing becomes more efficient if the forcing of fluid mixing process is time periodic. Chaos in duct flows can be achieved by time modulation or by spatial changes along the duct axis. The values of Lyapunov exponents for flow in PPM are calculated.
Keywords: partitioned-pipe mixer, chaos, Lyapunov exponents.

Interval analysis permits to calculate guaranteed a posteriori bounds for the solutions of problems with uncertain (interval) input data. Most of the methods of interval analysis assume that all input data vary independently within the given lower and upper bounds. In many practical applications it need not be a case, and the assumption of independence may lead to large overestimation of the set of solutions. The subject of this work is the problem of solving systems of linear interval equations with coefficients linearly dependent on a set of interval parameters called coefficient dependence problem. The purpose of this work is to present methods producing sharp bounds for the set of solutions of systems with dependent input data. The paper starts with an introduction to systems of linear interval equations and the problem of data dependencies in such systems. A parametric formulation of the coefficient dependence problem follows next. Finally, three algorithms to calculate tighter bounds for problems with linearly dependent coefficients, namely the Rump's method, its improved version developed by the author, and the IPM method based on the results from Neumaier [8] are presented and discussed. The algorithms are evaluated and compared using some examples of truss structure analysis.

The paper presents the project of object-oriented software system for modeling flows of fluids inside the area with moving boundary. The flow of a fluid is modeled by using Fluid Particle Model. Finite Elements mesh is generated on the boundary of the area, to allow calculations of stresses on the boundary, arisen from interaction of the fluid with the boundary. Here was presented the application of the system, that simulates the phenomenon of energy and mass transport in large arteries in man. The validity of the computational method was established by comparing the numerical results to medical measurements data. The architecture and results of Fluid Particle Model were presented to compare with the architecture and results of Finite Element models for blood flow in arteries, described in other publications.

Standard higher order finite elements often perform unsatisfactory in contact problems. The major difficulties are caused by uneven distribution of nodal forces resulting in oscillating contact pressures. The paper presents a new approach that eliminates this drawback. The weight functions are chosen in such a way that even distributions of nodal forces are obtained. It is achieved by applying piece-wise linear functions. Two new 2D isoparametric quadratic elements are derived: 6-node triangle and 8-node quadrilateral, and tested in many examples. The new elements have unsymmetric stiffness matrices, but the provided examples show their good performance in contact problems.

This paper describes the application of Trefftz method to the steady-state heat conduction problem on the functionally gradient materials. Since the governing equation is expressed as the non-linear Poisson equation, it is difficult to apply the ordinary Trefftz method to this problem. For overcoming this difficulty, we will present the combination scheme of the Trefftz method with the computing point analysis method. The inhomogeneous term of the Poisson equation is approximated by the polynomial of the Cartesian coordinates to determine the particular solution related to the inhomogeneous term. The solution of the problem is approximated with the linear combination of the particular solution and the T-complete functions of the Laplace equation. The unknown parameters are determined so that the approximate solution will satisfy the boundary conditions by means of the collocation method. Finally, the scheme is applied to some numerical examples.
Keywords: Trefftz method, computing point analysis method, steady-state heat conduction, functionally gradient materials.

The purpose of the research is the estimation of strain distribution in tibia bone. Resultant strain distribution constitutes necessary data for the calculations made in the process of simulation of bone tissue adaptation. Estimation of strain distribution in proximal part of tibia bone is made for different load conditions (including the one following total knee arthroplasty and a surgical correction of lower limb with the application of high tibial osteotomy). The model of tibia bone and soft tissues, prepared for finite element analysis, was made with the use of Ansys 5.6. The geometry of bone was estimated by 3-D digitalisation of a physical model of bone. Displacements distribution obtained from the simulation was compared with the measurements of the physical model of a knee joint. In the research the holographic interferometry method was applied. The results of this calculation are helpful in the estimation of boundary conditions for a simulation of bone tissue functional adaptation in the region of a knee joint. It has been found out that there are differences in strain distribution in different load conditions. However, the perfect agreement of experimental and numerical results for a simple static load indicates that the numerical model is valid for this simulation in a certain range of the applied load.
Keywords: tibia bone, bone tissue adaptation, high tibial osteotomy, knee joint arthroplasty.

A new approach called the "Variational Theory of Complex Rays'' has been developed in order to calculate the vibrations of slightly damped elastic plates in the medium-frequency range. The solution of a small system of equations, which does not result from a fine spatial discretization of the structure, leads to the evaluation of effective quantities (deformation energy, vibration amplitude, ...). Here we extend this approach, which was already validated for assemblies of homogeneous substructures, to the case of heterogeneous substructures.
Keywords: vibrations, medium-frequency range, complex rays, heterogeneous structures.

The limit analysis problem (LAP) for estimation of mechanical durability for non-linear elastic solids is examined. The appropriate dual problem is formulated. After the standard piecewise linear continuous finite-element approximation, the dual LAP is transformed into the problem of mathematical programming with linear limitations as equalities. This finite dimensional problem is solved by the standard method of gradient projection.
Keywords: non-linear elastic solid, limit analysis problem, duality method.

General strategy for developing finite elements of general geometric shape explained on quadrilateral folded plate structure element ensuring invariance properties is presented in this paper. The basic idea of this strategy consists in using the natural coordinate system only for defining the element geometry and performing the element integration in a mapped biunit square. For defining the approximation functions a suitable local Cartesian coordinate system defined from the directions of the covariant base vectors and the perpendicular contravariant base vectors is used. The origin of the local coordinate system is located at the element centroid (centre of gravity). Hybrid and boundary finite elements of reduced Trefftz type for analysing the folded plate structures are also presented. The folded plate structure element is a combination of a plate bending element and a plane stress element.

The hybrid stress boundary element method (HSBEM) was introduced in 1987 on the basis of the Hellinger-Reissner potential, as a generalization of Pian's hybrid finite element method. This new two-field formulation makes use of fundamental solutions to interpolate the stress field in the domain of an elastic body, which ends up discretized as a superelement with arbitrary shape and arbitrary number of degrees of freedom located along the boundary. More recently, a variational counterpart - the hybrid displacement boundary element method (HDBEM) - was proposed, on the basis of three field functions, with equivalent advantages. The present paper discusses these methods as well as the traditional, collocation boundary element method (CBEM). The mechanical properties of the resulting matrix equations are investigated and a series of concepts in both HDBEM and CBEM that have not been properly considered by previous authors, particularly in which concerns body forces, are redefined. This is not a review paper, but rather a theoretical, comparative analysis of three methods, with many physical considerations, some innovations and a few academic illustrations.
Keywords: boundary element methods, generalized inverse matrices, variational methods.

The paper presents an attempt to consolidate a formulation for the general analysis of the dynamic response of elastic systems. Based on the mode-superposition method, a set of coupled, higher-order differential equations of motion is transformed into a set of uncoupled second order differential equations, which may be integrated by means of standard procedures. The first motivation for these theoretical developments is the hybrid boundary element method, a generalization of T. H. H. Pian's previous achievements for finite elements which, requiring only boundary integrals, yields a stiffness matrix for arbitrary domain shapes and any number of degrees of freedom. The method is also an extension of a formulation introduced by J. S. Przemieniecki, for the free vibration analysis of bar and beam elements based on a power series of frequencies, that handles constrained and unconstrained structures, non-homogeneous initial conditions given as nodal values as well as prescribed domain fields (including rigid body movement), forced time-dependent displacements, and general domain forces (other than inertial forces).

The finite element method is applied in the time domain to establish formulations for the integration of first-order and parabolic (transient) problems. The modal decomposition concept is applied using two distinct approaches. The first is based on modal decomposition in the space domain to recover the well-established method for uncoupling the parabolic system of equations. To overcome the limitations of this approach in the implementation of large-scale, non-linear problems, the second approach that is reported consists in inducing uncoupling through modal decomposition in the time domain without using the periodic approximation that characterise analyses in the frequency domain. The methods of modal decomposition are related with the implementation of the Trefftz concept in both time and space.
Keywords: time integration, first-order problems, parabolic problems, Trefftz method.

The finite element method is applied in the time domain to establish formulations for the integration of second-order and hyperbolic (dynamic) problems. Modal decomposition in the space domain is used to recover the well-established method for uncoupling the equations of motion, which is extended to include general time approximation bases. The limitations of this approach in the implementation of large-scale, non-linear problems while preserving the uncoupling of the equations of motion are overcome by using the alternative concept of modal decomposition in the time domain. Both single- and double-field formulations are presented and the associated Trefftz formulations are established.
Keywords: Time integration, second-order problems, hyperbolic problems, Trefftz method

The finite element method (FEM) is widely accepted for the steady-state dynamic response analysis of acoustic systems. It exhibits almost no restrictions with respect to the geometrical features of these systems. However, its application is practically limited to the low-frequency range. An alternative method is the wave based method, which is an indirect Trefftz method. It exhibits better convergence properties than the FEM and therefore allows accurate predictions at higher frequencies. However, the applicability is limited to systems of moderate geometrical complexity. The coupling between both methods is proposed. Only the parts of the problem domain with a complex geometry are modelled using the FEM, while the remaining parts are described with a wave based model. The proposed hybrid method has the potential to cover the mid-frequency range, where it is still difficult for currently existing (deterministic) techniques to provide satisfactory prediction results within a reasonable computational time.

In the 1^st International Workshop, devoted to Trefftz Method, the author presented an indirect approach to Trefftz Method (Trefftz-Herrera Method), while in the Second one some of the basic ideas of how to integrate different approaches to Trefftz method were introduced. The present Plenary Lecture, corresponding to the 3^rd International Workshop of this series, is devoted to show that Trefftz Method, when formulated in an suitable framework, is a very broad concept capable of incorporating and unifying many numerical methods for partial differential equations. In this manner, the unified theory of Trefftz Method that was announced in the second publication of this series, has been developed. It includes Direct Trefftz Methods (Trefftz-Jirousek) and Indirect Trefftz Methods (Trefftz-Herrera). At present, the unified theory is fully developed and an overview is given here, as well as a brief description of its numerical implications.

Two types of Trefftz (T-) functions are often used - fundamental solutions with their singularities outside the given region and general solutions of homogenous differential equations. For elasticity problems the general solution of the homogeneous differential equation (equilibrium equation in displacements known as Lame-Navier equations) can be found in the polynomial form. In this paper we present the first type of T-functions. The paper deals with the investigation of accuracy and stability of the resulting system of discretized equations in relation to the position of the source (singularity) point. In this way non-singular reciprocity based boundary integral equations relate the boundary tractions and the boundary displacements of the searched solution to corresponding quantities of the known solutions. It was found that there exist an optimal relation of the distance of the singularity to the distance of the collocation points where both the integration accuracy and numerical stability are good.
Keywords: point and line Hertzian contact, infinitesimal displacements, large element/sub-domain concept, FEM/BEM technique.

Finite element method has, in recent years, been widely used as a powerful tool in analysis of engineering problems. In this numerical analysis, the behavior of the actual material is approximated with that of an idealized material that deforms in accordance with some constitutive relationships. Therefore, the choice of an appropriate constitutive model, which adequately describes the behavior of the material, plays a significant role in the accuracy and reliability of the numerical predictions. Several constitutive models have been developed for various materials. Most of these models involve determination of material parameters, many of which have no physical meaning [1, 2]. In this paper a neural network-based finite element analysis will be presented for modeling engineering problems. The methodology involves incorporation of neural network in a finite element program as a substitute to conventional constitutive material model. Capabilities of the presented methodology will be illustrated by application to practical engineering problems. The results of the analyses will be compared to those obtained from conventional constitutive models.
Keywords: finite element, neural network, constitutive modelling, soil.

This paper concerns the modelling of plate bending problems governed by Reissner-Mindlin theory when hybrid equilibrium elements of high polynomial degree are used. The fields of statically admissible stress-resultants are categorised into three types according to the nature of their incompatibilities, i.e. pure Trefftz or strongly compatible, weakly compatible, and hyperstatic or strongly incompatible. The effects of this categorisation are reflected in the element formulation. Incompatibilities are quantified in terms of local discontinuities which also account for transverse twist terms. The construction of bases for the three corresponding subspaces of stress-resultants by numerical and/or algebraic means is reviewed. The potential use of a reformulated element is considered in the context of glass plate structures where residual or hyperstatic stresses play an important role.

For several elasticity problems, solution representations for the displacements and stresses are available. The solution representations are given in terms of ``arbitrary'' complex valued functions. For any choice of the complex functions, the governing differential equations are automatically satisfied. Complex solution representations are therefore useful for applications of the Trefftz method. For the analysis of local stress concentrations, due to the local geometry of the boundary curve, such solution representations can be very helpful in the construction of appropriate series of Trefftz functions. In this paper, a few examples are given to demonstrate how to construct Trefftz functions for special purpose finite elements, which include the local solution behavior around a stress concentration or stress singularity.
Keywords: elasticity, complex solution representations, stress singularities, Trefftz functions, Trefftz-type finite elements.

A new numerical method for scattering from inhomogeneous bodies is presented. The cases of E and H-polarizated incident wave scattered by an infinite 2D cylinder are considered. The scattered field is looked for in two different domains. The first one is a bounded region inside the scattering body with an inhomogeneous permittivity ε(x,y). The second one is an unbounded homogeneous region outside the scatterer. An approximate solution for the scattered field inside the scatterer is looked for by applying the QTSM technique. The method of discrete sources is used to approximate the scattered field in the unbounded region outside the scattering body. A comparison of the numerical and analytic solutions is performed.

Starting from the governing equations, the general solution and the complete solution set for plane piezoelectricity are derived in this paper. Subsequently, the Trefftz collocation method (TCM) is formulated. TCM falls into the category of Trefftz indirect methods which adopt the truncated complete solution set as the trial functions. Similar to the boundary element method, the solution procedure of TCM requires only boundary discretization. Numerical examples are presented to illustrate the efficacy of the formulation.
Keywords: Trefftz, piezoelectricity, boundary element, collocation.

This paper is a continuation and development of the dissertation[1]. Complex folded-plate structures with holes are analyzed using the Trefftz-type finite elements, which appears very effective. The shape functions of these elements (Trefftz functions) fulfill respective differential equations. Then, a certain optimization algorithm is proposed, in which an optimized structure can have a large number of parameters used as optimization variables. Therefore, in particular stages of the proposed procedure, less important variables can be eliminated. The choice of the active variable set is based on investigation of sensitivity of the objective function and constraints on small changes of these variables.
Keywords: Trefftz-type finite elements, hybrid elements, folded-plate structures, optimization of structures.

In this work a hybrid-Trefftz formulation and a meshless approach based on the use of radial basis functions (RBF) are applied to the analysis of reinforced concrete beams. Resorting to the Mazars model, the concrete is represented by an elastic medium with progressive damage. In the hybrid-Trefftz formulation a stress field that satisfies a priori the equilibrium equations on the domain is used. The displacements on the static boundary are independently approximated, resulting in a governing system where the operators have to be integrated over the domain of the problem. In what concerns the meshless approach, radial basis functions are used to approximate the displacement fields but, as a collocation procedure is used, no integrations are required. A numerical example illustrates the results obtained with both techniques.

The solution of inhomogeneous elliptic problems by the Trefftz method has become increasingly more popular during the last decade [2, 3, 4]. One method of solution uses the fundamental solutions as trial functions and the inhomogeneous part is expressed by radial basis functions (RBFs). The purpose of this paper is to solve several boundary value problems that have exact solutions. Two error criteria are used for comparison of the exact solutions and the approximated solutions. The first is the mean least square global error. The second has a local character, as it measures the absolute maximal error.

In this study, a different coupling strategy is used for the coupling of finite element (FE) and boundary element (BE) methods. In the literature, the coupling is done by transforming nodal forces into nodal tractions using distribution matrix at the interface line. In this study, however, the stress-traction equilibrium is used at the interface line for coupling of both methods. A finite and boundary element program is written using FORTRAN 95 and ordinary and developed coupling methods are adapted to this program. The results of both methods are compared with each other, ANSYS, FE, BE and analytical solution whenever possible. It has been seen that the developed method supply more efficient results against the ordinary method.
Keywords: coupling, FEM, BEM, distribution matrix, stress-traction equilibrium.

This paper presents a global algorithm for parallel computers, suitable to solve nonlinear boundary value problems depending on one parameter. Our method offers a mixture of path continuation and scanning. The former is well-known, the latter is a novel approach introduced a few years ago, capable to find all equilibria in a given domain. The hybrid method combines the speed of path continuation with the robustness and generality of scanning, offering a transition between the two methods which depends on the choice of some characteristic control parameters. We introduce the algorithms on a small example and test it on large-scale problems.

In the present study, a recursive algorithm for generating the equations of motion of serial chains that undergo spatial motion is presented. The method is based on treating each rigid body as a collection of constrained particles. Then, the force and moment equations are used to generate the rigid body equations of motion in terms of the Cartesian coordinates of the dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotation matrices. For the open loop case, the equations of motion are generated recursively along the serial chains. Closed loop systems are transformed to open loop systems by cutting suitable kinematic joints and introducing cut-joint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.
Keywords: multibody system dynamics, equations of motion, system of rigid bodies, mechanisms, machine theory.

The paper presents an implementation and the performance of several preconditioners for the discontinuous Galerkin approximation of diffusion dominated and pure diffusion problems. The preconditioners are applied for the restarted GMRES method and test problems are taken mainly from subsurface flow modeling. Discontinuous Galerkin approximation is implemented within an hp-adaptive finite element code that uses hierarchical 3D meshes. The hierarchy of meshes is utilized for multi-level (multigrid) preconditioning. The results of numerical computations show the necessity of using multi-level preconditioning and insufficiency of simple stationary preconditioners, like Jacobi or Gauss-Seidel. Successful preconditioners comprise a multi-level block ILU algorithm and a special multi-level block Gauss-Seidel method.

This paper describes the topology and shape optimization scheme of continuum structures by using genetic algorithm (GA) and boundary element method (BEM). The structure profiles are defined by using the spline function surfaces. Then, the genetic algorithm is applied for determining the structure profile satisfying the design objectives and the constraint conditions. The present scheme is applied to minimum weight design of two-dimensional elastic problems in order to confirm the validity.
Keywords: topology and shape optimization, genetic algorithm (GA), boundary element method, spline function, two-dimensional elastic problem.

The extrusion temperature, extrusion ratio and ram speeds were varied and finite element simulations of the extrusion process were conducted to determine the effect of these extrusion parameters on temperature transients, strain rate, and metal flow uniformity for the high temperature plastic deformation of an aluminum-lithium alloy billet. The finite element simulations were important in determining temperature transients, metal flow patterns, and the distributions of strain and strain rate during the extrusion process. The contours showed that the strain, strain rate and metal flow were not uniform but varied as the billet was extruded; this might be due to the non-uniform distribution of temperature during the extrusion of the billet. The microstructure of the aluminum-lithium alloy was computer simulated and correlated to the processing parameters and flow stress based on the heat treating times and temperatures. The extrusion processing variables were correlated to the Zener-Hollomon parameter temperature compensated strain rates. Extrusion temperature and extrusion ratio were found to have very little effect on the strength or ductility. The as-extruded section geometry was found to have the largest effect on the strength and ductility.

Shape and non-shape optimization is carried out for metal forming processes. This means a unified treatment of both shape parameters and other process parameters which are assumed to be design variables. An optimization algorithm makes use of the results of the analysis problem and of the sensitivity parameters obtained as a byproduct of the basic solution, in the context of the direct differentiation method. The shape sensitivity stage is formulated within the domain parametrization approach. Two alternative mappings are proposed to obtain the required derivatives with respect to the shape parameters. The behaviour of different functionals considered and the effect of the boundary conditions on the optimal design are discussed.

In the paper, the numerical analysis of thermal processes proceeding in the domain of biological tissue subjected to an external heat source is presented. Heat transfer in the skin tissue was assumed to be transient and two-dimensional. The bioheat transfer in the domain considered is described by the system of Pennes equations determining the temperature field in successive skin layers. Between the layers the ideal contact is assumed. On the selected part of skin surface the Neumann condition determining the value of external heat source is given, on the conventionally assumed internal surface of the tissue the no-flux condition is accepted. For time t=0 the initial distribution of temperature is known. The degree of the skin burn can be predicted on the basis of the so-called Henriques integrals and the main subject of the paper is the sensitivity analysis of these integrals with respect to the skin parameters. On the stage of numerical computations the boundary element method has been used. In the final part of the paper the results obtained are shown.
Keywords: bioheat transfer, burn integrals, sensitivity analysis, boundary element method.

This paper presents an iterative method for solving two-dimensional wave problems in infinite domains. The method yields a solution that satisfies Sommerfeld's radiation condition, as required for the correct solution of infinite domains excited only locally. This problem occurs in the solution of the wave equation in infinite domains when using an asymptotic local DtN (Dirichlet-to-Neumann) map in computational procedures applied to a finite domain. We are demonstrating that the amplitudes of the reflected fictive harmonics depend upon the wave number, the location of the fictive boundary, as well as on the DtN operator used in the computations. A constant value of the operator cannot sufficiently eliminate the amplitudes of all reflected waves, while the results are poor especially for higher harmonics. Thus, we are proposing an iterative method, which varies the tangential dependence of the operator in each computational step.
Keywords: wave motion, infinite domains, fictive boundary, radiation condition, DtN operators.

The focus of this paper is on the development and implementation of a genetic algorithm (GA)-based software system using message passing interface (MPI) protocol and library. A customized form of simple GA used in previous research [1-4] is parallelized. This MPI-enabled version is used to find the solution to finite element based design optimization problems. Results show that an almost linear speedup is obtained on homogenous hardware cluster and, with proper reworking of the software, on heterogeneous hardware cluster.
Keywords: parallel processing, genetic algorithm, MPI, structural optimization.

In this article a method for calculation of the finite-difference Navier-Stokes equations with a time step Δt=h/u_flow (h is the average cell's size, uflow flow velocity) at the minimal expenses of computer time is suggested. To realize the Newton-type iteration scheme and in order to avoid solving large-volume linear systems of equations for points k, which contain the variations of unknowns not only at the point k but also at points k' neighbouring with the point k, we replace the unknown relations between the variations of quantities at nearest points k and k' with artificial ones. Therefore the unknowns at the point k can be directly determined via equations at the point k and one does not need to apply complicated technique. The introduction of artificial relations between the variations of quantities at nearest nodes or cells and the use of approximate equality c'≈-c relating geometric coefficients of both displaced and usual cells make it possible to obtain formulas for correct rates of change of the residuals of the equations. Consequently, only four global iterations and 4 to 5 (in average) inner pressure correction iterations for every global iteration suffice to provide the convergence.
Keywords: heat transfer flows, approximation technique, Newton iteration method, pressure correction.

New results about preconditioning of rotated trilinear nonconforming FEM elasticity systems in the case of mesh anisotropy are presented. The solver of the arising linear system is based on the constructed efficient preconditioner of the coupled stiffness matrix. Displacement decomposition of the stiffness matrix is used as a first step of the algorithm. At the second step, modified incomplete factorization MIC(0) with perturbation is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained block-diagonal matrix. The derived condition number estimates and the presented numerical tests well illustrate the behaviour of the theoretically studied algorithms as well as their robustness for some more realistic benchmark problems.

A discrete model consisting N straight links and N springs is defined. The originally straight model is bent into a discrete torus, then it is twisted. The C₂ symmetric shapes can be determined by four parameters, and there are three constrains. The equilibrium paths are determined by the simplex method (piecewise linear approximation). Global bifurcation diagrams, spatial equilibrium shapes and parasitic solutions are analysed.

A new analytic-numerical method has been developed for solving the Laplace equation in domains with cones of arbitrary base, in particular with polyhedral corners. The solution is represented as an expansion involving singular functions (the Multipoles), which play the role of basic functions. The method enables to find these functions explicitly and to compute efficiently their singularity exponents. The method possesses exponential rate of convergence and provides precise computation of the solution, its derivatives and intensity factors at the edges and at the corner point. In addition, an asymptotic expansion of the solution near the edges of polyhedral corner has been obtained.

In this paper Trefftz polynomials are used for the BEM (Boundary Element Method) based on the reciprocity relations. BEM provides a powerful tool for the calculation of dynamic structural response in the frequency and time domains. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE), which are discretized only on the boundary [1]. Trefftz polynomials or other non-singular (e.g. harmonic), Trefftz functions [2] (i.e. functions satisfying all governing differential equations but not the boundary conditions) used in the Betti's reciprocity relations lead to corresponding BIE that do not contain any (weak, strong, hyper) singularities. Fundamental solutions are not needed and evaluation of the field variables inside the domain is simpler.

The paper presents the possibility of the limit stress state approximation of the reinforced concrete wall structures by discontinuous stress fields with variable configuration. Heuristic optimization technique, simulated annealing, is applied to determine optimal configuration for approximation of load carrying capacity based on lower bound theorem of theory of plasticity. Model was tested by comparing with the results of several experimental tested beams, as well as with other numerical models.
Keywords: concrete stuctures, plastic design, carrying capacity, numerical methods, heuristic optimization, simulated annealing.

In this paper, meshless element free Galerkin method has been used to obtain the numerical solution of transient and steady state heat conduction problems in two-dimensional domains. The unknown function of temperature T(x) has been approximated by moving least square approximant} T^h(x). These approximants are constructed by using a weight function, a polynomial basis and a set of non-constant coefficients. Variational method is used to obtain the discrete equations. Essential boundary conditions are imposed by Lagrange multiplier technique. Two new weight functions namely hyperbolic and rational have been proposed. The results have been obtained for a two-dimensional model problem using different EFG weight functions and are compared with those obtained by finite element and analytical methods.
Keywords: meshless method, element free Galerkin method, two-dimensional transient and steady heat conduction.

A numerical method is presented for analyzing the mixed mode interface crack between two dissimilar isotropic materials. A simple and efficient solution procedure is developed based on the finite element method and the compliance approach in conjunction with the fundamental relations in fracture mechanics. The procedure makes it possible to separate the Mode I and Mode II stress intensity factors K_I and K_II respectively for an interfacial crack in bi-material media under different loading conditions. The strain energy release rate is first computed, then using the compliance method and the known auxiliary solutions, the values for K_I and K_II are evaluated. The procedure is investigated for different crack extensions. The formulations used for computing the strain energy release rate and the stress intensity factors are presented. The method converges to accurate solutions for small crack extensions. A numerical example is presented to demonstrate the accuracy of the proposed model.
Keywords: bi-material interface crack, strain energy release rate, stress intensity factors, finite element analysis, compliance approach.

Optimization theory has advanced considerably during the last three decades, as illustrated by a vast number of published books, surveys, and papers concerning this subject. However, for optimization of complex systems that may not be modeled exactly by Ludwig von Bertalanffy's general system theory, we may need a new philosophy based on rather non-conventional logics. It is represented bellow.
Keywords: complex systems, multi-objective optimization, fuzzy logic, modal logic, multi-valued logic.

In the paper three computational models for crack growth analysis in quasi-brittle materials in plane stress state are presented. These models have been worked out on the base of different methods of coupling the finite element method and the element free Galerkin method. Effectiveness of the methods of analysis are improved by the algorithm of dynamic domain decomposition into Ω, Ω_ρ, Ω_hρ parts. The usefulness of the methods in crack growth analysis has been confirmed in examples.

In the cellular automata simulation, the object under consideration is divided into small cells and the simulation is performed according to the local rule which is defined as the local relationship among cells. In this paper, the concept of cellular automata is applied to the design scheme of truss structures. First, truss elements are considered as the cells of the cellular automata and the local rule is derived from the optimization problem. The objective functions are defined to minimize the total weight of the structure and to obtain even stress distribution in the whole structure. The constraint conditions are introduced in order to define the local rule. The present method is applied to the design of the plane and the three-dimensional truss structures such as Schwedler and Lamella Domes. The convergence histories of the total weight and the mean and the maximum stresses are shown in order to discuss the property of the present method.
Keywords: structural design, cellular automata (CA), local rule, truss structure.

Thermal ignition for a reactive viscous flow between two symmetrically heated walls is investigated. The second order nonlinear boundary value problem governing the problem is obtained and solved analytically using a special type of Hermite-Padé approximation technique. We obtained very accurately the critical conditions for thermal ignition together with the two solution branches. It has been observed that an increase in viscous heating due to viscous dissipation can cause a rapid decrease in the magnitude of thermal ignition critical conditions.

In this paper possibilities of optimization of two torsional mechanical systems with one and two differential pneumatic clutches with self-regulation are shown. The systems are excited by harmonic components of the periodic moment caused by an engine. The advantage of the differential pneumatic clutch lies in the fact that its torsional stiffness can be controlled by the pressure of a gas medium in it. Optimization of such systems enables not only minimization of vibrations and dynamic effects but also avoiding resonance regimes in relatively wide frequency intervals (speeds of rotation of the system). As objective function the mean total amplitude of relative vibration is used. The constraints on the amplitudes of dynamic moments and also anti-resonance constraints are considered.
Keywords: mechanical system, torsional vibration, optimization, pneumatic clutch.

In Direct or Semi-Direct Numerical Simulations of turbulent reacting flows the exploitation of complex, realistic and detailed chemistry and transport models often results in prohibitive memory and CPU requirements when flows of practical relevance are treated. The integrated Combustion Chemistry approach has recently been put forward as a methodology suitable for the integration of complex chemical kinetic and chemistry effects into large scale computational procedures for the calculation of complex and practical reacting flow configurations. Through this procedure a reduced chemical kinetic scheme involving only a limited number of species and reactions is derived from a detailed chemical mechanism so as to include major species and pollutants of interest in the main flow calculation. The chemical parameters employed in this integrated scheme i.e. rates, constants, exponents are then calibrated on the basis of a number of constraints and by comparing computations over a range of carefully selected laminar flames so as to match a number of prespecified flame properties such as adiabatic temperatures, selected target species profiles, flame speeds, extinction characteristics. The present work describes such an effort for a commonly used fuel of both fundamental and practical importance, methane. The proposed nine-step scheme involves nine major stable species and in addition to the basic methane oxidation model also includes NO_X production and soot formation submodels.
Keywords: integrated combustion chemistry, reduced chemistry mechanisms, laminar flames, chemical reaction schemes.

The paper presents an analytical model to investigate the nonlinear dynamic behavior of rotor bearing system due to cage run-out. Due to run-out of the cage, the rolling elements no longer stay equally spaced. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force and cage run-out, resulting transition from no contact-to-contact state between rolling elements and races. The contact between the rolling elements and races is treated as nonlinear springs. The nonlinear stiffness is obtained by application of Hertzian contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton Raphson method is used to solve the nonlinear differential equations iteratively. The results are presented in the form of Fast Fourier Transformations (FFT) and contact force-time responses. It is implied from the obtained FFT that due to the cage run-out, the ball passage frequency is modulated with the cage frequency.
Keywords: nonlinear dynamic response, chaotic vibration, Newmark-β, ball passage frequency.

The mechanical modeling of foams is discussed on a microscopic, mesoscopic and macroscopic scale. A homogenization procedure is proposed to relate the models and to give detailed insight into the deformation behavior of foams. The mesoscopic model of open-cell foams is based on beam elements and evaluated for regular hexagonal structures considering small deformations. This approach gives rise to a Cosserat continuum on the macroscopic scale. Especially the misfit in the parameters governing the standard macroscopic model can be explained by the proposed homogenization procedure. This misfit results from the neglect of the rotations of the cell walls, see Diebels and Steeb [6, 7].

The paper presents application of the Refined Least Squares method to the initial value problems that are instable in the Lyapunov sense. There is shown that the method is not sensitive to this kind of instability. The method is especially useful in search of particular integral of the considered problem. The method has an additional tool to evaluate quality of approximation. The approach is based on minimization of the functional, which square root can is generalized norm L₂ and can be used to estimate global error of approximation. The expected value of the functional is equal to zero. The approximation is satisfactory if both results converge and functional reaches value close to zero. The consideration is illustrated with examples. There are shown initial-value problems which have physical sense and are applicable in mechanics. Whereas numerical approach may fail for these tasks, Refined Least Squares approach returns reliable approximation. The last example presents application of the special feature of the method, which allows neglecting influence of general integral on the solution. The method may be used in sensitivity analysis, search of the problem parameters, verification of numerical methods and an antonymous method in computational physics and mechanics.

This paper is focused particularly on application of fuzzy logic approach for solving fault isolation problem of some class of industrial actuators described in the benchmark actuator definition [1]. Particular attention was paid for searching of applicable and acceptable solutions in terms of industrial implementations. The rational solution of the problem of setting fuzzy partitions for residual evaluation was proposed. The industrial benchmark study was applied for evaluating of proposed approach by means of the real process data acquired in normal and abnormal process states. The chosen examples of achieved results concerning fault isolability issues are presented.
Keywords: fault detection and isolation, industrial actuators, benchmark study, modelling, diagnosis.

Bayesian belief networks represent and process probabilistic knowledge. This representation rigorously describes the knowledge of some domains and it is a human easy-use qualitative structure that facilitates communication between a user and a system incorporating the probabilistic model. Learning Bayesian network from data may be grouped into two modelling situations: qualitative learning and quantitative learning. The first one consists in establishing the structure of the network, whereas the second concerns determining parameters of the network (conditional probabilities). Both modelling methods were applied on exemplary data to show the possibilities and benefits of this methods. The results and conclusions are presented. It was necessary to preprocess the date first. The used method, described in detail in the paper, consists in discretization into linguistic states on the basis of evaluated signal derivative. Some remarks about adjusting the network, as a part of model identification, are also presented.
Keywords: Bayesian network, learning, diagnostic models.

The aim to the paper is to optimize 2-dimensional elastic structures subjected to cyclic load. The loading can result in crack forming, so the aim of the optimization is to reduce the possibility of crack growth. The number of loading cycles necessary to crack growth is maximized. To solve the optimization task the evolutionary algorithm is used. The boundary element method is applied to solve the crack problem. In order to reduce the number of design variables the parametrical NURSB curves are used to model the geometry of parts of the structural element boundary.
Keywords: boundary element method, optimization, evolutionary algorithm, crack, parametric curves.

System identification of a parametric "black box" model for the purpose of electrical motor diagnostics is discussed in this paper. The measured acoustic pressure signal is used for identification of a model which structure is considered as a transfer function. Poles of denominator are calculated and collected on a complex plane. Fuzzy, two-stage algorithm is used for clustering and classification of poles which are assumed as symptoms of the motor conditions. The statistical uncertainty and fuzzy imprecision of the poles placement is taken into account by the clasterization procedure. The aim of this procedure is a separation of classes regarding a priori information of their number. Classification was performed with the use of the faulty electrical motors.
Keywords: fuzzy classification algorithm, acoustic process control, parametric model.

This paper describes briefly the development and verification of a probabilistic system for the rapid diagnosis of plant status and radioactive releases during postulated severe accidents in a Boiling Water Reactor nuclear power plant. The probabilistic approach uses Bayesian belief network methodology, and was developed in the STERPS project in the European Union 5-th Euroatom Framework program.
Keywords: nuclear reactors, source term, Bayesian belief network, severe accidents, probabilistic safety assessment.

The paper describes shape optimisation of a turbine blade shank. The turbine blade shank zone with a compound fillet is a critical location where a high risk of failure exists. The APDL language operating in Ansys environment is used to write a parametric turbine blade shank FEM models generator, which is a basic part of evolutionary optimisation routine. The goal of the optimisation is the 1st principal stress reduction with maximum allowable mass constraint imposed. Parameterisation routine and optimisation results are presented and discussed.
Keywords: AI, evolutionary optimisation, APDL, turbine blade, shape optimisation, Finite Element Method (FEM).

During the manufacturing process of multilayered fibre-reinforced composites with variable fibre orientations, residual stresses build up due to the di­rectional expansion of the single unidirectionally reinforced layers. Dependent on the laminate lay-up, these inhomogeneous residual stresses, which are caused by thermal effects, moisture absorption and chemical shrinkage, can lead to large multistable out-of-plane deformations. Instead of avoiding these laminate's curvatures, they can be advantageously used for technical applications following the near-net-shape technology. However, due to the effect that the laminate curvature depends on huge amount of different parameters such as anisotropic, hygroscopic and thermomechanical material properties, fibre orientations and ply thickness of each single layer as well as technological processing parameters, a search in a multi-dimensional search area is necessary. In order to solve such a task, Genetic Algorithms in combination with a fitness function based on a nonlinear semi-analytical calculation model for the laminate shape prediction have been applied and described in the paper. Using this approach, one can purposefully adapt the laminate lay-up dependent on the loading and process parameters.

The paper is devoted to computational grids applications in evolutionary optimization of structures. The two grid middleware are used, UNICORE and LCG2. The distributed evolutionary algorithm is used for optimizataion. The fitness function is computed using finite element method. Numerical examples are presented.

In the paper, Artificial Neural Network with hidden layers is used to approximate the functional dependence of the effective properties of a composite on the physical properties of its micro-components. Two numerical examples have been examined in order to demostrate this approach. The first one introduces geometrical parameters of the cell of periodicity into ANN training process. It proves the ability of ANN to catch the behaviour of the composite material based on the properties of the components and their spatial arrangement at micro level. The second example deals with a special case of the self-repetitive composite structure. It has been shown that, in the limit, the geometry and behaviour of such a composite is consistent with the fractal form known in the literature as the Sierpinski's carpet.
Keywords: neural network, homogenisation, hierarchical composite.

Fault diagnosis becomes more and more difficult and sophisticated task. This is so mainly due to growing complexity - contemporary technological systems are assembled from numerous components which cooperate and recursively include other components. The main goal of this paper consists in presentation of an approach which is able to reduce time of diagnosis and quantity of produced diagnoses by using hierarchical, logic-based approach. The reduction is achieved here due to two main factors. The first one is that a hierarchical model of systems is used. Such approach limits search space, because the system is considered at various levels of details and some diagnoses which are possible potential ones at more abstract levels can be verified to be impossible at more detailed levels. The second factor is that levels can be described with use of different kinds of a logic-based knowledge representation, what lets fit some best representation to a particular level.

Automatic knowledge base generation using techniques such as genetic algorithms tend to be highly dependent on the quality and size of the learning data. First of all, large data sets can lead to unnecessary time loss, when smaller data sets could describe the problem as well. Second of all, the presence of noise and outliers can cause the learning algorithm to degenerate. Clustering techniques allow compressing and filtering the data, thus making the generation of fuzzy knowledge bases faster and more accurate. Different clustering algorithms are compared and the validation of the results through a theoretical 3D surface, shows that when compressing the data to 5% of its original size, clustering algorithms accelerate the learning process by up to 94%. Moreover, when the learning data contains noise and/or a large amount of outliers, clustering algorithms can make the results more stable and improve the fitness of the obtained FKBs.

This paper focuses on features extraction based on cyclostationarity for diagnosis purpose. The objective is to derive new indicators for the diagnosis of rotating machinery. These indicators are based on cyclic higher order statistics and generalize some existing ones for the second order statistics. A comprehensive methodology is proposed for obtaining a diagnosis objective; a crucial example is presented, relating to vibration signals of a gearbox. Results demonstrate the effectiveness of these features to detect spalling in gearbox.

Standard for the Exchange of Product Model Data (STEP-ISO 10303) contains product information models covering most of the aspects of product lifecycle management (PLM). In designing ontology of knowledge base concerning any aspects of PLM it is necessary to use such product information models. Unfortunately, a model based on STEP is based on EXPRESS language which is not compatible with common technologies for ontology creation. The paper presents contemporary methods of ontology description and it describes the importance as well as current level of advancement in development of STEP standard. Attention has been paid to drawbacks in possibilities of already existing methods, included in STEP for ontology creation, which could form a foundation for knowledge base designing methodology founded on the defined ontologies. A method of ontology creation has been proposed, including STEP model and examples of this method application in knowledge base implementation have been given.
Keywords: knowledge base, ontology, object-oriented modeling, STEP, UML, XML.

The paper deals with the problem of new projects acceptance into the multi project environment, where constraints are limiting the number of projects that a company is able to carry out concurrently. The objective of this paper is to answer the question: Is it possible to execute new project on time in the multi-project environment? For answering the question combination of Theory of Constraints and conditions guaranteeing project due dates with constraint-based scheduling are proposed. As a result the decision of the project implementation and the schedule of project activities, which the company is able to implement concurrently are obtained.
Keywords: Theory of Constraints, multi-project scheduling, constraint programming.

The utility of Bayesian neural networks to predict concrete fatigue durability as a function of concrete mechanical parameters of a specimen and characteristics of the loading cycle is investigated. Bayesian approach to learning neural networks allows automatic control of the complexity of the non-linear model, calculation of error bars and automatic determination of the relevance of various input variables. Comparative results on experimental data set show that Bayesian neural network works well.
Keywords: Bayesian neural networks, concrete fatigue durability, prediction.

At present, inference about technical state of machinery or industrial processes on the basis of analysis of residual signals is one of the most developed fields of technical diagnostics. Results of analysis are usually huge sets of signal features, whose changes carry information about technical state of an object. Correct interpretation of such results is the most important problem of technical diagnostics. It is particularly important in the case of complex machinery and processes, whose operation parameters vary in time and additionally the environment of investigated objects, can not be assumed to be unchangeable. The approach described in the paper was based on the assumption that signal features can be presented in the form of a dynamic scene. Changes in the scene are determined by means of simple methods of image processing. The background of diagnostic inference is context-based reasoning (CxBR).

The paper deals with an application of the theory of optimum experimental design to the problem of selecting the data set for developing neural models. Another objective is to show how to design a robust fault detection scheme with neural networks and how to increase its fault sensitivity by decreasing model uncertainty. It is also shown that the optimum design is independent of the parameters that enter linearly into the neural network. The final part of this paper shows a comprehensive simulation study regarding modelling and fault detection with the proposed approach. In particular, the DAMADICS benchmark problem is utilized to verify the performance and reliability of the proposed technique.

An analysis of the dynamic behaviour of a reinforced concrete beam and a deep beam taking into account the physical non-linearities of structural materials is presented in this paper. The modified model of the elastic/visco-perfectly plastic material with regard to delayed yield effect was applied to the reinforcing steel. The non-standard model of dynamic deformation was applied to the concrete. The model describes the elastic properties until attaining the dynamic strength of concrete, perfectly plastic properties in the limited range of deformation, material softening, and smeared cracking or crushing which are concentrated in the regions of the tensile or compressive residual stress states. Interaction between the reinforcing steel and the concrete is conditioned by the assumption of perfect consistency of displacements of both materials. The ratio of this interaction depends on the phase of deformation of the concrete. The method of analysis of the structural system was developed using the finite element method. The results of numerical solutions are presented. The effectiveness of the method of analysis and computational algorithms for problems of numerical simulation of the reinforced concrete beam and the deep beam dynamic behaviour is indicated in this paper.
Keywords: R/C deep beam, physical non-linearity, dynamics, numerical analysis.

The paper presents a model which allows to estimate the elastic properties of thin-walled structures manufactured by means of injection molding. The starting point is the numerical prediction of the microstructure of a short fiber reinforced composite induced during the filling stage of the manufacturing process. For this purpose the commercial program Moldflow Plastic Insight$^\circledR$ (MPI) is used. The result of the filling simulation characterizing the fiber microstructure is a second rank orientation tensor. The elastic material properties after the processing are locally dependent on the orientational distribution of the fibers. The constitutive model is formulated by means of the orientational averaging for the given orientation tensor. The tensor of elastic material properties is computed and translated into the format suitable for the stress-strain analysis based on the ANSYS® finite element code. The influence of technological manufacture parameters on the microstructure and the elastic properties is discussed with the help of two examples a center-gated disk and a shell of revolution.

The paper develops a theory of physically non-linear vibrations of a rail-vehicle moving on a rectilinear and non-deformable track. The vibrations are excited by snaking and lateral impacts of the wheel sets. De Pater's microspin model and a new simplified model of lateral impacts are applied. An algorithm for determining quasi-steady-state vibrations of the vehicle has been formulated and programmed in Pascal. The simulations have been performed for a Shinkansen rail-vehicle moving at service velocities 160--300~km/h.

The paper demonstrates a specific power series expansion technique used to obtain the approximate solution of the two-dimensional wave equation in some unusual cases. The solution for inhomogeneous wave equation, for more complicated shape geometry of the body, discrete boundary conditions and a membrane whose thickness is not constant is shown. As solving functions (Trefftz functions), so-called wave polynomials are used. Recurrent formulas for the particular solution are obtained. Some examples are included.
Keywords: wave equation, wave polynomials, Trefftz method, membrane vibrations.

A neural procedure was formulated in [4] as BPNN (Back-Propagation Neural Networks) for the simulation of generalized RMA (Return Mapping Algorithm). This procedure was evaluated to be too large to make a corresponding hybrid FEM/BPNN numerically efficient. That is why two new procedures NP1 and NP2 were formulated. A description of their efficiency is presented in the paper, related to the computation number of computer operations and CPU time, carried out by FEM program FEAP and two hybrid programs FEAP/NP1 and FEAP/NP2.

In the paper an algorithm for design reliability improvement is proposed. Its key part consists in the computation of the correlations between constraint functions and design variables which are subsequently used to find the new design iteration. It is shown that the optimal Latin hypercube (OLH) sampling provides an extremely efficient technique for assessing the values of correlation coefficients. Since finding the large OLH designs is not a trivial task, a study on the OLH generation algorithms was performed. Two algorithms were found to be particularly effective, namely, the columnwise-pairwise algorithm and the genetic algorithm. The presented strategy proves to be especially useful when alternative gradient-based methods cannot be used, which is often the case for computationally expensive problems involving noisy and highly nonlinear responses. The method is best suited for problems where the probability of failure for the initial design is large and the main interest is to find a more reliable design rather than the optimal one in the sense of reliability-based optimization. The method is illustrated with two numerical examples. One model example and one concerning the problem of thin-walled beam crash.

A Core Disruptive Accident in a Liquid Metal Fast Breeder Reactor (LMFBR) results from the interaction between molten fuel and liquid sodium, which creates a high-pressure bubble of gas in the core. The violent expansion of this bubble loads and deforms the vessel and the internal structures. The MARS experimental test simulates a hypothetical Core Disruptive Accident in a small-scale mock-up containing all the significant internal components of a LMFBR. This paper presents a numerical simulation of the test with the EUROPLEXUS code.

The detection of defects as well as their location, orientation and size is performed using measurements of surface temperature either at some selected points or on selected surface areas or lines. The response temperature of a structure is caused by statically, quasi-statically or dynamically applied thermal load on some structural boundary parts or within its domain. On the basis of results of measurements, an inverse heat transfer problem is formulated for a model structure and next solved. The inverse solution is constructed by minimizing the properly defined distance norm of measured and model temperatures. The model temperature distribution is calculated using the finite element model of a structure, while in minimizing the distance norm functional the gradient-oriented methods are used. The proper sensitivities of introduced identification functional are also derived. Some simple examples illustrate the applicability of the proposed approach.
Keywords: identification, sensitivity, thermographic methods, path-independent integrals.

The paper demonstrates the potential of Discrete Wavelet Transform (DWT) in damage detection. Efficiency of the method is demonstrated by the way of examples. In this study the numerically simulated static and dynamic experiments were used. One dimensional DWT was used to signal processing. Measurement errors were accounted for by introduction of white noise.
Keywords: damage detection, wavelet transformation.

A non-destructive method of damage detection based on heat transfer experiments and 2-D Discrete Wavelet Transform (DWT) is discussed. In this paper real experiments with the use of thermography measurement techniques are substituted by numerically simulated experiments. The plates were modeled as 2-D and 3-D structures. Two kinds of structures are considered: homogeneous in undamaged state and non-homogenous. Measurement errors are accounted for by introduction of a white noise. The efficiency of the method is demonstrated by the way of numerous examples.
Keywords: damage detection, wavelet transformation, infrared thermography.

The paper concerns layout optimization of elastic three dimensional bodies composed of two isotropic materials of given amount. Optimal distribution of the materials corresponds to minimization of the total compliance or the work of the given design-independent loading. The problem is discussed in its relaxed form admitting composite domains, according to the known theoretical results on making the minimum compliance problems well posed. The approach is based upon explicit formulae for the components of Hooke's tensor of the third rank stiff two material composites. An appropriate derivation of these formulae is provided. The numerical algorithm is based on COC concept, the equilibrium problems being solved by the ABAQUS system. Some of the optimal layouts presented compare favourably with the known benchmark solutions. The paper shows how to use commercial FEM codes to find optimal composite designs within linear elasticity theory.

In the paper the problems connected with numerical modelling of bio-heat transfer processes are discussed. The mathematical model of phenomena discussed bases on the Pennes equation, at the same time the steady and transient tasks are considered. The basic equation is supplemented by the adequate geometrical, physical, boundary and (in the case of transient heat transfer) initial conditions. In the first part of the paper the examples of direct solutions are discussed. Next the possibilities of sensitivity analysis applications in the domain of bio-heat transfer are presented. In the final part the selected solutions of inverse problems are shown. On the stage of numerical simulations both in the case of direct and inverse problems, as a rule, the different variants of the boundary element method have been used.

This paper presents certain results of the analysis of elastic wave propagation in one-dimensional (1-D) and two-dimensional (2-D) elements of structures with damage. The problem of the elastic wave propagation has been solved by the use of the Spectral Element Method (SEM). In this approach elements of structures are modelled by a number of spectral finite elements with nodes defined at appropriate Gauss-Lobatto-Legendre points. As approximation polynomials high order orthogonal Lagrange polynomials are used. In order to calculate the elements characteristic stiffness and mass matrices the Gauss-Lobatto quadrature has been applied. In the current analysis damage in the form of crack has been considered. It has been assumed that the damage can be of an arbitrary length, depth, and location and can be simulated as a line spring of varying stiffness. Numerical calculations illustrating the phenomena of the elastic wave propagation in isotropic media have been carried out for the case of an aluminium rod and beam as well as a flat aluminium panel and plate.

The main goal of the paper is to show great potential of Artificial Neural Networks (ANNs) as a new tool in the identification analysis of various problems in mechanics of structures and materials. The basics of ANNs are briefly written focusing on the Back Propagation Neural Networks (BPNNs) and their features and possibilities in the analysis of inverse problems. Two groups of problems are analyzed: I) BPNNs are used in five problems as independent tools for the parametric identification and implicit modelling of physical relations, II) BPNNs are parts or procedures in three hybrid FEM/ANN systems or programs. Using measured eigenfrequencies the following problems are discussed: 1) identification of damage parameters of a steel beam, 2) attachment of an additional mass to increase the accuracy of prediction of damage parameters in a beam, 3) identification of location an additional mass attached to a steel plate. Implicit simulation of physical relations is discussed on two problems: 1) concrete fatigue durability of concrete as a function of concrete strength and characteristics of fatigue cycles (besides BPNN also the Fuzzy Weight NN was applied), 2) soil-structure interaction of displacement response spectra of a real building subjected to paraseismic excitations (besides BPNN the application of Kalman filtering is discussed for the NN learning). The following problems of Group II are investigated: 1) using BPNN in the hybrid Monte Carlo method for the reliability analysis of a steel girder, 2) application of BPNN to the calibration of control parameters in the updating of a FE program for dynamic analysis of a plane frame, 3) on-line methods for the NN constitutive model formulation basing on measurements of structural displacements.

This paper presents a review of intelligent computing techniques in solving inverse mechanics problems. These techniques are based on Evolutionary Algorithms (EAs) and the coupling of Evolutionary Algorithms (EAs) and Artificial Neural Networks (ANNs) in the form of Computational Intelligence Systems (CISs). The main attention was focused on the identification of the defects such as voids or cracks in structures on the basis of the knowledge about displacements, temperature and eigenfrequencies. The identification of the unknown number, position, size and kind of defects in the elastic structures is shown. The paper contains a lot of tests and numerical examples.
Keywords: intelligent computing (IC), evolutionary algorithms (EAs), artificial neural networks (ANNs), fuzzy inference system (FIS), computational intelligent system (CIS), finite element method (FEM), boundary element method (BEM).

In the paper a general survey of existing finite element (FE) models is presented using a conceptual description in diagram form, which was initiated in paper [1]. The analysis is focused on the description of FE models, which is uniform in its concept but specific for each FE type. All FE models are associated with certain variational principles (and their stationarity conditions) in their original or modified versions. The diagrams are used to visualize the equations which are satisfied inside an individual FE and on interelement boundaries. The use of conceptual diagrams is very convenient in the presentation of finite element method (FEM), it simplifies the understanding and teaching of this method.

The paper presents the computational approach to the process of creation of complex three-dimensional finite elements models. The data are automatically received by the measuring unit and sent directly to the computer. The process of numerical treatment of measuring points' coordinates is shown. As an example of above mentioned method, the construction of human femoral head model is demonstrated. Finally the geometrical model of the object, which can be used by PATRAN system is obtain. Paper presents results of numerical calculations and compares it with a photoelastic experiment.

A critical review of earlier works on optimality of finite element grids has been made. A material force method of r-adaption to obtain optimal initial grids has been described. The study focuses on determining the configurational driving force and its convergence rate across an interior patch node for one-dimensional linear, quadratic element and two-dimensional bilinear quadrilateral elements. Numerical implementation is made on one and two-dimensional problems. Various aspects considered to define optimality in earlier works along with their predefined guidelines have also been worked out with some modifications for the material force method and it is shown that this method of adaption provides good optimal grids. The method is advantageous owing to its physical basis and mathematical vigor than earlier works. Based on the numerical studies conducted a combined adaptive strategy incorporating node disposition and mesh enrichment has been evolved to obtain an optimal mesh for a specified accuracy.

In the case of a Hypothetical Core Disruptive Accident in a Liquid Metal Fast Breeder Reactor, the core of the nuclear reactor is assumed to have partially melted, and the interaction between molten fuel and liquid sodium creates a high-pressure gas bubble in the core. The violent expansion of this bubble loads and deforms the reactor vessel and the internal structures, thus endangering the safety of the nuclear plant. The MARA 10 experimental test simulates a HCDA in a 1/30-scale mock-up schematising simply a reactor block. The vessel is filled with water, topped with an air blanket. The test is fired using an explosive charge. This paper presents the numerical models implemented in the EUROPLEXUS code, and a numerical simulation of the test. The evolution of the fluid flows and the deformations of structures are analysed in detail to understand the progress of the explosive phenomenon.
Keywords: accident, simulation, dynamic, mechanics, nuclear, reactor, explosion.

The goal of this contribution is to provide, based on the asymptotic homogenization method, helpful exact formulae to compute the overall stiffnesses and engineering moduli of a transversely isotropic two-phase fibre reinforced composite with isotropic constituents. Comparison of the exact solution with known bounds is shown. In certain cases a bound is very close to the exact solution over a large interval. The bound then could be used as a good approximation to the exact solution. The exact formulae explicitly display Avellaneda and Swart's microestructural parameters, which have a physical meaning, and provide formulae for them. Hill's universal relations follow from the formulae. Limiting cases of rigid and empty fibers are included. An application of these results to improve bounds for the effective energy density of nonlinear dielectric fibrous composites is shown. Another application is related to bone poroelasticity.
Keywords: fibers, mechanical properties, microstructure, anisotropy, elastic properties.

Gives a bibliographical review of the finite element analyses of rotating systems from the theoretical as well as practical points of view. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1998-2004. It is a continuation of the author's earlier bibliography with the same title published in Shock Vibration 6 (1999) 209-222 where papers published between 1994-1998 are listed. At the end of this paper 479 references are listed.
Keywords: finite elements, rotor dynamics, shafts, blades, bibliography.

The paper is devoted to the application of the evolutionary algorithms, gradient methods and artificial neural networks to identification problems in mechanical structures. The special intelligent computing technique (ICT) of global optimization is proposed. The ICT is based on the two-stage strategy. In the first stage the evolutionary algorithm is used as the global optimization method. In the second stage the special local method which combines the gradient method and the artificial neural network is applied. The presented technique has many advantages: (i) it can be applied to problems in which the sensitivity is very hard to compute, (ii) it allows shortening the computing time. The key problem of the presented approach is the application of the artificial neural network to compute the sensitivity analysis. Several numerical tests and examples are presented.

A meshless method for the solution of linear and non-linear Poisson-type problems involving high gradients is presented. The proposed method is based on collocation with 3rd order polynomial radial basis function coupled with the fundamental solution. The linear problem is solved by satisfying the boundary conditions and the governing differential equations over selected points over the boundary and inside the domain, respectively. In the case of the non-linear case, the resulted equations are highly non-linear and therefore, they are solved using an incremental-iterative procedure. The accuracy and efficiency of the method is verified through several numerical examples.
Keywords: meshless method, fundamental solution, RBF, high gradients.

The boundary element formulation for dynamic analysis of inelastic two-dimensional structures subjected to stationary or transient inertial loads is presented. The problem is solved by using simultaneously the displacement and stress integral equations. The numerical solution requires discretization of the boundary displacements and tractions, and stresses in the interior of the body. The boundary is divided into quadratic elements and the domain into constant or quadratic quadrilateral cells. The unknown stresses in the coupled system of equations are computed using an iterative procedure. The mass matrix of the structure is formulated by using the dual reciprocity method. The matrix equation of motion is solved step-by-step by using the Houbolt direct integration method. Several numerical examples show the influence of the discretization on the accuracy and new applications of the method. The solutions are compared to the analytical results or those computed by the finite element method.
Keywords: boundary element method (BEM), dual reciprocity method (DRM), inelasticity, elastoplasticity, dynamic analysis.

The problem of determination of Poiseuille number for a steady gravitational flow of liquid in an inclined open trapezoidal groove is addressed. The solution comprises of two parts. First, for a given groove's dimension, liquid-solid contact angle, and the Bond number, the shape of the free surface is determined starting from the Young-Laplace equation. The shooting method is used for solution of a two-point boundary value problem. Then, having determined the shape of the free surface and slope the groove, the fully developed laminar flow is determined. The boundary value problem is solved using the method of fundamental solutions. Given the distribution of liquid velocity, the Poiseuille number, as a function of the other parameters of the model is analysed.
Keywords: flow in trapezoidal groove, liquid-vapor interface, method of fundamental solutions, Bond number, Mathematica.

The large deflection of thin plates by means of Berger equation is considered. An iterative solution of Berger equation by the method of fundamental solutions is proposed. In each iterative step the Berger equation can be considered as an inhomogeneous partial differential equation of the fourth order. The inhomogeneous term is interpolated by radial basis functions using thin plate splines. For the optimal choice of parameters of the fundamental solutions method an evolutionary algorithm is used. Numerical results for square plate with simply supported edges are presented to compare the obtained results with previous solutions.

The paper contains three different multi-domain formulations using Trefftz (T-) displacement approximation/interpolation, namely the hybrid-displacement FEM, reciprocity based FEM (multi-domain BEM) and the Boundary Meshless Method (BMM) for a single and multi-domain (MD) formulation. All three methods can lead to compatible formulation with the isoparametric FEM, when the displacements along the common boundaries are defined by same interpolation function. All three T-formulations enable to define more complicated elements/subdomains (the T-element can be also a multiply connected region) with integration along the element boundaries, only.

This paper reviews a wave based prediction technique for steady-state acoustic analysis, which is being developed at the K.U. Leuven Noise and Vibration Research group. The method is a deterministic technique based on an indirect Trefftz approach. Due to its enhanced convergence rate and computational efficiency as compared to conventional element based methods, the practical frequency limitation of the technique can be shifted towards the mid-frequency range. For systems of high geometrical complexity, a hybrid coupling between wave based models and conventional finite element (FE) models is proposed in order to combine the computational efficiency of the wave based method with the high flexibility of FE with respect to geometrical complexity of the considered problem domain. The potential to comply with the mid-frequency modelling challenge through the use of the wave based technique or its hybrid variant, is illustrated for some three-dimensional acoustic validation cases.

Simulation of the long term behavior of a metacarpal bone with a prosthesis is presented with the help of an evolutive 3D finite element model taking into account "the stress shielding" phenomena. The same model allows to improve the shape of the prosthesis.
Keywords: prosthesis, bone remodeling, optimisation, iterative method.

Hybrid-Trefftz (HT) finite element (FE) analysis of two-dimensional elastic contact problems is addressed with the aid of interface elements and an interfacial constitutive relation. This paper presents the formulation of a four-noded HT finite element for discretizing the contacting bodies and a four-noded interface element that could be embedded in the prospective contact zone for simulating the interaction behaviour. Due to the superior performance, the Simpson-type Newton-Cotes integration scheme is utilized to compute interface element formulation numerically. In order to evaluate the applicability of the present approach two benchmark examples are investigated in detail. Comparisons have been made between the results by the present approach and analytical as well as traditional FE solutions using ABAQUS software.

Any direct boundary-value problem is defined in a certain area $\Omega$ by a system of differential equations and respective set of boundary conditions. In structural inverse problems the above conditions can be partly unknown. Instead, we can measure certain quantities inside the investigated structure and then approximately define the whole boundary-value problem. Usually, the solutions of inverse problems are connected with the minimization of a certain functionals, which results in optimization procedures. The applications of the trial functions identically fulfilling governing partial differential equations of a discussed problem (the Trefftz approach) can considerably improve these procedures. The original idea of Erich Trefftz was based on modelling objects of simple geometry. In the case of more complex structures the division of the whole object into sub-regions (Trefftz elements) is necessary. This kind of formulation is presented in this paper and is illustrated by numerical examples. The properties of the Trefftz finite elements allow the formulation of effective algorithms, which considerably shorten the time of computer calculations in comparison to standard finite element solutions.

This state-of-the-art paper reports the last ten year results, obtained by an informal research group completed of participants of some Polish universities at the Institute of Computer Methods in Civil Engineering (now Institute of Computational Civil Engineering) of the Cracow University of Technology, and supervised by the author of the paper. After a short introduction and brief discussion of ANNs basic ideas, the activities in five areas are described: i) ANNs as a new independent computational tool for the analysis of C&SE problems, ii) neural networks in FEM/ANN hybrid systems developed for the C&SE problems analysis, iii) various problems analyzed by ANNs, iv) modifications of BPNNs (Back-Propagation Neural Networks) and new learning methods, as well as other ANNs than those applied in problems mentioned above, v) promotion of ANNs. The representative six selected study cases are discussed: 1) concrete fatigue failure, 2) buckling of cylindrical shells with geometrical imperfections, 3) acceleration response spectra, 4) reliability of a plane frame, 5) hybrid updating of a thin-walled beam FE model, 6) hybrid identification of equivalent material in a perforated strip. Some general conclusions on prospects of ANNs applications in C&SE are given at the end of the paper.
Keywords: artificial neural networks (ANNs), back-propagation neural network (BPNN), finite element method (FEM), hybrid FEM/ANN system, civil and structural engineering (C&SE), Cracow University of Technology.

The Bodner-Partom elastic-visco-plastic constitutive equations [1] were used for numerical analysis of inelastic problems. This rate-dependent model makes it possible to describe elastic, plastic and viscous processes in metals, including temperature and continuum damage effects. The adaptive finite element method [2] was applied to approximate solution of the governing equations with two a posteriori error estimates that control accuracy of time and space discretization of displacements and internal variables. The paper addresses a further development of the methodology proposed by the author in previous works [3,4] and used in [5]. We present here certain additional theoretical background and propose a novel strategy of adaptation as well as verify the method of solution transfer. [1] S.R. Bodner, Y. Partom, J. Appl. Mech., 42: 385-389, 1975. [2] L. Demkowicz, J.T. Oden, W. Rachowicz, O. Hardy, Comp. Meth. Appl. Mech. Engng., 77: 79-112, 1989. [3] W. Cecot, W. Rachowicz, CAMES, 7: 479-492, 2000. [4] W. Cecot, Int. J. Num. Meth. Engng., 61: 2139-2158, 2004. [5] W. Cecot, Analysis of selected in-elastic problems by h-adaptive finite element method, Cracow University of Technology, 2005.
Keywords: h-adaptive finite element method, error estimate, elastic-visco-plasticity.

Wood exhibits an intrinsic structural hierarchy. It is composed of wood cells, which are hollow tubes oriented in the stem direction. The cell wall is built up by stiff cellulose fibrils which are embedded in a soft polymer matrix. This structural hierarchy is considered in a four-step homogenization scheme, predicting the macroscopic elastic behavior of different wood species from tissue-specific chemical composition and microporosity, based on the elastic properties of nanoscaled universal building blocks. Special attention is paid to the fact that the fibrils are helically wound in the cell wall, at an angle of 0°-30°, generally denoted as microfibril angle. Consideration of this microfibril angle in the continuum micromechanics model for wood is mandatory for appropriate prediction of macroscopic stiffness properties, in particular of the longitudinal elastic modulus and the longitudinal shear modulus. The presented developments can be readily extended to the prediction of poroelastic properties, such as Biot and Skempton coefficients.
Keywords: wood, continuum micromechanics, anisotropic elasticity, wood cell wall, experimental validation.

This paper deals with the second-order computational homogenisation of a heterogeneous material undergoing small displacements. Typically, in this approach a representative volume element (RVE) of nonlinear heterogeneous material is defined. An a priori given discretised microstructure is considered, without focusing on detailed specific discretisation techniques. The key contribution of this paper is the formulation of equations coupling micro- and macro-variables and the definition of generalized boundary conditions for the microstructure. The coupling between macroscopic and microscopic levels is based on Hill's averaging theorem. We focus on deformation-driven microstructures where overall macroscopic deformation is controlled. In the end a numerical example of a thin layer shear is presented.

The concept of experimental data interpretation in mechanics using Dirac function is presented. The objective is to find general differential equation, which may be used to approximate the stress field sought. Application of this method may convert problem from general spline to variational one. Basic idea has been presented earlier in [1] where both theoretical data and results of experiments have been taken into account. Here, the method has been used to solve a 2D problem. Numerical tests performed for both generated and experimental data proved its usefulness. [1] W. Karmowski, J. Orkisz, Inverse Problems in Engineering Mechanics, pp 61-70, Springer-Verlag, 1993.

The object under study reported on in this paper was an aortic valve based on a natural aortic valve as the original. Simulations were carried out to examine the functioning of a valve which was loaded with varying pressure until a buckling of the leaflets and a full opening of the valve were observed. The aim of the study was the optimal choice of the geometric and mechanical parameters for the class of construction assumed for analysis.

A mathematical model describing coupled heat, moisture and salt transport in porous materials is presented. Salt dissolved in water can be transported due to various mechanisms: dispersion caused by the salt concentration gradient, and advection resulting from the capillary pressure gradient. The influence of salt on the physical properties of water such as density and dynamic viscosity is also considered. The isotherms of water sorption are modified to take into account both osmosis and effects of the salt presence on the surface tension and contact angle. Salt precipitation in the state of thermodynamic equilibrium between dissolved and crystallized salt is also considered. Finally, the model equations were discretized in space by means of FEM and the HMTRA-SALT software was developed. An example concerning a wall drying process was numerically solved to show the robustness of the code.
Keywords: porous materials, salt transport, hydrodynamic dispersion, coupled transport.

Kalman filtering is used as a learning method for the training of Feed-forward Layered Neural Networks (FLNN) and Recurrent LNNs (RLNN). These networks were applied to the simulation of hysteresis loops obtained by the experiment on a cable-in-conduit superconductors by the test carried out in a cryogenic press [1]. The training and testing patterns were taken from nine selected, characteristic hysteresis loops. The formulated FLNN: 4-4-5-1 gives the computer simulation of higher accuracy than the standard network FLNN: 4-7-5-1 discussed in [2]. [1] A. Nijuhuis, N.H.W. Noordman, H.H.J. ten Kate, Mechanical and Electrical Testing of an ITER CS1 Model Coil Conductor under Transverse Loading in a Cryogenic Press, Univ. of Twente, 1998. [2] M. Lefik, in Fusion Engineering and Design, 105-117, Elsevier, 2002.
Keywords: Kalman filtering, neural network, simulation, conductor, hysteresis loops.

In the paper presented is an application of the physically based global method (PBGM) to a posteriori estimation of experimental data error. It is proposed here to build data error measures by spanning a high quality physically reasonable smoothing fit to data and treat it as a reference field for error estimation in a very similar way it is done in the postprocessing type error estimates used widely in FE or meshless methods, where the higher order (superconvergent) solutions are used for building error estimates (post-processing type of error estimators). The new technique is different from classical methods of experimental data error estimation as it provides non-statistical estimates of the data error and as such it may be applied to a wider range of problems, including cases when only a single data set is available (e.g., destructive testing). And because the new approach builds the estimates while performing its standard physically based global-type approximation, it fully integrates other features of the PBGM approach like data interpolation, extrapolation or differentiation. In the paper the whole PBGM approach is presented, including the concept of the method formulated for the case of analysis of residual stress in railroad rails, discretisation with MFDM, then several PBGM a posteriori error estimates are introduced and results for test problems (benchmark and actual data) are shown.
Keywords: hybrid methods, physically based approximation, meshless finite differences method, smoothing of experimental data, error estimation techniques.

Frost heave in soils is a common phenomenon in cold regions, yet the previous efforts toward its mathematical description did not result into a generally accepted model. The model described in this paper is based on the concept of porosity rate function, which characterizes well the heaving phenomenon in variety of soils. The concept is simple enough so that it can be easily incorporated in numerical methods. The description of the model is followed by brief considerations of energy transfer and phase change. Calibration results are shown, and the model is implemented to solve a practical boundary value problem. The influence of thermal insulation on the performance of a retaining wall with frost-susceptible backfill is discussed.
Keywords: soil freezing, frost heave, constitutive model, heat transfer, phase change, retaining wall.

Possible yielding of the cross-section of a structure, which may arise as a result of external actions or the (micro)defects, might significantly decrease the safety margin of the considered structure [1]. Since the cross-section yielding affects the structure stiffness, the dynamic characteristics (eigenvalues and eigenvectors) might be significantly different then the ones of the original structure. The measurement of the changes of the dynamic parameters may provide the information necessary to identify the load causing the yielding of the cross-section and further the yielding index (which may be calculated when the load causing the yielding is know) enables the evaluation of the structure safety margin. This paper presents the application of Artificial Neural Networks (ANN) [2,3] in the identification of the load casing partial yielding of simply-supported beam and one- or two-column frames. [1] W.F. Chen, H. Zhang, Structural Plasticity: Theory, Problems and CAE Software, Springer-Verlag, 1991. [2] S. Haykin, Neural Networks. A Comprehensive Foundation, Prentice-Hall, 1999. [3] Z. Waszczyszyn, L. Ziemiański, CAMES, 13: 125-159, 2006.
Keywords: finite element method, identification, dynamics, artificial neural networks.

In the paper the structure optimization system based on the surface remodeling is presented. The base of algorithm formulation was the trabecular bone surface remodeling phenomenon leading to optimization of the trabecular net in the bone as well as the design with optimal stiffness principle. The closed system including Finite Element mesh generation, decision criterion for structure adaptation and Finite Element Analysis in parallel environment are presented. The issues concerning the use of the tool for the mechanical design are discussed. Some results of computations, using special prepared software are presented.
Keywords: biomechanics, structural optimization.

The paper is concerned with a class of generalized structural optimization problems, in which geometrical nonlinearities play an important role in a response of dynamically loaded structure. Forced, steady-state periodic vibrations of linear elastic frame and beam structures are considered. Both, viscous and complex modulus damping models are used. Using the adjoint variable method, sensitivity operators with respect to variation of stiffness, damping and mass parameters, as well as loading and support conditions are derived. The loading corresponds to an excitation induced by a rotational machine founded on vibro-isolation. The forms of response functionals expressed in displacements are discussed. Numerical examples of frame structures illustrate the theory and demonstrate the accuracy of the derived sensitivity operators.
Keywords: sensitivity analysis, optimal design, second order geometric effects, structural dynamics, vibrations.

The focus of this paper is the application of two nonlinear regression models in the context of Bayesian inference to the problem of failure prediction of concrete specimen under repeated loads based on experimental data. These two models are compared with an empirical formulae. Results on testing data show that both models give better point predictions than empirical formulae. Moreover, Bayesian regression approach makes it possible to calculate prediction intervals (error bars) describing the reliability of the models predictions.
Keywords: Bayesian inference, concrete, fatigue failure, Gaussian process regression, feed-forward neural network.

The influence of fluid phase on soil instabilities is investigated using the modified Cam-clay model within a two-phase description. Spurious mesh dependence of finite element results is prevented by a gradient enhancement of the model. The results of numerical tests for one-phase and two-phase model are compared. The influence of permeability on the stabilizing role of the fluid phase is assessed.
Keywords: two-phase medium, finite element method, plasticity, Cam-clay model, gradient regularization, localization.

Large deflection analysis of laminated composite plates is considered. The Galerkin method along with Newton-Raphson method is applied to large deflection analysis of laminated composite plates with various edge conditions. First order shear deformation theory and von Kármán type nonlinearity are utilized and the governing differential equations are solved by choosing suitable polynomials as trial functions to approximate the plate displacement functions. The solutions are compared to that of Chebyshev polynomials and finite elements. A very close agreement has been observed with these approximating methods. In the solution process, analytical computation has been done wherever it is possible, and analytical-numerical type approach has been made for all problems.
Keywords: Galerkin method, large deflection, composite plates.

The finite element in time method (FET) is a fast and reliable implicit numerical method for obtaining steady state solutions of the periodically forced dynamical systems with clearances. Delineation of the stable and unstable solutions could help in predicting regular and chaotic motions of such dynamical systems and transitions to either type of response. Stability of the FET solutions can be investigated via the Floquet theory, without any special effort for calculating the monodromy matrix. The applicability of the stability analysis is demonstrated through the study of two-degree-of-freedom systems with clearances. Close agreement is found between obtained results and published findings of the harmonic balance method and the piecewise full decoupling method.

The steady laminar flow and heat transfer of an incompressible, electrically conducting, non-Newtonian Bingham fluid in an eccentric annulus are studied in the presence of an external uniform magnetic field. The inner cylinder is subject to a constant heat flux while the outer cylinder is adiabatic and, the viscous and Joule dissipations are taken into consideration. The governing momentum and energy equations are solved numerically using the finite difference approximations. The velocity, the temperature, the volumetric flow rate and the average Nusselt number are computed for various values of the physical parameters.

This paper reviews the important concepts presented by Trefftz in 1926 regarding bounds to solutions, error estimation, and hybrid fields for use with domain decomposition. Observations are offered from the perspective of today's relatively mature state of the art in finite element methods. The numerical examples presented by Trefftz are also reviewed with the benefit of `exact' solutions made available from current commercial finite element methods. The accuracies of the solutions given by Trefftz are quantified and compared, and the effectivity indices of Trefftz's proposed error estimates are also quantified. An English translation of the original German version of Trefftz's paper is included for reference in an Appendix.

This paper presents the basis of an adaptive mesh refinement technique aimed at reducing a local error, i.e. the error in a local quantity, which is defined as the integral of a stress or a displacement in a given subregion. Two pairs of dual solutions, one corresponding to the applied load and the other to the virtual action, dual of the local quantity, are used to bound the local error and to provide the element error indicators for the adaptive process. A test case is used to exemplify the behaviour of the technique.

This paper discusses a domain-based formulation for hybrid-Trefftz\ thick plate elements. The formulation can be applied to triangular and quadrilateral elements, and enables an analytical formulation of these elements to be used. Techniques for improving the computational efficiency are explored, and a simple and accurate triangular element is formulated in this manner.

Solution representations are available for several differential equations. For elasticity problems some of the solution representations are considered in this paper. The solution representations can be used for a systematic construction of Trefftz functions for the derivation of Trefftz-type finite elements. For the example of a thick plate a set of Trefftz functions is presented.
Keywords: Trefftz functions, Trefftz-type finite elements.

This paper presents a simple computing procedure for the analysis of the wave motion in infinite layered waveguides via the analysis of the propagating wave modes. Waveguides may have irregular inclusions, which yields complicated reflections of waves, and an analytical solution is practically not feasible. The section of the waveguide, where we want to analyze the displacements and stress waves, is modelled by finite elements using standard programs for FEM. The external problem is solved as an internal one, while the radiation conditions are satisfied exactly. The procedure only some simple mathematical manipulations and is performed in the frequency domain. It yields exact results and a clear insight into the propagating wave modes. The results of the first presented numerical example are compared to the exact ones, while in the second example the foundation represents an irregularity in the waveguide composed of two layers

This paper presents numerical solution to a problem of the transient flow of gas within a two-dimensional porous medium. A method of fundamental solution for space variables and finite difference method for time variable are employed to obtain a solution of the non-linear partial differential equation describing the flow of gas. The inhomogeneous term is expressed by radial basis functions at each time steps. Picard iteration is used for treating nonlinearity.
Keywords: isothermal gas flow, porous medium, Trefftz method, fundamental solution.

This paper describes the simulation of the traffic flow through toll gate. A two-lane road is considered as the object domain and then, the local rules are defined to control the vehicle behavior. First, one simulates the traffic flows through the road with two non-ETC gates or the road with two ETC gates. The maximum traffic amount on the roads with two ETC gates is less than that on the road without gates by about 10%, while, in the case of the roads with two non-ETC gates, the maximum traffic amount decreases by 80%. Next, one simulates the traffic flows through the road with one non-ETC gate and one ETC gate. The traffic amount depends not only on the vehicle occupancy but also on the percentage of ETC vehicles among all driving vehicles.
Keywords: traffic flow, toll gate, traffic cognition, stochastic velocity model, cellular automata.

This work gives some applications of genetic algorithms for shape optimization of thin axisymmetric shells and axisymmetric structures. Calculations are relatively fast for thin axisymmetric shells. For general axisymmetric structures, the concept of mobile or fixed substructures is used and associated to an automatic mesh generator, so calculations are also relatively fast for axisymmetric structures. The limitations or the optimization constraints are included in the chromosomes coding. Three applications are presented; the first one deals with the optimization of the shape of a drop of water, the second one deals with the optimization of the shape of a bottle, and the third one deals with the optimization of the shape of a hydraulic hammer's rear bearing.
Keywords: shape optimization, axisymmetric shells, axisymmetric structures, genetic algorithms.

This paper proposes an improvement of the artificial boundary node approach using the least square method. The original artificial boundary node approach requires the selection of an offset by the user. The success of the original method depends on the correct choice of the offset. However, the improved version uses a least square line and the solution does not depend on a single offset. The solution is carried on using at least two different offsets and final solution is obtained by replacing the offset as zero in the least square equation. The improved version supplies good accuracy and stability in the boundary element solution. Three different case studies are solved to validate proposed method in 2-D elasticity. All results are compared with each others, conventional BEM, FEM, ANSYS and analytical results whenever possible.
Keywords: Artificial boundary node, boundary element method, least square method, singular integrals.

In recent years, there has been interest in research related to hyperthermia combined with radiation and cytotoxic drugs to enhance the killing of tumors. The objective is to control laser heating of the tumor so that the temperature of the normal tissue surrounding the tumor remains low enough so as not to cause damage to the tissue. To achieve this objective, it is important to obtain an optimal temperature field of the entire treatment region. In this paper, we develop a numerical algorithm for obtaining an optimal temperature distribution in a 3D triple layered cylindrical skin structure by pre-specifying the temperatures to be obtained at the center and perimeter of the treated region on the skin surface. The method is comprised of designing a laser irradiation pattern, solving a 3D Pennes' bioheat equation by a numerical scheme, and optimizing the laser power.

This paper uses an interval and fuzzy finite element approach for the eigenfrequency analysis of a mechanical structure with uncertain parameters. The component mode synthesis method is applied for the numerical reduction of the structure, in order to reduce the calculation time of the interval and fuzzy analyses. Special attention is paid to the effect of uncertainties on the description of the substructuring technique and the consequences on the calculation time. All concepts are illustrated through a benchmark structure example.

Forging of practical products from simple billet shapes is a complex and nonlinear process due to the multi-disciplinary phenomenon of material flow and processing conditions. General forgings are usually produced in a number of stages in order to avoid defects such as underfill, extra flash, voids, and folds. In spite of advancements in analysis techniques, forging process simulations do not provide function sensitivity information. Hence, the research focuses on exploring efficient non-gradient based preform shape optimization methods. In this research, an attempt is made to develop a preform shape design technique based on interpolative surrogate models, namely Kriging. These surrogate models yield insight into the relationship between output responses and input variables and they facilitate the integration of discipline-dependent analysis codes. Furthermore, error analysis and a comparison between Kriging and other approximation models (response surface and multi-point approximations) are presented. A discussion about what the results mean to a designer is provided. A case study of an automotive component preform shape design is presented for demonstration.
Keywords: preform shape optimization, surrogate models, Kriging, response surface model, multi-point approximation model.

This paper presents a two-dimensional model for the analysis of interaction between surface and internal cracks in the railheads subjected to wheel loading. The shape of the railhead, the surface crack and the internal crack are modelled as curved cracks defined by the theory of continuous distribution of dislocation in an infinite body. From the boundary conditions along these cracks, a system of singular integral equations is deduced. Influence functions in these singular integral equations are first expanded into the Cauchy kernel multiplying normal functions and later are reduced to a system of linear equations and solved numerically. Stress intensity factors (SIFs) of the surface crack tip are calculated from the numerical solution of distribution function along these cracks directly, eliminating need for any indirect integral method. The method does not require meshing and hence idealisation of the shapes of the cracks, thereby improving accuracy and reducing pre- and post processing efforts. Interaction between the internal crack and the surface crack is examined in detail through several examples.
Keywords: railhead, surface crack, internal crack, curved crack, SIF, crack angle.

The present paper examines the crystal orientation effects on the energy at the crack-tip of niobium/alumina joints. The analyses have been done using crystal plasticity theory. The single crystal parameters are identified for each family of slips system in [1]. These identified parameters are being used to examine the orientation effects of the niobium single crystal on the energy at the crack-tip. Differences in the fracture energy are explained based on the plastic slip (strain) induced in different slip systems during deformation. A qualitative comparison of the crystal plasticity analysis with the experiments of [2,3] is also been presented. [1] A. Siddiq, S. Schmauder. Steel Grips: J. Steel Rel. Materials, 3: 281-286, 2005. [2] D. Korn, G. Elssner, R.M. Cannon, M. Rühle. Acta Materialia, 50: 3881-3901, 2002. [3] R.M. Cannon, D. Korn, G. Elssner, M. Rühle. Acta Materialia, 50: 3903-3925, 2002.
Keywords: crystal plasticity, finite element methods, fracture, metal-ceramic interface.

The discrete counterpart of a class of Hopfield neural networks with periodic impulses and finite distributed delays is introduced. A sufficient condition for the existence and global exponential stability of a unique periodic solution of the discrete system considered is obtained.

One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical postprocessing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moments of system responses and which enables more advanced statistical post-processing.

The paper discusses methods of diagnosing the technical condition of reinforced concrete beams, based on the change in dynamic characteristics. The objects of research were 12 reinforced concrete (RC) beams. Testing of RC beams included both static and dynamic tests. A series of step loaded static tests was aimed to produce successive damage to the beams. After each load step (at the moment of displacement and strain stabilization), dynamic testing followed. To carry out the concept of concrete beams diagnosis, on the basis of frequency changes, Artificial Neural Networks (ANNs) were applied.
Keywords: estimation, reinforced concrete beam, dynamics, artificial neural networks

This paper deals with the second-order CH of a heterogeneous material undergoing small displacements. Typically, in this approach an RVE of a heterogeneous material is investigated. A given discretized microstructure is determined a priori, without focusing on details of specific discretization techniques. Application of BNN as a tool for identification of characteristic length of a microstructure is discussed. An indentation test was analyzed under plane strain constraints for generating pseudo-experimental patterns by means of FEM. A single input of BNN was formulated due to the application of PCA. The BNN of structure 1-16-1 with sigmoid hidden neurons was designed. The Bayesian inference approach was applied to obtain pdf of the characteristic length. Numerical efficiency of the proposed approach is demonstrated in the paper.
Keywords: micro- and macrolevels, second order continuum, computational homogenization (CH), representative volume element (RVE), finite element method (FEM), Bayesian neural network (BNN), probability density function (pdf), principal component analysis (PCA), indentation test.

A concept is presented of a system for automatic processing of the civil engineering data. It may concern designing, optimisation or diagnostics of constructional materials. The main point of interest was concrete and various concrete like composite materials. The applied methods are a combination of various soft computing techniques, like artificial neural networks, machine learning and certain techniques originating in statistics. The system is aimed at taking advantage of varied information available in publications, reports, monographs and direct experimental results, perhaps including even the grey information resources. After preparation of a database collected from laboratory or in-situ observations concerning the behaviour of various concrete materials, and gathered during the two last decades, a number of experiments were performed on the system dedicated mainly to prediction of compressive strength and frost resistance of concrete. The proposed approach allows more efficient control of information in problems of concrete technology.

This paper describes an application of feedforward neural network to analyse the SASW (Spectral Analysis of Surface Waves) measurements of the soil. The free field dynamic experiment was performed to determine the soil dynamic properties. An inversion process is based on the comparison of experimental and theoretical phase velocity curves. The results of the experiment are pre-processed by a neural network. The dynamic soil profile is compared with the real soil profile based on the geotechnical site prospect.

A new procedure based on layered feed-forward neural networks for the microplane material model parameters identification is proposed in the present paper. Novelties are usage of the Latin Hypercube Sampling method for the generation of training sets, a systematic employment of stochastic sensitivity analysis and a genetic algorithm-based training of a neural network by an evolutionary algorithm. Advantages and disadvantages of this approach together with possible extensions are thoroughly discussed and analyzed.

The paper deals with an application of neural networks for computation of fundamental natural periods of buildings with load-bearing walls. The identification problem is formulated as a relation between structural and soil parameters and the fundamental period of building. The patterns are based on long-term tests performed on actual structures. Various splitting up of the set of patterns into training and testing sets are considered in the analysis. The carried out analysis leads to conclusion that, even in "the worst'' case of randomly selected testing patterns, the natural periods of vibrations of buildings are obtained with accuracy quite satisfactory for engineering practice.

This article presents recent developments in the field of stochastic finite element analysis of structures and earthquake engineering aided by neural computations. The incorporation of Neural Networks (NN) in this type of problems is crucial since it leads to substantial reduction of the excessive computational cost. In particular, a hybrid method is presented for the simulation of homogeneous non-Gaussian stochastic fields with prescribed target marginal distribution and spectral density function. The presented method constitutes an efficient blending of the Deodatis-Micaletti method with a NN based function approximation. Earthquake-resistant design of structures using Probabilistic Safety Analysis (PSA) is an emerging field in structural engineering. It is investigated the efficiency of soft computing methods when incorporated into the solution of computationally intensive earthquake engineering problems.

The paper deals with application of AI tools in experimental modal analysis. The example of Stabilization Diagram processing, that is an intermediate stage of modal parameter estimation procedure, was selected. In order to automate decision-making carried out during Stabilization Diagram processing a set of tools employing: fuzzy reasoning and artificial neural nets was applied. The application of these tools enabled to ease and shorten execution time of Stabilization Diagram processing. Additionally, the result of processing has become operator-independent.

The paper deals with the application of soft computing used in uncertainty analysis in the field of structural dynamics. Employing Genetic Algorithms, fuzzy sets theory as well as interval algebra authors show quite useful extension of well known approaches of solving eigenproblems considering assumed model uncertainties. During performed calculation, ranges of the first natural frequency of a simple FE model are found and then compared to those ones obtained with Monte Carlo simulation. As input uncertain parameters some of material properties are taken into account. The main objective of the work is to highlight possible advantages of the application in terms of reducing computation time meant for uncertainty analyses.

Gaussian mixture models (GMM) and support vector machines (SVM) are introduced to classify faults in a population of cylindrical shells. The proposed procedures are tested on a population of 20 cylindrical shells and their performance is compared to the procedure, which uses multi-layer perceptrons (MLP). The modal properties extracted from vibration data are reduced into low dimension using the principal component analysis and are then used to train the GMM, SVM and MLP. It is observed that the GMM gives 98% classification accuracy, SVM gives 94% classification accuracy while the MLP gives 88% classification accuracy. Furthermore, GMM is found to be more computationally efficient than MLP which is in turn more computationally efficient than SVM.

This paper is devoted to the application of the evolutionary algorithms and artificial neural networks to uncertain optimization problems in which some parameters are described by fuzzy numbers. The special method of global optimization: Two-Stages Fuzzy Strategy (TSFS) for structures in uncertain conditions is proposed. As the first stage of the TSFS the fuzzy evolutionary algorithm is used. As the second stage the local optimization method with neuro-computing is proposed. The presented approach is applied in the identification problems of mechanical structures, in which material parameters and loadings are uncertain. To solve the direct problem the fuzzy boundary element method (FBEM) is used. Several numerical tests and examples are presented.

This paper proposes a neural network model using genetic algorithm for a model for the prediction of the damage condition of existing light structures founded in expansive soils in Victoria, Australia. It also accounts for both individual effects and interactive effects of the damage factors influencing the deterioration of light structures. A Neural Network Model was chosen because it can deal with `noisy' data while a Genetic Algorithm was chosen because it does not get `trapped' in local optimum like other gradient descent methods. The results obtained were promising and indicate that a Neural Network Model trained using a Genetic Algorithm has the ability to develop an interactive relationship and a Predicted Damage Conditions Model.

The objective of this paper is to investigate the efficiency of nonlinear Bayesian regression for modelling and predicting strength properties of high--performance concrete (HPC). A multilayer perceptron neural network (MLP) model is used. Two statistical approaches to learning and prediction for MLP based on the likelihood function maximization and Bayesian inference are applied and compared. Results of experimental data sets show that Bayesian approach for MLP offers some advantages over classical one.
Keywords: Bayesian inference, regression, high-performance concrete, neural network.

The identification of the industrial processes is a complex problem, especially in the case of signals denoising. The holistic approaches used for signal denoising processes are recently considered in various types of applications in the domain of experimental simulations, feature extraction and identification. A new signal filtering method based on the dynamic particles (DP) approach is presented. It employs physics principles for the signal smoothing. The presented method was validated in the identification of two kinds of input data sets: artificially generated data according to a given function y=f(x) and the data obtained in laboratory mechanical tests of metals. The algorithm of the DP method and the results of calculations are presented. The obtained results were compared with commonly used denoising techniques including weighted average, neural networks and wavelet analysis. Moreover the assessment of the results' quality is introduced.

Mathematical-model-based structural identification algorithms for the damage detection and performance evaluation of civil engineering structures have been widely proposed and their performance for small and simple structural models has been studied in the past two decades. Actual civil engineering structures, however, usually have a great number of degrees of freedom (DOFs). It is unpractical to directly apply these conventional methods for the identification of large-scale structures, because excessive computation time and computer memory are necessary for the search of optimal solutions in inverse analysis, which is often computationally inefficient and even numerically unstable. Moreover, for the identification of large-scale structures, it is difficult to obtain unique estimates of all structural parameters by the optimization search processes involved in the conventional identification algorithms requiring the use of secant, tangent, or higher-order derivatives of the objective function. The ability of artificial neural networks to approximate arbitrary continuous function provides an efficient soft computing strategy for structural parametric identification. Based on the concept of localized and decentralized information architecture, novel decentralized and localized identification strategies for large-scale structure system by the direct use of structural vibration response measurements with neural networks are proposed in this paper. These methodologies does not require the extraction of structural frequencies and mode shapes from the measurements and have the potential of being a practical tool for on-line near-real time and damage detection and performance evaluation of large-scale engineering structures.

This paper gives a review of the new Bejan's constructal theory and its various applications to design and optimization. According to Bejan, the objective and constraints principle used in engineering is the same mechanism from which the geometry in natural flow systems emerges. This observation is the basis of the new constructal theory. The topics covered in this review are: mechanical structure, thermal structure, heat trees, and structure in transportation and economics. In the conclusion, remarks on possibility of coupling this approach with computational mechanics are given.
Keywords: optimization, constructal theory, constructal design, review.

Analytical models are often used to analyse behaviour of structures, particularly in the field of structural dynamics. The application of such models demands that they must predict the effects of structural modifications with a reasonable accuracy. Unfortunately, lacks of correlation between initial analytical predictions and experimental results are usually observed so that the analytical model needs to be updated with respect to an experimental reference. Many updating methods, involving two main categories of techniques, have been developed in recent years. In the first group of methods, the model to be adjusted is modified by means of correcting parameters associated with the regions containing dominant errors in modelling. The techniques require a localization of modelling errors and are essentially iterative. The second category involves one-step algorithms to globally correct the model in terms of its representative mass and stiffness matrices. These methods have come to be called direct or global methods. Each class of methods presents advantages and disadvantages. The main disadvantage of the iterative methods is the errors localization phase that may require an extensive amount of computational efforts. In addition, the convergence is not ensured for all iterative algorithms. The present paper deals with a direct approach to correct the whole mass and stiffness matrices of a derived finite element model. A modal analysis and a quantitative study of matrix changes are performed to evaluate the capability of the proposed algorithm and to investigate its potential usefulness in model updating.

A finite element implementation of the unified elasto-viscoplastic theory of Bodner-Partom for non-linear analysis is investigated in detail. Description of the Bodner-Partom constitutive equations is presented. Proposed UVSCPL procedure has been applied into MSC.Marc system and can be introduced into wide range of different finite elements (e.g. shell, solid, truss). For the validation of the proposed FE procedure the numerical simulations are presented. Additionally, the first part of the paper gives brief characterization of the engineering applications of the Bodner-Partom constitutive equations used for the different modelling of materials.
Keywords: elasto-viscoplastic constitutive model, Bodner-Partom, FEM.

A survey of three forms (strong, weak and variational) of mathematical models is presented using expressive diagrams [1,2]. The primary and intermediate variables, governing field equations, constraint equations and variables specified by boundary conditions are components of the graphic representation of various FE (finite element) formulations. The attention is focused on linearly elastic plate element QUAD for Mindlin-Reissner theory and shell elements EAS4-ANS, EAS7-ANS based on CBRST (Continuum Based Resultant Shell Theory). In both cases the mixed FE models with the EAS (enhanced assumed strain) and ANS (assumed natural strain) concepts are used. [1] C. Fellippa, Advanced Finite Element Methods (ASEN 5367), Course materials, 2003 [2] Commun. Numer. Methods Engng., 11: 105-115, 1995

This paper paper discusses accuracy of WENO reconstruction used for unstructured grids and applied to two common discretization approaches within Finite Volume Method (FVM). They are Cell Centered and Vertex Centered methods. The numerical results are shown for 3D supersonic flow in a channel and for ONERA M6 wing. The comparison of computational performance of both methods is included.

Numerical results are presented for the effects of thermal radiation, buoyancy and heat generation or absorption on hydromagnetic flow over an accelerating permeable surface. These results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. This qualitatively agrees with the expectations, since the magnetic field exerts a retarding force on the free convection flow. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, Prandtl number, Grashof number and Schmidt number on the profiles of the velocity components and temperature. The effects of the different parameters on the velocity and temperature profiles as well as the skin friction and wall heat transfer are presented graphically. Favorable comparisons with previously published work confirm the correctness of numerical results.
Keywords: heat and mass transfer, hydromagnetic flow, perturbation technique.

The paper presents problem of discrete multicriteria optimization of two-layer regular orthogonal spatial trusses. Three criteria of evaluation are taken into account, namely: minimum of weight, maximum of reliability and maximum of stiffness of the structure. To simplify the problem, decomposition techniques are applied. The decision variables are cross-sections of the truss members. The best possible cross section is selected for each bar from a discrete catalogue. Other decision variables (coordinated variables) describe also the geometry of the structure. The multicriteria reliability-based algorithm allows for evaluating the objective functions values and then finding sets of nondominated evaluations and solutions. Reliability of the structure is expressed by the Hasofer-Lind reliability index beta.

The paper is a development and continuation of paper [1] where the Panagiotopoulos approach was extended for the elastoplastic analysis. In case of elastic analysis the parameters of the Hopfield?Tank Neural Network (HTNN) are calibrated only once but the updating of the elastoplastic stiffness matrix needs an iteration of HTNN and FE system. The main problem is the matrix condensation repeated for each iteration step of the Newton-Raphson method. Besides all the improvements proposed in [2], a new interacting program has been implemented which enables a significant decrease of the processing time (number of iterations) in comparison with the time achieved in [1]. The results of the extensive numerical analysis are discussed for a tension perforated strip with a rigid bolt placed frictionlessly in a circular hole in the middle of the strip. [1] E. Pabisek, Z. Waszczyszyn, in: B.H.V. Topping, ed., Computational Engineering Using Metaphors from Nature, pp. 1-6, Civil-Comp Press, 2000 [2] Z. Waszczyszyn, E. Pabisek, CAMES, 7: 757-765, 2000
Keywords: neural network, finite element method, elastoplastic problem, unilateral constraints.

The problem of empirical data modeling is pertinent to several mechanics domains. Empirical data modeling involves a process of induction to build up a model of the system from which responses of the system can be deduced for unobserved data. Machine learning tools can model underlying non-linear function given training data without imposing prior restriction on the type of function. In this paper, we show how Support Vector Machines (SVM) can be employed to solve design problems involving optimizations over parametric space and parameter prediction problems that are recurrent in engineering domain. The problem considered is diffuser design where the optimal value of pressure recovery parameter can be obtained very efficiently by SVM based algorithm even in a large search space. In addition, locating the position of points on a string vibrating in a damped medium serves as an appropriate prediction problem. A grid-searching algorithm is proposed for automatically choosing the best parameters of SVM, thus resulting in a generic framework. The results obtained by SVM are shown to be theoretically sound and a comparison with other approaches such as spline interpolation and Neural Networks shows the superiority of our framework.
Keywords: conical diffuser, turbulent flow, string vibration, support vector machine, parameter grid searching, optimal pressure recovery, neural networks.

The purpose of the paper is to present solution to design additional diagnostic system for, based on cutting-edge technology, purifying fumes installation. Neural networks, which determine the core of the system, were used as predictive models. Designed very efficient neural structures have served to build simulative diagnostic advisory system.
Keywords: artificial intelligence, neural networks, advisory systems, diagnostics.

Constraint-based scheduling is an approach for solving real-life scheduling problems by combining the generality of AI techniques with the efficiency of OR techniques. Basically, it describes a scheduling problem as a constraint satisfaction problem and then uses constraint satisfaction techniques to find a solution. In this paper we study three constraint models describing complex state transitions that are going beyond the existing models of resources (machines) used in scheduling. These models can naturally handle any setup/changeover/transition scheme as well as special counter constraints imposed on the sequence of activities. The proposed models have been implemented and tested in the commercial scheduling engine of Visopt ShopFloor system.
Keywords: constraint satisfaction, scheduling, machine setups.

Rotating machines are often described using linear methods with acceptable accuracy. Some malfunctions, however, are of non-linear nature. Accurate detection and identification of such malfunctions requires more accurate methods. One of such methods can be NARX- Non-linear AutoRegressive model with eXogenous input. The paper presents how NARX models can be applied for modeling rotating machinery malfunctions. Idea of the diagnostic algorithm based on such modeling is presented. Proposed algorithm was verified during research on a specialized test rig, which can generate vibration signals. The paper presents results of application of NARX models for detection of typical rotating machinery failures and the variations of NARX model parameters due to propagation of damage. In the paper authors present also a blade crack detection using the NARX models. The last chapter of the paper discusses the applicability of this method for damage detection in real machines.
Keywords: rotating machinery diagnostics, blade crack detection, neural networks, NARX models.

The aim of the paper is to prepare an efficient method of the optimization of the hybrid fibre-reinforced laminates. Since the several optimization criteria which cannot be satisfied simultaneously are proposed, the multi-objective optimization methods have been employed. Different optimization criteria connected with the laminates' cost, the modal properties and the stiffness are considered. The multi-objective evolutionary algorithm which uses the Pareto approach has been used as the optimization method. To solve the boundary-value problem the finite element method commercial software has been employed. Numerical examples presenting the effectiveness of the proposed method are attached.
Keywords: multi-objective optimization, evolutionary algorithm, multi-layered laminate, modal analysis.

This paper presents a new dual model combining binary and real-valued representations of samples for negative selection algorithms. Recent research show that the two types of encoding can produce quite good results for some types of datasets when they are applied separately in such algorithms. Besides a number of efficient algorithms, various affinity (or similarity) functions fitted to particular implementation was investigated. Basing on a series of experiments, we propose a dual representation enabling overcome some of the existing drawbacks of these algorithms, and allowing significant speed up the classification process. This new model was designed mainly for detecting anomalies in real-time applications, were the time of classification is crucial, e.g. intrusion detection systems.
Keywords: anomaly detection, negative selection, binary receptors, real-valued receptors, intrusion detection.

The authors of the paper took up Aoyama's concept of the integrated industrial processes intent analysis and linked it with the ideas of the designer's IPA (Intelligent Personal Assistant). In many cases it is not sufficient to analyze the engineer's intent depot when trying to explain the origin of a fault. Often computer models are built or real experiments are done with which the considered classes of problems can be analyzed better. The IPA concept was expanded for the process of building computer models and stands for the fault analysis.
Keywords: personal knowledge management, fault analysis.

Thermovision is more and more often used in machinery and apparatus diagnostics. With the aid of a thermographic camera non-contact simultaneous temperature measurements can be carried out at many points of an object and they can be recorded in a form of a thermographic image. The thermographic image can be a source of diagnostic information. Extraction of this information requires the necessity of application of different methods of the analysis of thermographic images. From thermographic image a huge amount of features can be extracted which causes problems with efficient assessment of technical state due to informational noise. There are methods which allow to search and find relevant features that are useful for diagnostic processes. In the paper application of evolutionary algorithm for selection of optimal diagnostic features has been shown. In case of assessment of selected features neural classifier has been used. A set of 259 features for each image has been considered. After searching process two features have been selected and the obtained classification results have been of very good quality. Efficiency of classifier has been in some cases 100% and not less than 97%. The results have shown that the evolutionary algorithm can be applied to selection of relevant diagnostic features.
Keywords: infrared thermography, evolutionary algorithms, neural networks, diagnostic.

In this work diagnostics of railway point drive supported by Data Mining methods was considered. Results of FEM calculations of switching forces acting on the considered point are qualitatively correct, so Data Mining methods efficiency was examined on data obtained from FEM multi-body model. Hidden structures in data and patterns describing particular faults were identified. Proposed algorithms of Kohonen's neural networks and k-means clustering are easy to apply to classifying. Their implementation on the Digital Signal Processor is not difficult and memory consumption is low so diagnostic module supported by implemented Data Mining methods was proposed in order to preliminary asses technical state of railway points and to assure current state monitoring and supporting maintenance activities.
Keywords: artificial neural networks, data mining, diagnostics.

This paper describes results of the research concerning an augmented reality (AR) system for CAD design, developed within the framework of MSc Thesis in the Department of Fundamentals of Machinery Design. The authors present advantages resulted from utilization of AR systems allowing to combine the interactive computer-generated world with an interactive real world in such a way that they appear as one environment, especially in CAD design. The authors decided to apply the system to aid the designer of the machinery systems by choosing standard parts. The system enables the user to easily view the 3D models of standard parts from any perspective, in more natural, intuitive way than traditional one (on the computer screen). Next, the user can export the model to the modeling software and use it to model some machinery system. This paper presents possibilities of using AR technology in CAD design with the hope that maybe someday it would become an integral part of a standard design process.
Keywords: augmented reality, image processing, CAD design, visualization, marker, VRML.

Numerical modeling of the human pelvic bone is a complex process in which many important factors are taken into account. One of them concerns material properties. Numerical calculations require the characteristics of the material properties and the material parameters from the beginning. The material properties of the living body depend on age, health, gender, environment and many others factors. To determine correct material parameters, health details of a group of patients need to be taken into consideration. In this paper authors assumed interval values of the selected material parameters and proposed interval and fuzzy analysis of the pelvic bone.
Keywords: human pelvic bone, interval and fuzzy analysis, finite element method, material properties.

The article contains presentation of application of three-dimensional vision methods in realization of vibration measurements and their analysis. For this purpose algorithms were developed of discrete epipolar geometry and structure from motion, with the usage of one camera. Vibration amplitude is determined for selected measurement points on the analyzed object. Each point is represented by flat or three-dimensional marker attached on a construction. The article includes algorithms of the discussed methods and verification of those methods based upon simulation data, as we as preliminary experimental tests carried out on a test bed.
Keywords: 3D vision techniques, epipolar geometry, structure from motion, vibration measurements.

An adaptive information system is constructed in order to approximate a set of multidimensional data. To get better approximation properties a pre-processing stage of data is proposed in which the set of points, forming the multidimensional data base and called a training set TRE, undergoes a clustering analysis. In the analysis two independent clustering algorithms are used; on each cluster a feed-forward neural network is trained and a membership function of a fuzzy set is constructed. The constructed system contains a module of two-conditional fuzzy rules consequent parts of which are of the functional type. Each rule is designed on a pair of clusters.

The integration of electronic units, sensors and actuators into complex function-oriented systems is one of the key points in the development of intelligent fibre composites. A wide range of materials is available for that purpose, for example piezoelectric textile sensors, fibre-optic fibres as well as shape memory alloys and prefabricated information elements. These elements can be used to create active fibre composites ("smart composites") with selective properties, which are suitable especially for application in stressed lightweight components. While the functionality of these solutions could be proved on a laboratory scale, appropriate manufacturing strategies for a competitive series production of components in automotive and mechanical technologies have not been realised so far. One crucial obstacle which impedes a breakthrough for such active lightweight components is the lack of technologies suitable for large-scale production. Generally, these complex systems are manually integrated into the fibre composite with either prefabricated layer materials or as individual elements, or applied to the surface of the fibre composite compound, thus preventing process automation. Therefore, the goal of the Institute of Mechanical Engineering and Plastics Technology (Chemnitz University of Technology) is to develop application-oriented technological solutions for series production.

The aim of the paper is to combine the evolutionary algorithms method, optimal dynamic filtration method and measurement data for the simultaneous identification of the thermal properties or their temperature characteristics of anisotropic solids. The idea of the proposed method depends on measuring the time-dependent temperature distribution at selected points of the sample and identification of the thermal parameters (heat conductivity and specific heat) by solving a transient inverse heat conduction problem. In the paper the discrete mathematical model has been formulated basing on the control volume method. The inverse problem was solved by using a hybrid method. Information about measurement data which are necessary to solve the inverse heat conduction problem was obtained by solving the direct heat conduction problem. The chosen results of analysis have been presented.
Keywords: control volume method, discrete mathematical model, parameter inverse problem, evolutionary algorithms method, optimal dynamic filtration method, thermal properties of anisotropic materials.

The mathematical model of solidification process can be formulated using the macro or micro-macro approach. In this paper the second generation model (micro-macro one) is considered. The driving force of crystallization is the local and temporary undercooling below solidification point T_cr. The nucleation and nuclei growth are proportional to the second power of undercooling. Formulas determining the phenomena previously mentioned contain coefficients called the nucleation coefficient and nuclei growth one. These coefficients are assumed to be interval values. For above assumptions the problem has been solved by means of interval boundary element method. In the final part of the paper the results of computations are shown.
Keywords: interval boundary element method, interval arithmetic, crystallization

The exploration of protein conformation can be supported by methods of similarity searching that allow seeking the 3D patterns in a database containing many molecular structures. We developed a novel search method called EAST (Energy Alignment Search Tool), which serves as a tool for finding strong structural similarities of proteins. It differs from other algorithms that concentrate on fold similarities. We use the EAST to find protein molecules representing the same structural protein family and inspect conformational modifications in their molecular structures as an effect of biochemical reactions or environmental influences. The similarity searching is performed through the comparison and alignment of protein energy profiles. Energy profiles are received in the computational process based on the molecular mechanics theory. These profiles are stored in the special database (Energy Distribution Data Bank, EDB) and can be used later by the search engine to find similar fragments of protein structures on the energy level. In order to optimize the alignment path we use modified, energy-adapted Smith-Waterman method, which is one of the main phases of the EAST. The use of fuzzy techniques improves the fault tolerance of presented method and allows to measure the quality of the alignment. In the paper, we present the main idea of the EAST algorithm and brief discussion on its basic parameters. Finally, we give an example of the system usage regarding proteins from the RAB family that play an important role in intracellular reactions in living organisms.
Keywords: bioinformatics, proteins, soft computing, data mining, protein structure comparison.

The paper is devoted to applications of evolutionary algorithms in identification of structures being under the uncertain conditions. Uncertainties can occur in boundary conditions, in material parameters or in geometrical parameters of structures and are modelled by three kinds of granularity: interval mathematics, fuzzy sets and theory of probability. In order to formulate the optimization problem for such a class of problems by means of evolutionary algorithms the chromosomes are considered as interval, fuzzy and random vectors whose genes are represented by: (i) interval numbers, (ii) fuzzy numbers and (iii) random variables, respectively. Description of evolutionary algorithms with granular representation of data is presented in this paper. Various concepts of evolutionary operator such as a crossover and a mutation and methods of selections are described. In order to evaluate the fitness functions the interval, fuzzy and stochastic finite element methods are applied. Several numerical tests and examples of identification of uncertain parameters are presented.
Keywords: evolutionary algorithms, granular computing, intervals, fuzzy sets, theory of probability, identification.

Inside the EU countries significant investments are expected in both the electricity production and energy transfers within the next 15 years. Such investments will need the precise decision-making processes, supported with very versatile engineering tools. The major objective of this paper is to propose an application of a new methodology to design power systems in a fully automatic way. The proposed methodology utilizes such artificial intelligence tools like genetic algorithms and expert systems.
Keywords: genetic algorithms, expert systems, combined heat and power (CHP), power plant.

The focus of this paper is on the problems of system identification, process modeling and time series forecasting which can be met during the use of locally recurrent neural networks in heuristic modeling technique. However, the main interest of this paper is to survey the properties of the dynamic neural processor which is developed by the author. Moreover, a comparative study of selected recurrent neural architectures in modeling tasks is given. The results of experiments showed that some processes tend to be chaotic and in some cases it is reasonable to use soft computing models for fault diagnosis and control.
Keywords: chaotic dynamic systems, recurrent neural networks, gradient-based and soft computing learning algorithms, nonlinear system identification, time-series forecasting.

This paper considers decision systems with decision attributes which are hierarchical. Atomic queries are built only from values of decision attributes. Queries are constructed from atomic queries the same way as we construct terms in logic using functors {+,*, ¬}. Negation symbol "¬" is only used on the atomic level. Queries are approximated by terms built from values of classification attributes. We only consider rule-based classifiers as the approximation tool for queries. When a user query fails, then the cooperative module of the query answering system (QAS) constructs its smallest generalization which does not fail and which is approximated by rules of the highest confidence discovered by the classifier. Two interpretations of queries are proposed: user-based and system-based. They are used to introduce the precision and recall of QAS. The implementation of QAS follows system-based interpretation. Automatic indexing of music by instruments and their types is an example of the application area for the proposed approach.
Keywords: information systems, knowledge discovery, cooperative query answering, music information retrieval.

Humans find it extremely easy to say if two words are related or if one word is more related to a given word than another one. For example, if we come across two words - "car" and "bicycle", we know they are related since both are means of transport. Also, we easily observe that "bicycle" is more related to "car" than "fork" is. In the paper we describe our approach on quantifying the semantic relatedness of concepts based on the theory of associative learning of concepts.
Keywords: semantic surrounding, associative learning, concept similarity, grammar, relatedness.

This paper presents an Ant Colony Optimization (ACO) approach to the resource-constrained project scheduling problem (RCPSP). RCPSP as a generalization of the classical job shop scheduling problem belongs to the class of NP-hard optimization problems. Therefore, the use of heuristic solution procedures when solving large problem is well-founded. Most of the heuristic methods used for solving resource-constrained project scheduling problems either belong to the class of priority rule based methods or to the class of metaheuristic based approaches. ACO is a metaheuristic method in which artificial ants build solutions by probabilistic selecting from problem-specific solutions components influenced by a parametrized model of solution, called pheromone model. In ACO several generations of artificial ants search for good solution. Every ant builds a solution step by step going through several probabilistic decisions. If ant find a good solution mark their paths by putting some amount of pheromone (which is guided by some problem specific heuristic) on the edges of the path.
Keywords: resources constrained scheduling problem, project scheduling, multi-project scheduling, ant colony optimization, swarm intelligence.

The process of engineering analysis, especially its preprocessing stage, comprises some knowledge-based tasks which influence the quality of the results greatly, require considerable level of expertise from an engineer; the support for these tasks by the contemporary CAE systems is limited. Analysis of the knowledge and reasoning involved in solving these tasks shows that the appropriate support for them by an automated system can be implemented using case-based reasoning (CBR) technology and ontological knowledge representation model. In this paper the knowledge-based system for intelligent support of the preprocessing stage of engineering analysis in the contact mechanics domain is presented which employs the CBR mechanism. The knowledge representation model is formally represented by the OWL DL ontology. Case representation model, case retrieval and adaptation algorithms for this model and the automated system are described.
Keywords: artificial intelligence, case-based reasoning, ontologies, finite element analysis.

In the paper an intelligent monitoring system of local water supply system is described. The main task of this system concerns water leakages detecting. For inputs, this system uses information from few pressure or flow sensors, mounted on the pipeline network, the output is a piece of information about leakage detection and localization. A heuristic model of water supply network makes the main part of intelligent diagnostic system. The model was built with the use of artificial neural networks. This paper presents the structure and optimization of a heuristic model. The authors took advantage of methods of artificial intelligence and methods known from model-based process diagnostics to increase the accuracy with which system detects of water leakages.
Keywords: water supply systems, diagnostics, genetics algorithm, artificial neural network.

The paper deals with the application of the differential quadrature method based on a piecewise polynomial to the nonlinear vibration analysis of beams. The initial-boundary-value problem is solved to study the computational stability of the method. The results are compared with those, obtained by the conventional differential quadrature. The effects of the spline degree, the number of nodes and the distribution of sampling points on the convergence and stability is also presented. The nonlinear free vibration analysis is carried out to verify the accuracy of the method.

MHD nonlinear steady flow and heat transfer over a porous surface stretching with a power-law velocity and of constant heat flux is investigated. The governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation. As the presented solution method requires the magnetic field to vary in space in a specific manner, a special form for the variable magnetic field is chosen. Resulting equations are numerically solved by Runge-Kutta shooting method. Values of skin-friction and rate of heat transfer are obtained. The effect of magnetic field, stretching parameter, magnetic interaction parameter, suction parameter and Prandtl number over a flow field and other physical quantities have been discussed in detail.

Balancing is the process of improving the mass distribution of a body so that it rotates in its bearings without unbalanced centrifugal forces. It is thus critical to the performance of any high speed equipment. The problem is mathematically modeled and a genetic algorithm is presented for obtaining optimal solutions for balancing problems on rotating shafts. This is eventually converted into computer package titled BALANCER, developed using the VisualBASIC platform. Examples are presented to illustrate implementation of the methodology. The model was tested by using typical problems, correctly solved in the literature using conventional methods. The results of the three examples gave same match with those obtained from analytical approach. The accuracy of analysis using the model and the students' feedback suggest that integration of the software tool will be beneficial for improving students' performance in any dynamics course.
Keywords: modeling, balancing, rotating shaft, off-line, imbalance.

Problem of locally disordered atomic structure is solved by using a hybrid formulation in which nonlinear elastic finite elements are linked with discrete atomic interaction elements. The continuum approach uses nonlinear hyperelasticity based upon the generalized strain while the atomistic approach employs the Tight-Binding Second-Moment Approximation potential to create new type of elements. The molecular interactions yielding from constitutive models of TB-SMA were turned into interactions between nodes to solve a boundary value problem by means of finite element solver. In this paper we present a novel way of modelling materials behaviour where both discrete (molecular dynamics) and continuum (nonlinear finite element) methods are used. As an example, the nanoindentation of a copper sample is modelled numerically by applying a hybrid formulation. Here, the central area of the sample subject to nanoindentation process is discretised by an atomic net where the remaining area of the sample far from indenters tip is discretised by the use of a nonlinear finite element mesh.

This paper describes the application of the Trefftz method to the temperature rise in human skin exposed to radiation from a cellular phone. A governing equation is given as the Poisson equation. An inhomogeneous term of the equation is approximated with a polynomial function in Cartesian coordinates. The use of the approximated term transforms the original boundary-value problem to that governed with a homogeneous differential equation. The transformed problem can be solved by the traditional Trefftz formulation. Firstly, the present method is applied to a simple numerical example in order to confirm the formulation. The temperature rise in a skin exposed to radiation is considered as a second example.
Keywords: Trefftz method, Poisson equation, polynomial function.

The prototypes of Falling-Object Protective Structures (FOPS), which are used in self-propelled mining machines, undergo obligatory laboratory strength tests. The stand tests should be preceded with virtual prototyping of computer models to reduce the number of prototypes to an indispensable minimum. The Finite Element Method was used for the virtual prototyping. At the same time, after tests, the real protective structure was transformed by the Reverse Engineering method into a computer model. The deformations were compared on both models, at the same cross sections. The anthropometric model of operator was placed inside the reconstructed model.
Keywords: falling-object protective structures (FOPS), virtual prototyping, reverse engineering, human body modelling, finite element method.

The autoprogressive and cumulative algorithms, basing on `on line' formulation of patterns and the training of NMM (Neural Material Model), are evaluated to be comparable in case of uniaxial stress state problems. It is shown in the paper that for the plane stress boundary value problems the autoprogressive algorithm, in which NMM is trained for each load increment, is superior to the cumulative algorithm. In order to formulate a small NMM and accelerate the convergence of the iteration of computed equilibrium paths to the monitored paths, a smaller number of inputs NMM is discussed and a modified selection of the training patterns is applied. A new approach is proposed with respect to the designing of NMMs, combining the 'on line' and 'off line' training of neural networks. The discussed problems are illustrated with two study cases. They are related to the formulation of NMMs for the identification of equivalent materials in plane trusses made of the Ramberg-Osgood material and for elasto-plastic plane stress boundary value problems.
Keywords: neural networks; material model; constitutive modelling.

Stochastic Schemata Exploiter (SSE) is one of the evolutionary optimization algorithms for solving the combinatorial optimization problems. We present the Extended SSE (ESSE) algorithm which is composed of the original SSE and new ESSE operations. The ESSE is compared with the original SSE, simple genetic algorithm (SGA), and GA with Minimal Generation Gap (MGG) in some test problems in order to discuss its features.
Keywords: Genetic Algorithm (GA), Stochastic Schemata Exploiter (SSE), Extended SSE (ESSE), Minimal Generation Gap (MGG).

This paper describes the application of the method of fundamental solutions to the solution of the boundary value problems of the two-dimensional steady heat transfer with heat sources. For interpolation of an inhomogeneous term in Poisson equation the radial basis functions are used. Three cases of boundary value problems are solved and five cases of radial basis functions are used. For comparison purposes the boundary value problems for which exact solution exists were chosen. Application of method of fundamental solutions with boundary collocation and radial basis function for solution of inhomogeneous boundary value problems introduces some number of parameters related with these tools. For optimal choosing of these parameters the genetic algorithm is used. The results of numerical experiences related to optimal parameters are presented.
Keywords: method of fundamental solutions, meshless method, radial basis functions, steady heat transfer, Poisson's equation, genetic algorithm, particular solution.

To design foundations, embankments and other soil structures, geotechnical engineers require methods of assessing engineering properties of soils. Some of the more complex phenomena that occur in soils have often been difficult to recreate in a laboratory: seismic activity, vibration, unsaturated condition, control of principal stresses etc. are areas which have proven difficult to replicate, despite their importance of being understood. This was partly due to the lack of test systems capable of reproducing these effects and the complexity of test systems that were developed to carry out such work. A number of advanced computer/software controlled systems allow the geotechnical engineer to perform the most complex test regimes via a user-friendly software interface. However, it is difficult to determine firstly parameters needed, e.g. shear speed in soil triaxial testing. In this paper we represent a new approach to determine this shear speed by solving the inverse problem using testing results obtained by the forward procedure. Direct search method, i.e. Adaptive Neuro-Fuzzy Inference System (ANFIS), is developed and applied to soil triaxial shear tests. It allows us to use the advanced sensor and actuator technologies in order to change the traditional triaxial shear apparatus from a mechanical system to a mechatronics system in next work.
Keywords: soil triaxial testing, shear speed, fuzzy logic, neuro-fuzzy inference system.

It has been recognized by many authors that the enforcement of the essential boundary conditions is not an easy task, when it comes to moving least square (MLS)-based meshfree methods. In particular, the modelling of non-linear problems requires high approximation accuracy in order to obtain a solution. This paper addresses the boundary approximation accuracy of MLS-based meshfree methods and shows more specifically its significance with respect to the imposition of essential boundary conditions by the penalty, the Lagrange multiplier method and their combination which results in a modified variational principle. The later is augmented by a stabilization term which uses individual stabilization parameters determined for each numerical integration point by an iteration procedure. This methodology is demonstrated on shell deformations in non-linear structural mechanics involving the Green strain tensor and two different hyper-elastic material laws.
Keywords: Meshfree methods, moving least square method, essential boundary conditions, shell analysis.

A presentation of the modern issues related to the symbolic computing is contained here together with the detailed discussion of its application to the education of various scientific and engineering academic disciplines. The future expansion of the symbolic environment is described here on the basis of their historical and modern developments presentation. As it is shown on the example of the MAPLE system, symbolic computational environments play the very important role in supporting the lectures and the classes in the computer labs. Those environments may be also very useful in teaching basic natural sciences in all those cases, when some algebraic or differential equations appear, must be solved and their results should be precisely discussed. The application of the MAPLE and similar computer systems in the engineering education seems to be unquestionable now and some examples are contained here to show how to improve the lectures and make them very interesting and exciting. The key feature offered by the symbolic computing is the opportunity to discover the knowledge that the students may do by themselves, when they are specifically leaded by the instructors.
Keywords: symbolic computations, computer science, computers in education.

In the paper the stationary 2D inverse heat conduction problems are considered. To obtain an approximate solution of the problems three variants of the FEM with harmonic polynomials (Trefftz functions for Laplace equation) as base functions were used: the continuous FEMT, the non-continuous FEMT and the nodeless FEMT. In order to ensure physical sense of the approximate solution, one of the aforementioned physical aspects is taken into account as a penalty term in the functional, which is to be minimized in order to solve the problem. Three kinds of physical aspects that can smooth the solution were used in the work. The first is the minimization of heat flux jump between the elements, the second is the minimization of the defect of energy dissipation and third is the minimization of the intensity of numerical entropy production. The quality of the approximate solutions was verified on two test examples. The method was applied to solve inverse problem of stationary heat transfer in a rib.

The Trefftz method pioneered by Trefftz in 1926 is described as follows: The particular solutions or the fundamental solutions are chosen, a linear combination of those functions is regarded as an approximate solution of partial differential equations (PDEs), and their expansion coefficients are sought by satisfying the interior and exterior boundary conditions. When the solution domain is not rectangular or sectors, the piecewise particular solutions may be chosen in different subdomains, and some coupling techniques must be employed along their interior boundary conditions. In Li et al. [1], the collocation method is used for the Trefftz method, to lead to the collocation Trefftz method (i.e., the indirect Trefftz method). In this paper, we will also discuss other four coupling techniques: (1) the simplified hybrid techniques, (2) the hybrid plus penalty techniques, (3) the Lagrange multiplier techniques for the direct Trefftz method, and (4) the hybrid Trefftz method of Jirousek [2] and Qin [3]. Error bounds are derived in detail for these four couplings, to achieve exponential convergence rates. Numerical experiments are carried out, and comparisons are also made. [1] Z.C. Li, T.T. Lu, H.Y. Hu, A.H.-D. Cheng, Trefftz and Collocation Methods, WITpress 2008. [2] J. Jirousek, Comput. Meth. Appl. Mech. Engrg., 14: 65-92, 1978. [3] Q.H. Qin, The Trefftz Finite and Boundary Element Methods, WITpress 2000.

This paper describes the application of the method of fundamental solutions for 2-D harmonic and biharmonic problems. Also, genetic algorithm is presented as a numerical procedure used for the determination of source points positions. Choosing good locations of source points is crucial in the MFS as it has a great impact on the quality of the solution. Genetic algorithm is applied in order to find such an arrangement of source points, which provides the solution of sufficient accuracy.
Keywords: method of fundamental solutions, genetic algorithm, multicriteria optimization, Motz problem, biharmonic problem.

The main purpose of this paper is the investigation of the boundary effect in bending problem of perforated plates and its influence on the effective flexural rigidity. The considered strip plate is loaded by constant uniformly distributed load and has square penetration pattern. The boundary value problem for determination of deflection repeated element of structure is solved by means of boundary collocation method with a use of the special purpose Trefftz functions. These functions fulfil exactly not only governing equation but also boundary conditions on holes and some symmetry conditions. The number of perforations is discussed on effective rigidity.
Keywords: Trefftz method, special purpose Trefftz functions, perforated plate, effective flexural rigidity.

The TRBF's are radial functions satisfying governing equation in the domain. They can be used as interpolation functions of the field variables especially in boundary methods. In present paper discrete dipoles are used to simulate composite material reinforced by stiff particles using with boundary point collocation method which does not require any meshing and any integration. The better the interpolation function satisfies also the boundary conditions, the more efficient it is. In examples it is shown that a triple dipole (which is a TRBF) located into the center of the particle can approximate the inter-domain boundary conditions very good, if the particles are not very close to each other and their size is not very different. In general problem the model can be used as very good start point for international improvements in refined model. Composite reinforced by short fibres with very large aspect ratio continuous TRBF were developed. They enable to reduce problem considerably and to simulate complicated interactions for investigation such composites.
Keywords: fibre reinforced composites, meshless method, Trefftz Radial Basis Functions, continuous source functions.

When solving complex boundary value problems, the primary advantage of the Trefftz method is that Trefftz functions a priori satisfy the governing differential equations. For the treatment of three-dimensional isotropic elasticity problems, it is proposed that the bi-harmonic solutions in Boussinesq's method can be expressed as half-space Fourier series to bypass the difficulties of integration. A total of 29 Trefftz terms for each component of the displacement vectors are derived from the general solutions of the elasticity system. Numerical assessments on the proposed formulations are performed through two examples (a cubic and a cylindrical body). Results are compared with those from the method of fundamental solutions (MFS) and the commercial finite element method (FEM) software STRAND 7, suggesting that Trefftz functions can provide pseudo-stability, faster convergence and reduced error margins.

The paper presents solutions of a two-dimensional wave equation by using Trefftz functions. Two ways of obtaining different forms of these functions are shown. The first one is based on a generating function for the wave equation and leads to recurrent formulas for functions and their derivatives. The second one is based on a Taylor series expansion and additionally uses the inverse Laplace operator. Obtained wave functions can be used to solve the wave equation in the whole considered domain or can be used as base functions in FEM. For solving the problem three kinds of modified FEM are used: nodeless, continuous and discontinuous FEM. In order to compare the results obtained with the use of the aforementioned methods, a problem of membrane vibrations has been considered.
Keywords: Trefftz functions, wave functions, inverse operations, FEM.

This paper is concerned with hybrid stress elements in the context of modelling the behaviour of plates subject to out of plane loading and based on Reissner?Mindlin assumptions. These elements are considered as equilibrium elements with statically admissible stress fields of which Trefftz fields form a special case. The existence of spurious kinematic modes in star patches of triangular elements is reviewed when boundary displacement fields are defined independently for each side. It is shown that for elements of moment degree > 1, the spurious modes for stars only exist at specific locations and/or for certain configurations. The kinematic properties of these modes are used to define sufficient conditions for the stability of a complete mesh of triangular elements. A method is proposed to check mesh stability, and introduce local modifications to ensure overall stability.

The displacement and stress models of the hybrid-Trefftz finite element formulation are applied to the dynamic analysis of two-dimensional bounded and unbounded saturated porous media problems. The formulation develops from the classical separation of variables in time and space. A finite element approach is used for the discretization in time of the governing differential equations. It leads to a series of uncoupled problems in the space dimension, each of which is subsequently discretized using either the displacement or the stress model of the hybrid-Trefftz finite element formulation. As typical of the Trefftz methods, the domain approximation bases are constrained to satisfy locally all domain equations. An absorbing boundary element is adopted in the extension to the analysis of unbounded media. The paper closes with the illustration of the application of the alternative hybrid-Trefftz stress and displacement elements to the solution of bounded and unbounded consolidation problems.

The paper deals with solution of 3D problems with stress concentration using the Trefftz functions. The modelled stress concentrators are holes and cavities of spherical and ellipsoidal shapes. Moreover, the random spherical cavity microstructure is modelled. The Method of External Finite Element Approximation (MEFEA) is applied to simulate detailed stress state of mentioned stress concentrators. This boundary-type method was developed to build special approximation functions that are associated with surface which causes the stress concentration. The method does not need discretization by classical finite elements, however, instead of elements the domain is divided into Trefftz type subdomains. The displacement and force boundary conditions are met only approximately whereas the governing equations are fulfilled exactly in the volume for linear elasticity, making it possible to assess accuracy in terms of error in boundary conditions.

A contact algorithm, based on the hybrid-Trefftz (HT) finite element method (FEM), is developed for the solution of contact problems with Coulomb friction. Contact conditions are directly imposed with the aid of a direct constraint approach. On the other hand, static condensation technique is used to reduce the contact system to a smaller one which involves nodes within the potential contact surfaces only so that it may save computing time significantly. The final contact interface equation is constructed by considering contact conditions as additional equations. An incremental-iterative algorithm is introduced to determine proper load increments and find correct contact conditions. The applicability and accuracy of the proposed approach are demonstrated through three numerical problems.

This paper reports on the development of a novel wave based prediction technique for the steady-state sound radiation analysis of three-dimensional semi-infinite problems. Instead of simple polynomial shape functions, this method adopts an indirect Trefftz approach, in which it uses the exact solutions of the governing differential equation for the field variables approximation. Since a fine discretization is no longer required, the resulting wave based models are substantially smaller than the element-based counterparts. Application of the proposed approach to various validation examples illustrates an enhanced computational efficiency as compared with element-based methods.

Investigation of crack propagation can sometimes be a crucial stage of engineering analysis. The T-element method presented in this work is a convenient tool to deal with it. In general, T-elements are the Trefftz-type finite elements, which can model both continuous material and local cracks or inclusions. The authors propose a special T-element in a form of a pentagon with shape functions analytically modelling the vicinity of the crack tip. This relatively large finite element can be surrounded by even larger standard T-elements. This enables easy modification of the rough element grid while investigating the crack propagation. Numerical examples proved that the "moving pentagon" concept enables easy automatic generation of the T-element mesh, which facilitates observation of crack propagation even in very complicated structures with many possible crack initiators occurring for example in material fatigue phenomena.

The problem on proper and forced vibrations of the loosely leant rectangular orthotropic plate with massive circular inclusion is considered in the paper. The flexure of the plate is described by modified equations of Timoshenko's theory of plates. Numerical solution of the problem is found by the indirect method of boundary elements based on the sequential approach to constructing generalized functions and on collocation method. The problem can be generalized on the case of arbitrary located inclusion and the arbitrary number of them. The influence of the mass of the massive circular inclusion on the proper frequencies of the plate is investigated.

In this paper some types of nonlinear potential problems are discussed and some of these problems are solved by the Trefftz method. The attention is paid to Fundamental Solutions Method (FSM) supported by Radial Basis Functions (RBF) approximation. Application of FSM to nonlinear boundary problem requires certain modifications and special algorithms. In this paper two methods of treating the nonlinearity are proposed. One on them is Picard iteration. Due to some problems of application of this method the Homotopy Analysis Method (HAM) is implemented for nonlinear boundary-value problems. The results of numerical experiment are presented and discussed. The conclusion is that the method based on FSM for solving nonlinear boundary-value problem gives result with demanded accuracy.

The recurrent approach constructed via the stochastic central difference (SCD) is a very fast method for analyzing non-stationary random responses. However, the computational results depend to a great extent upon the discrete time-step size. A new recurrent approach is proposed in this report. It is based on the theory of linear differential equations. Theoretical analysis shows that this algorithm is unconditionally stable for all damped systems. Two examples show that the proposed approach is not sensitive to the time-step.


Keywords: non-stationary response, linear differential equations, variance, finite difference, stochastic central difference.

In this article one of the greatest generalized methods for establishing the equilibrium equations of a rigid body and the set of rigid bodies is proposed. It is related to six equations of moments of force about six the edges of a reference tetragon. It is possible to obtain different alternatives by substituting the force moment-equation for the force project-equation. Four different forms of equilibrium are established. It is important writing equilibrium equations of bodies possible to apply the special software as Mathcad, Maple.


Keywords: equilibrium of a rigid body, equilibrium of mechanical system, matrix method, frame tetragon, generalized tetragon frame of axis.

Graph theory has many applications in structural mechanics and there are also numerous topological transformations which make the related problems simpler. The skeleton graph and natural associate graph of finite element models are among such transformations. These transformations can efficiently be used for nodal and element ordering of regular finite element models. Natural associate graph and its mesh basis play a key role in optimal finite element analysis by combinatorial force method. In this paper, an efficient method is presented for generation of skeleton graph, natural associate graph as well as their mesh bases for finite elements models, using graph and digraph products.


Keywords: finite elements, graph products, digraph products, associate graph, mesh bases.

The presented method is used in finite-element analysis software developed for multicore and multiprocessor shared-memory computers, or it can be used on single-processor personal computers under the operating systems Windows 2000, Windows XP, or Windows Vista, widely popular in small or mediumsized design offices. The method has the following peculiar features: it works with any ordering; it uses an object-oriented approach on which a dynamic, highly memory-efficient algorithm is based; it performs a block factoring in the frontal matrix that entails a high-performance arithmetic on each processor and ensures a good scalability in shared-memory systems. Many years of experience with this solver in the SCAD software system have shown the method's high efficiency and reliability with various large-scale problems of structural mechanics (hundreds of thousands to millions of equations).


Keywords: finite element method, large-scale problems, multifrontal method, sparse matrices, ordering, multithreading.

A new method is proposed to identify the distinct mechanisms derived from a given kinematic chain in this paper. The kinematic chains and their derived mechanisms are presented in the form of a flow matrix. Two structural invariants, sum of the absolute values of the characteristic polynomial coefficients (SCPC) and maximum absolute value of the characteristic polynomial coefficient (MCPC) are determined using the software MATLAB. These invariants are used as the composite identification number of a kinematic chain and mechanisms and clearly identify the distinct mechanisms derived from the family of 1-F, 8-links and 10-links KC as well as 2-F, 9-links simple joined KC. This study will help the designer to select the best possible mechanism to perform the specified task at the conceptual stage of design. The proposed method does not require any test for isomorphism separately. Some examples are provided to demonstrate the effectiveness of this method.


Keywords: kinematic chain (KC), distinct mechanism (DM), flow matrix, SCPC, MCPC.

This paper presents the results of an extensive investigation evaluating and improving the development of artificial neural network (ANN) models for turbomachinery design purposes. A set of 1100 differing axial compressor geometries based on 5 single-stage compressor rigs was prepared. Computations with the mean line analysis tool AXIAL™ took place to determine the according compressor maps defined by 15 operating points each. The challenge of ANN model development in terms of dimensionality reduction (feature selection), data normalization, defining the networks necessary plasticity, and network training is discussed using the example of three different models. As a result, the first model is able to predict the total pressure loss of the rotor blade row with a mean magnitude of the relative error (MMRE) of 3.6%. The second model predicts the total pressure ratio with an average accuracy of 0.8%. The third and last model was trained to predict basic geometrical parameters by presenting the load level and the performance data as an input. The achieved MMRE varied between 2.4% and 5.6% in respect of the particular output variable. The results show that ANNs are applicable to develop efficient models for turbomachinery design and analysis purposes, respectively.

This paper deals with homogenization of non linear fibre-reinforced composites in the coupled thermomechanical field. For this kind of structures, i.e. inclusions randomly dispersed in a matrix, the self consistent methods are particularly suitable to describe the problem. Usually, in the framework of the self consistent scheme the homogenized material behaviour is obtained with a symbolic approach. For the non linear case, that method may become tedious. This paper presents a different, fully numerical procedure. The effective properties are determined by minimizing a functional expressing the difference (in some chosen norm) between the solution of the heterogeneous problem and the equivalent homogenous one. The heterogeneous problem is solved with the Finite Element method, while the second one has its analytical solution. The two solutions are written as a function of the (unknown) effective parameters, so that the final global solution is found by iterating between the two single solutions. Further, it is shown that the considered homogenization scheme can be seen as an inverse problem and Artificial Neural Networks are used to solve it.


Keywords: Generalized Self-Consistent-Like method, non-linear homogenization, Artificial Neural Networks, inverse problems, thermo-mechanical analysis, multiscale modelling, unsmearing.

The paper deals with the analysis of residual stress fields in the riveted joint and the estimation of the internal stress magnitude releasing by partial and complete removing of the rivet material. Stress relieving causes deformations around the rivet hole, which can be measured and compared to the deformation state before removal. Numerical FE simulations of the upsetting process are carried out to determine the residual stress and strain fields. The contact with friction is defined between the mating parts of the joint. Non-destructive testing methods are used in combination with numerical calculations.


Keywords: riveted joint, FEM local model, destructive and non-destructive methods.

The paper presents a new method of approximate solving of the two- and three-dimensional thermoelasticity problems in a finite body. The method presented here can be used for solving direct and inverse problems as well. System of thermoelasticity equations is reduced to the system of wave equations where the temperature occurs as inhomogeneity in one of them. The thermal field is approximated by linear combination of heat polynomials (Trefftz functions for heat conduction equation). The system of wave equations is solved by means of wave polynomials (Trefftz functions for wave equation). Convergence of the T-functions method is proved. The procedure of solving direct and inverse thermoelasticity problems by means of Trefftz functions is tested on an example. Sensitiveness of the method according to data disturbance was checked.

The paper presents a specific technique of solving the non-homogenous wave equation with the use of Trefftz functions for the wave equation. The solution was presented as a sum of a general integral and a particular integral. The general integral was expressed in the form of a linear combination of Trefftz functions for the wave equation. In order to obtain the particular integral polywave functions were used. They were generated by using the inverse operator L^-1 of the equation taking into consideration the Trefftz functions.


Keywords: polywave functions, Trefftz functions, wave polynomials, wave equation.

In this paper a fast multipole boundary element method (FMBEM) analysis of internal stress in twodimensional linear elastic structures is presented. The expansions of the potentials occurring in the stress integral equation are obtained by the differentiation of local series built for the displacement equation potentials, and application of the strain-displacement and stress-strain relations. Results of the analysis are presented. To illustrate the accuracy of the method a stress concentration problems are considered, which are a square plate with a circular hole under tension, and a gear. The application of the FMBEM can reduce the analysis time in relation to the conventional BEM case, providing similar accuracy. Presented method can be applied in the BEM analysis of non-linear structures, which requires the evaluation of internal strains or stresses.


Keywords: linear elasticity, stress analysis, boundary element method, fast multipole method.

This paper presents the model based on the theory of multicomponent media that allows modelling of rebar corrosion processes. The presented model extends and consolidates the dissertations that have been described in the papers [8-10]. The aim of the present work is a creation of the model consistent with the thermodynamics of multicomponent media with internal parameters, allowing description and numerical modelling of reinforced concrete structures degradation as the result of corrosion by using FEM.


Keywords: theory of plasticity, corrosion of reinforced concrete, mass transport, concrete cover splitting.

The problem of thermal stresses in a hollow cylinder is considered. The problem is two-dimensional and the cross-section of the hollow cylinder is approximated as a long and thin rectangle as the ratio of the inner and outer radiuses is close to one. On the outer boundary of the hollow cylinder the heat source moves with a constant velocity. In the case of the rectangle the heat source moves on the upper side and the conditions of equality of temperatures and heat fluxes are assumed on the left and right boundaries. The stresses are to be found basing on the temperature measured inside the considered region, which means that an inverse problem is considered. Both for the temperature field and the displacements and stresses the finite element method is used. Thermal displacement potentials are introduced to find displacements and stresses. In order to construct the base functions in each element the Trefftz functions are used. For the temperature field the time-space finite elements are used and for the thermal displacement potentials the spatial elements are applied. Thanks to the use of the Trefftz functions a low-order approximation has given a solution very close to the exact one.


Keywords: Trefftz function, finite element method, thermal stresses, inverse problem, heat polynomials.

The sensitivity analysis of transient temperature field in the tissue domain with respect to its thermophysical parameters is discussed. In particular, the influence of tissue specific heat, thermal conductivity, perfusion rate and metabolic heat source on the temperature distribution is considered. In order to determine the influence of variations of these parameters on temperature distribution the direct approach of sensitivity analysis is applied. Perfusion rate is treated as dependent on tissue injury which is estimated on the basis of Arrhenius integral. On the stage of numerical realization the boundary element method is used. In the final part of paper the results obtained are shown.


Keywords: bioheat transfer, Arrhenius scheme, tissue necrosis, boundary element method.

The main aim of this paper is to demonstrate the application of the generalized stochastic perturbation technique to model the lognormal random variables in structural mechanics. This is done to study probabilistic characteristics of the eigenvibrations for the high telecommunication towers with random stiffness, which are modeled as the linear elastic 3D trusses. The generalized perturbation technique based on the Taylor expansion is implemented using the Stochastic Finite Element Method in its Response Function version. The main difficulty here, in a comparison to this technique previous applications, is a necessity of both odd and even order terms inclusion in all the Taylor expansions. The hybrid numerical approach combines the traditional FEM advantages with the symbolic computing and its visualization power and it enables for a verification of probabilistic convergence of the entire computational procedure.


Keywords: stochastic dynamics, Stochastic Finite Element Method, response function method, stochastic perturbation technique.

The aim of the present paper is to revisit some known truss optimization problems by applying the genuine Strongin and Sergeyev's algorithm of the global search [8]. By employing the space-filling Hilbert-Peanotype curves, the wide class of non-convex and multidimensional constrained global optimization problems is reduced to one-dimensional ones. Then, the global minimum of the objective function in one-dimensional problem can be effectively found by means of Multivariate Index Method (MIM) that can be treated as a special version of one-dimensional Global Search Algorithm (GSA) over the set of open intervals adopted to constrained problems.

The paper is devoted to the problems with quality of numerical modeling for two-dimensional incompressible flow around two models of buildings with different heights. The calculations have been made with use of the turbulence model k-ε in the standard version and with the Finite Volume Method. The quality evaluation for the calculation is based on the comparison of the results with measurements in a wind tunnel. Hence, in this paper there have been presented the graphs of averaged velocities which are results of author's own measurements, as well as the graphs presenting the error in the calculated flow velocities. The main conclusion drawn from the research is that the flow around two models is more complicated than the flow around the single one and therefore the calculation results for the set of models are less accurate in comparison with the ones obtained for the single model.

This paper presents a simple and efficient method for finding complex roots of dispersion equations occurring in many problems of elastodynamics. The method is characterized by high accuracy in root finding and absence of restrictions on function representation. The essence of the method is explained geometrically; initial guesses are found as the solutions to the appropriate problems of elastostatics. Numerical solutions to dispersion equations are obtained for two elastic isotropic waveguides: a plate of infinite cross-section and a rod of rectangular cross-section. For an infinite plate, the calculated results are in full conformity with those obtained by Newton-Raphson and bisection methods. For a waveguide of rectangular cross-section, the earlier unsolved problem of finding complex roots of dispersion equations is solved by the proposed method.

Parallel processing, the method of considering many small tasks to solve one large problem, has emerged as a key enabling technology in modern computing. Parallel computers can be simply classified into shared memory systems and distributed memory systems. The shared memory computers have a global memory attached to a number of processors enabling several processors to work concurrently on different parts of the same computation. A different approach towards building large parallel computers is to connect several processors via a network. Each processor has its own local memory. The cost of building these computers increases with the number of processors. The distributed memory multiprocessor systems are scalable over a wider range than the shared memory computers. There are many intermediate computer architectures, each with its distinct programming model. Common between them is the notion of message passing. In all parallel processing, data must be exchanged between cooperating tasks. Several research groups have developed software packages such as Parallel Virtual Machine (PVM), the Message Passing Interface (MPI), and others. In this paper, hardware implementation of parallel information processing is introduced by application of a multicellular computer idea, in which working cells were composed of general purpose one-chip microcomputers. The influence of the cellular computer's structure size on quality and efficiency of calculations was analyzed. The optimal structure consisted of 4x4 cells which guaranteed achieving satisfactory recurrence of results for an assumed set of working parameters. This paper presents an idea and the results of trial computations regarding the problem of slope stability evaluation by variational calculus assisted by genetic algorithm.


Keywords: hardware implementation, slope stability, variational calculus, parallel genetic algorithm.

Compaction is the method of in-situ soil modification to improve its engineering properties. Two key compactibility parameters are: the maximum dry density ρ_{d max} and the corresponding optimum water content w_opt. They are basic parameters for designing, constructing and controlling the compaction quality of earth structures (e.g. earth dams, highway embankments). Soil compactibility can be determined from the laboratory compactibility curve basing on Proctor's test. However, this test is destructive, time-consuming and expensive. To facilitate the determination of the cohesionless soil compactibility parameters, correlations between ρ_{d max} and w_opt and the basic parameters characterizing soil grain-size distribution (C_U, D₁₀, D₂₀, D₃₀, D₄₀, D₅₀, D₆₀, D₇₀, D₈₀, and D₉₀) were developed. Artificial neural networks are applied to determine models with good prediction quality. The neural models have higher accuracy than the classic statistical models.


Keywords: geotechnical engineering, cohesionless soil, compactibility characteristics, Artificial Neural Network.

The paper is devoted to the shape optimization of piezoelectric and electro-thermo-mechanical devices by the use of multiobjective evolutionary algorithm. In this paper, special implementation of multiobjective evolutionary algorithm is applied (MOOPTIM). Several test problems are solved in order to test efficiency of the algorithm. The results are compared with the Non-Dominated Sorting Genetic Algorithm (NSGA-II). The objective function values are calculated for each chromosome in every generation by solving a boundary value problem for the piezoelectricity and electro-thermal-mechanical analysis. In order to solve the boundary value problems, the finite element method is used. Different functionals based on the results derived from coupled field analyses are formulated. The aim of the multiobjective problem is to determine the specific dimensions of the optimized structures. Numerical examples for multiobjective shape optimization are enclosed.


Keywords: multiobjective optimization, evolutionary algorithm, piezoelectricity, electro-thermomechanical analysis, coupled problems, finite element method, MEMS.

The paper deals with the identification of material constants in simple and hybrid laminates. It is assumed that identified constants are non-deterministic and can be described by means of different forms of the information granularity represented by interval numbers, fuzzy numbers or random variables. The Two- Stage Granular Strategy combining global (Evolutionary Algorithm) and local (gradient method supported by an Artificial Neural Network) optimization techniques is used to solve the identification problems. Finite Element Method in the granular form is used to solve the direct problem for laminates. Modal analysis methods are employed to collect measurement data


Keywords: laminate, information granularity, identification, evolutionary algorithm, artificial neural network, interval numbers, fuzzy numbers, random variables.

In the paper, the identification problems connected with estimation of cast iron and mould thermophysical parameters are discussed. The additional information necessary to solve the problem results from the knowledge of cooling (heating) curves at the set of points from casting (mould) domain. The course of cooling (heating) curves results from the temperature measurements done in the real conditions of technological process, but at the present stage of research the numerical solution of direct problem plays the role of measured temperatures. In this place the problem of optimal sensors position in a system castingmould appears. Both the choice of measuring points and also the solution of inverse problem, using the gradient methods, require the application of sensitivity analysis methods. The theoretical considerations are illustrated by the examples of computations.


Keywords: solidification process, numerical techniques, sensitivity analysis, inverse problems, identification methods.

The computational accuracy of three versions of the method of fundamental solutions (MFS) is compared. The first version of MFS is based on the Laplace transformation of the governing differential equations and of the boundary conditions. The second version of MFS is based on the fundamental solution of the governing differential equation and discretization in time. The third method approximates the temperature time derivative by finite difference scheme. As the test problems the 2D boundary-initial-value problems (2D_BIVP) in square rectangular region Ω with known exact solutions are considered. Our numerical experiments show that all discussed methods achieve relatively accurate approximate solution but the third one offers less computational complexity and better efficiency.


Keywords: method of fundamental solutions, meshless method, transient heat conduction, initial- boundary volume problem, boundary collocation method.

An efficient numerical procedure is proposed to obtain mean-square stability regions for both single-degree-of-freedom and two-degree-of-freedom linear systems under parametric bounded noise excitation. This procedure reduces the stability problem to a matrix eigenvalue problem. Using this approach, ranges of applicability to the well-known stochastic averaging method are discussed. Numerical results show that the small parameter size in the stochastic averaging method can have a significant effect on the stability regions. The influence of noise on the shape of simple and combination parametric resonances is studied.


Keywords: random vibration, stochastic averaging, mean square stability, bounded noise.

The torsion of bars with multiply connected cross section by means of the method of fundamental solutions (MFS) is considered. Random numbers were used to determine the minimal errors for MFS. Five cases of cross sections are examined. The numerical results for different cross sectional shapes are presented to demonstrate the efficiency and accuracy of the method. Non-dimensional torsional stiffness was calculated by means of numerical integration of stress function for one of the cases. This stiffness was compared with the exact stiffness for the first case and with the stiffness resulting from Bredt's formulae for thin-walled cross sections.

This paper presents a coupling technique for integrating the fractal finite element method (FFEM) with element-free Galerkin method (EFGM) for analyzing homogeneous, isotropic, and two-dimensional linearelastic cracked structures subjected to Mode I loading condition. FFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus ensuring convergence of the proposed coupled FFEM-EFGM. The proposed method combines the best features of FFEM and EFGM, in the sense that no structured mesh or special enriched basis functions are necessary and no post-processing (employing any path-independent integrals) is needed to determine fracture parameters such as stress-intensity factors (SIFs) and T -stress. The numerical results show that SIFs and T -stress obtained using the proposed method, are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack-length to width ratio, on the quality of the numerical solutions.


Keywords: crack, Element-free Galerkin method, Fractal Finite Element Method, Stress-Intensity Factor, T -stress, Linear-Elastic Fracture Mechanics, Mode I.

The paper presents an analysis of the efficiency of the application of heap lists data structures to the 2D triangular mesh generation algorithms. Such efficiency is especially important for the frontal methods for which the size of the generated mesh is controlled by a prescribed function in the considered domain. In the presented approach two advancing front procedures are presented: first for points insertion and the second for the Delaunay triangulation. If the heap lists are applied to the minimal size of frontal segment selection, a better quality mesh is obtained.


Keywords: tree and lists data structure, frontal methods, Delaunay triangulation, grid generation, mesh adaptation.

The main goal of the paper is to analyze convergence of a remeshing scheme evaluated by the author [8] on the example of a potential flow around a profile. It is assumed that flow is stationary, irrotational, inviscid and compressible. The problem is led to solving nonlinear differential equation with additional nonlinear algebraic equation representing the so called Kutta-Joukovsky condition. For adaptation a remeshing scheme is applied. For every adaptation step mesh is generated using grid generator [7], which generates meshes with mesh size function. The mesh size function is modified at every adaptation step by nodal values of the error indicator interpolation. The nonlinear algebraic system of equations obtained from discretizing of the problem, is solved by the application of the Newton-Raphson method.


Keywords: finite element method, fluid mechanics, grid generation, remeshing, Kutta-Joukovsky condition.

For man, possessing the ability to recognize the specific situation that has arisen at any instant of time and taking the appropriate decision without using a mathematical model is what ?adaptation? means. Adaptive principles are being extended to more complex systems in widely different areas, in which we need to replace the traditional metaphor of a fixed environment with a dynamic and constantly changing one. Each mechatronic system, for example, is usually, faced with a multiplicity of choices and objectives of the system change with it. Its modeling requires more than a mathematical model that is based on clear definitions and axioms using the rules of logic deduction theory. To solve this problem, the new concept of system integration by software control, such as real-time multi-tasking operating system using fuzzy logic, is emphasized in the education of modem mechatronics engineering. In this paper, I would like to return, firstly, to the fundamental element of truth measure, which we can use as basis for constructing a way to spread the binary philosophy rather than its rejecting and to increase our ability to describe the real world. Next, in order to explanation into details one aspect of real-time software using fuzzy logic, applied in control of mechatronic systems, we present a fuzzy control technology that combines artificial intelligence and control methodologies. It achieves control purposes based on expert knowledge and experience expressed in the form of IF-THEN rules (Sugeno-type) or neural networks using neuro- fuzzy based intelligent control scheme in order to create a real-time-adaptive control process. Application of this technology is presented in numerical example of trajectory control of PUMA 560 robot manipulators using Fuzzy Artificial Neural Network, FANN, rather than using Artificial Neural Network, ANN, only.


Keywords: fuzzy control, neural network, fuzzy-neural network, mechatronics, real-time software.

The paper presents the method of fundamental solutions (MFS) for solving electromagnetic problems. We compare the MFS with the method of boundary integral equations in solution of potential problems. We demonstrate the MFS technique together with the Laplace transform in application to the problem of scattering of electromagnetic pulses. A modification of the MFS - the method of approximate fundamental solutions (MAFS) is also considered in the paper. The method is applied to axisymmetric field problems. Numerical examples justifying the methods are presented.


Keywords: fundamental solution, potential field, measurement data, electromagnetic scattering, axisymmetric problems.

An assessment of structural reliability requires multiple evaluations of the limit state function for various realizations of random parameters of the structural system. In the majority of industrial applications the limit state functions cannot be expressed explicitly in terms of the random parameters but they are specified using selected outcomes of the FE analysis. In consequence, in order to be useful in practice, a structural reliability analysis program should be closely integrated with a FE module or it should be interfaced with an advanced external FE program. When the FE source code is not available, which is usually the case, the only option is to establish a communication between the reliability analysis program and an external FE software through the batch mechanism of data modification, job submission and results extraction. The main subject of this article is to present the reliability analysis capabilities of STAND software, which is being developed in the Institute of Fundamental Technological Research of Polish Academy of Sciences. A special emphasis is put on the issues related to its interfacing with external general purpose FE codes. It is shown that when shape type random variables are used, leading to modifications of the FE mesh, or when the limit state function contains numerical noise, standard algorithms for localizing the design point often fail to converge and a special method based on some response surface approximation is needed. A proposition of such a strategy that employs an adaptive response surface approximation of the limit state function is presented in this article. Development of a reliability analysis program is a challenging project and calls for such a code organization, which would facilitate a simultaneous work of many programmers and allow for easy maintenance and modifications. The so-called object-oriented programming seems to provide a convenient framework to realize these objectives. The object-oriented approach is used in STAND development. The advantages of this programming paradigm and a short description of the STAND's class hierarchy are presented in the text. The study is concluded with two numerical examples of interfacing STAND with state of the art commercial FE programs.

One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to estimate the overall response of particulate composites with rigid- brittle interfaces are investigated. The first approach is based on a detailed numerical representation of a composite microstructure. The resulting problem is discretized using the Finite Element Tearing and Interconnecting method, which, apart from computational efficiency, allows for an accurate representation of interfacial tractions as well as mutual inter-phase contact conditions. The candidate solver employs the assumption of uniform fields within the composite estimated using the Mori-Tanaka method. A set of representative numerical examples is presented to assess the added value of the detailed numerical model over the simplified micromechanics approach.


Keywords: first-order homogenization, particulate composites, debonding, FETI method, micromechanics.

Recent developments in Computational Fluid Dynamics (CFD) increased interest in quantifying quality of the numerical models. One of the necessary steps is the so-called code validation procedure, an assessment of a numerical simulation by comparisons between simulation results and laboratory measurements. The focus of the present review is application of modern full field experimental techniques, mostly based on the digital image analysis, in validating numerical solutions of complex flow configurations. Each validation procedure opens new issues of quantifying its outcome to find directions for model updating, limits of computer simulation quality, and to perform uncertainty quantification.


Keywords: CFD validation, experimental methods.

In this paper an approach of optimization of suspension system parameters is described. Taking into consideration the stiffness and damping coefficients of springs and shock absorbers of a heavy road transport vehicle semitrailer, process of adjusting those values has been undertaken by means of the response surface methodology and a desirability function application, supported by the sensitivity computations. Two different methods of constructing metamodels: Kriging and polynomial regression have been tested and compared with a set of results obtained from the numerical multibody dynamic analysis. The objective of the undertaken efforts was to minimize the loads in the crucial points of the structure, identified as the high-risk failure areas. A number of simulations have been carried out under the set of different load cases, specially established to represent a wide range of operating conditions possible to be met during the vehicle life cycle.


Keywords: multibody modeling, lightweight structures, response surface method, dynamics of multibody system.

This paper reviews multi-scale computational homogenisation frameworks for the non-linear behaviour of heterogeneous thin planar shells. Based on a review of some of the currently available methods, a computational homogenisation scheme for shells is applied on to representative volume elements for plain weave composites. The effect of flexural loading on the potential failure modes of such materials is analysed, focusing on the reinforcement-matrix delamination mechanism. The attention is next shifted toward failure localisation in masonry unit cells. Subsequently, a recently developed computational FE2 solution scheme accounting for damage localisation at structural scales based on RVE computations is applied.


Keywords: thin planar shells, computational homogenisation, failure, textile reinforced composites, masonry.

The paper addresses various scale-bridging modeling and discretization strategies for multiphase porous materials, starting with a micromechanics model for ion transport within the pore space to generate homogenized diffusion coefficients. Using homogenized macroscopic properties, the theory of poromechanics provides the modeling framework for the macroscopic representation of transport and phase change processes as it is demonstrated for freezing of porous materials using a three-field formulation. The theory of poromechanics is again employed as an appropriate representation of more or less intact porous materials, in conjunction with a two-field Extended Finite Element model as a scale bridging tool to describe coupled hydro-mechanical processes in cracked porous materials at a macroscopic level.


Keywords: micromechanics, poromechanics, Extended Finite Element Method, homogenization, multi-phase models, diffusion, durability, soil freezing.

In this paper we discuss two multi-scale procedures, both of mathematical nature as opposed to purely numerical ones. Examples are shown for the two cases. Attention is also devoted to thermodynamical aspects such as thermodynamic consistency and non-equilibrium thermodynamics. Advances for the first aspect are obtained by adopting the thermodynamically constrained averaging theory TCAT as shown in the case of a stress tensor for multi-component media. The second aspect has allowed to solve numerically, with relative ease, the case of non-isothermal leaching. The absence of proofs of thermodynamic consistency in case of asymptotic theory of homogenization with finite size of the unit cell is also pointed out.


Keywords: multiphysics problems, multi-scale models, asymptotic homogenisation.

The paper deals with transient heat conduction in functionally gradient materials. The spatial variation of the temperature field is approximated by using alternatively two various mesh free approximations, while the time dependence is treated either by the Laplace transform method and/or by the polynomial interpolation in the time stepping method. The accuracy and convergence of the numerical results as well as the computational efficiency of various approaches are compared in numerical test example.


Keywords: heat transfer, boundary value problems, numerical analysis, integral equations, meshless methods.

Preface and Editorial

This state-of-the-art-paper is a resume of research activity of a non-formal Research Group on Artificial Neural Networks (RGANN) applications in Civil Engineering (CE). RGANN has been working at the Cracow University of Technology, Poland, since 1996 under the supervision of the author of this paper. Ten years 1996-2005 of the research and teaching activity of RGANN was reported in paper [61]. The present paper briefly reports on the activities originated in the ten year period and their continuation after 2005. The main attention is focused on new research carried out in the five year period 2006-2011. The paper discusses some selected problems which are included in fourteen supplementary papers, marked in references of these papers as published in this CAMES Special Issue. The attention is focused on: Hybrid Computational Systems, development of modifications of ANNs and methods of their learning, Bayesian neural networks and Bayesian inference methods, damage identification in CE structures, structure health monitoring, applications of ANNs in mechanics of structures and materials, joining of ANNs with measurements on laboratory models and real structures, development of new non-destructive measurement methods, applications of ANNs in health structure monitoring and repair, applications of ANNs in geotechnics and geodesy. The paper is based on the supplementary papers which were presented at the Special Session on Applications of ANNs at the 57th Polish Civil Engineering Conference in Krynica, 2011, see [74].


Keywords: Civil Engineering Artificial (CE), Neural Network (ANN), Standard NN (SNN), Multi-Layred Perceptron (MLP), Fuzzy Weight NN (FWNN), Kalman Filtering (KF), Bayesian NN (BNN), True-BNN (TBNN), Semi-Bayesian NN (SBNN), Gaussian Process (GP), Recurrent Cascade NN (RCNN), Principle Component Analysis (PCA), Hybrid Computational System (HCS), Finite Element Method (MES), Em- pirical Data (EMP), Hybrid Monte Carlo Method (HMCM), Hybrid Updated Algorithm (HUA), Neural Material Model (NMM), Structural Health Monitoring (SHM).

A study of the capabilities of artificial neural networks in respect of selected problems of the analysis of mine-induced building vibrations is presented. Neural network technique was used for the prediction of building fundamental natural period, mapping of mining tremors parameters into response spectra from ground vibrations, soil-structure interaction analysis, simulation of building response to seismic- type excitation. On the basis of the experimental data obtained from the measurements of kinematic excitations and dynamic responses of actual structures, training and testing patterns of neural networks were formulated. The obtained results lead to a conclusion that the neural technique gives possibility of efficient, accurate enough for engineering, analysis of structural dynamics problems related to mine-induced excitations.


Keywords: neural network, neural simulation, data compression, data pre-processing, mining tremors, experimental data.

The article presents possibilities of using different artificial neural networks and neuro-fuzzy systems to solve certain engineering geodesy tasks. Special attention is paid to tasks connected with the construction of a numerical terrain model, transformation of coordinates from the "1965" system into the "2000" system, and prediction of a time series on the basis of results of GPS measurements. The paper also includes a short description of those neural networks and neuro-fuzzy systems that provided good quality solutions of the tasks undertaken. The goal of the article is to review the papers published in the years 2005-2010.


Keywords: neural networks, neuro-fuzzy systems, geodesy.

The paper presents a structure test system developed for monitoring structural health, and discusses the results of laboratory experiments conducted on notched strip specimens made of various materials (aluminium, steel, Plexiglas). The system takes advantage of elastic wave signals actuated and sensed by a surface-mounted piezoelectric transducers. The structure responses recorded are then subjected to a procedure of signal processing and feature's extraction, which includes digital filters, wavelets decomposition, Principal Components Analysis (PCA), Fast Fourier Transformation (FFT), etc. A pattern database defined was used to train artificial neural networks and to establish a structure diagnosis system. As a consequence, two levels of damage identification problem were performed: novelty detection and damage evaluation. The system"s accuracy and reliability were verified on the basis of experimental data. The results obtained have proved that the system can be used for the analysis of simple as well as complex signals of elastic waves and it can operate as an automatic Structure Health Monitoring system.


Keywords: artificial neural networks, damage detection, structural health monitoring, elastic waves.

The paper presents the application of Artificial Neural Networks (ANNs) for finite element (FE) models updating. The investigated structures are beams and frames, their models are updated by ANNs with input vectors composed of dynamic characteristics of structures measured on laboratory models. The ANNs (multi layer feed-forward networks and Bayesian neural networks) are trained on numerical data disturbed by an artificial noise. The responses of the structures are measured on laboratory models. The updating procedure is also applied in identification of defects or additional masses attached to the structure.


Keywords: artificial neural networks, updating, dynamics, vibrations, identification.

The paper develops the idea of [8], i.e., the application of Artificial Neural Networks (ANNs) in probabilistic reliability analysis of structures achieved by means of Monte Carlo (MC) simulation. In this method, a feed-forward neural network is used for generating samples in the MC simulation. The patterns for network training and testing are computed by a Finite Element Method (FEM) program. A high numerical efficiency of this Hybrid Monte Carlo Method (HMC) is illustrated by two examples of the reliability analysis that refer to a steel girder [4] and a cylindrical steel shell [2].


Keywords: reliability, Artificial Neural Networks (ANNs), Finite Element Method (FEM), Hybrid Monte Carlo Method (HMC), steel girder, cylindrical steel shell.

The paper is a development of research originated in [8]. The identification problem deals with searching the location of a small mass attached to a steel plate. The corresponding inverse problem is based on measurement of dynamic plate responses on a laboratory model of the plate, taking into account only the bending plate eigenfrequencies. In the inverse analysis the Recurrent Cascade Neural Network was applied, developed in [3]. Much attention is paid to recognition of identification possibilities of RCNN. The testing process is in fact an unsupervised learning, which can lead to unstable and inaccurate recurrence procedure. That is why the verification testing process was carried out adopting the barrier bound approach. These problems are discussed in the present paper.


Keywords: laboratory model of plate, plate eigenfrequencies, Recurrent Cascade Neural Network (RCNN), supervised and unsupervised learning, verification testing, barrier bound.

The paper presents a discussion of some applications of Artificial Neural Networks (ANNs) in geoengineering using the analysis of the following six geotechnical problems, related mainly to prediction and classification purposes: 1) prediction of Overconsolidation Ratio (OCR), 2) determination of potential soil liquefaction, 3) prediction of foundation settlement, 4) evaluation of piles bearing capacity, 5) prediction of compaction parameters for cohesive soils, 6) compaction control of embankments built of cohesionless soils. The problems presented are based on the applications of the Multi-Layered Perceptron (MLP) neural networks.


Keywords: geotechnical problems, artificial neural networks (ANNs), Multi-Layer Perceptron (MLP), Overconsolidation Ratio (OCR), bearing capacity of piles, settlement of foundation, soil liquefaction, compaction control.

The paper describes the applications of back propagation neural networks with the ability to process input and output variables expressed as fuzzy numbers. The presentation of an algorithm for finding fuzzy neural network weights is followed by three examples of applications of this technique to the problems of implicit modelling of material and structure behaviour. The following problems are considered: prediction of concrete fatigue failure, high performance concrete strength prediction, and prediction of critical axial load for eccentrically loaded reinforced concrete columns.


Keywords: neural networks, fuzzy weight neural network, strength of high performance concrete, buckling of reinforced columns.

An advisory system for repairs of industrial concrete floors is a supporting tool for making material and technological decisions in the sphere of problems of recurrent character. The presented advisory system has the character of a hybrid system. Various elements of tools from the artificial intelligence group have been used in it. Artificial neural networks are of particular importance for functioning of the system. They act as an inference engine. The article presents, inter alia, an approach in the sphere of teaching artificial neural networks on the basis of an expert's knowledge, as well as utilization of fuzzy sets for data transformation and for increasing the size of the case set. The conclusions indicate the profits resulting from utilization of artificial neural networks like speed of operation or absence of the need to possess complete knowledge.


Keywords: neural networks, advisory system, repairs, industrial floors.

The paper is a continuation of [9], where new experimental data were analysed. The Multi-Layered Perceptron and Semi-Bayesian Neural Networks were used. The Bayesian methods were applied in Semi-Bayesian NNs to the design and learning of the networks. Advantages of the application of the Principal Component Analysis are also discussed. Two compaction characteristics, i.e. Optimum Water Content and Maximum Dry Density of granular soils were identified. Moreover, two different networks with two and single outputs, corresponding to the compaction characteristics, are analysed.


Keywords: granular soils, compaction characteristics, Optimum Water Content (OWC), Maximum Dry Density (MDD), neural networks, Multi-Layered Perceptron (MLP), Semi-Bayesian NN (SBNN), Principal Component Analysis (PCA).

The article is related to the results of research on Node Decoupled Extended Kalman Filtering (NDEKF) as a learning method for the training of Multilayer Perceptron (MPL). Developments of this method made by the author are presented. The application of NDEKF and MPL and other methods (pruning of MLP, Gauss Process model calibrated by Genetic Algorithm and Bayesian learning methods) are discussed on the problem of hysteresis loop simulations for tests of compressed concrete specimens subjected to cyclic loading.


Keywords: Artificial Neural Networks (ANN), Kalman Filter (KF), Node Decoupled Extended Kalman Filtering (NDEKF), Multilayer Perceptron (MPL), Genetic Algorithm (AG), Bayesian methods, concrete specimens, cyclic loading, hysteresis loops.

The application of FEM/NMM/p-EMP computational hybrid system in formulation of the Neural Material Model (NMM) for granular soils is presented. NMM is a Multi Layer Preceptron formulated 'on-line'. The cumulative algorithm of the autoprogressive method was implemented into the FEM program. The patterns for NMM training were generated in the rigid strip footing analysis. Pseudo-empirical equilibrium paths p-EMP for verification of the NMM were computed by a FEM program for the elastic-plastic Drucker-Prage material model. The discussed inverse problem of NMM identification is illustrated by two study cases of footing: 1) rigid strip footing on plane semispace, 2) inclined slope analysis. It was numerically proved that the NMM identified in the first study case can be successfully applied to the analysis of the latter one.


Keywords: Artificial Neural Network (ANN), Neural Material Model (NMM), hybrid computational system, constitutive modelling.

This paper gives a concise overview of concrete properties prediction using advanced nonlinear regression approach and Bayesian inference. Feed-forward layered neural network (FLNN) with Markov chain Monte Carlo stochastic sampling and Gaussian process (GP) with maximum likelihood hyperparameters estimation are introduced and compared. An empirical assessment of these two models using two benchmark problems are presented. Results on these benchmark datasets show that Bayesian neural networks and Gaussian processes have rather similar prediction accuracy and are superior in comparison to linear regression model.


Keywords: nonlinear regression, Bayesian methods, concrete, neural network, Gaussian process.

In this paper, an artificial neural network (ANN) is used to approximate response of deep excavation numerical model on input parameters. The approximated model is then used in minimization procedure of the inverse problem, i.e. minimization of the differences between the response of the model (now, neural network) and the field measurements. ANN based objective function is continuous and differentiable thus gradient based optimization algorithm can be efficiently used in this problem. It is showed that initial approximation of the numerical model by means of ANN increase efficiency of the identification process without loss of accuracy.


Keywords: artificial neural network, parameter identification, deep excavation.

In this paper, we present finite element formulations for general three-dimensional convex polyhedra for use in a common finite element framework that are well suited, e.g., for modeling complex granular materials and for mesh refinements. Based on an universally applicable interpolant for any convex polyhedron, different interpolation schemes are investigated in the context of nonlinear elastostatics. The modeling benefits and the numerical performance regarding the mechanical response and the computational cost are analyzed by several examples.


Keywords: nonlinear finite elements, polyhedral elements, 3D interpolation, finite elasticity.

The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The compared methods include sampling techniques, the perturbation approach, the dimension reduction method and the polynomial chaos expansion method. For comparison, two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the eight-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbo-generator. The most important reason for the observed scatter of the rotor-shaft vibration responses is the inherently random nature of residual unbalances as well as stiffness and damping properties of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. It was found that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. On the other hand, methods based on Taylor series expansion in most of the analyzed cases fail to approximate the rotor-shaft response statistics.


Keywords: stochastic moment estimation, Latin hypercube sampling, polynomial chaos expansion, rotor- shaft system, lateral vibration analysis.

This paper describes results of the mathematical modelling of steady-state and transient physical phenomena taking place in the heating channels of a coke oven battery. A formulated system of standard Computational Fluid Dynamics (CFD) equations coupled with User Defined Functions is solved numerically using commercial software Ansys Fluent. Finally, the developed 3-D model is used to examine the influence of selected operating parameters on the resulting temperature, velocity and concentration fields within considered object. The obtained results are briefly discussed considering their physical correctness related to industrial measurements.


Keywords: computational fluid dynamics, coupled thermal problems, coke oven battery, combustion, radiative heat transfer.

This paper proposes the wave based method for the steady-state dynamic analysis of the in-plane behaviour of 2D structural solids. This novel prediction technique relaxes the frequency limitations of the commonly used finite element method through an improved computational efficiency. This efficiency is obtained by selecting basis functions which satisfy the governing equations a priori, in accordance with the indirect Trefftz approach. Special attention is paid to problems in which singularities appear in the problem solution. For these problems, the conventional set of basis functions is extended with functions which can represent the singularity accurately. The capabilities of this novel method for mid-frequency applications, as compared to the standard finite element method, are demonstrated by means of two numerical examples.


Keywords: structural dynamics, wave based method, indirect Trefftz method, plate membrane, stress singularities, corner functions.

This work deals with the construction of a mixed and extensible domain decomposition method for incompressible flows. In the scheme proposed here, the solution is sought at the intersection of two spaces, one containing the solution of the Navier-Stokes equations considered separately in each subdomain, and the other one containing the solutions of the compatibility equations on the interfaces. A solution verifying all the equations of the two spaces is achieved iteratively. One difficulty is that the interface problem is large and dense. In order to reduce its cost while maintaining the extensibility of the method, we defined an interface macroproblem in terms of a few interface macro unknowns. The best option takes advantage of the incompressibility condition to prescribe an interface macroproblem which propagates the information to the whole domain by making use of only two unknowns per interface. Several examples are used to illustrate the main properties of the method.


Keywords: Navier-Stokes, Domain Decomposition Method, Multiscale Method.

Nonlinear electroelasticity is not a new problem, its theory involving nonlinear deformation and nonlinear material behavior has been well established. However, the numerical simulation of nonlinear electroelasticity is until now still far from satisfactory, especially when the interaction between electric fields and matter cannot be considered as confined in the finite space occupied by the matter. It is understood that under the application of an electric field, the deformation of an elastic body is governed not always by what happens inside the material body but in many cases also by the environment surrounding it. This is notably true in the case of electronic electroactive polymers, the materials that emerge today as a leading candidate in developing artificial muscles. In this work, we present a numerical analysis of nonlinear electroelasticity by assuming large deformation, nonlinear polarization and by paying attention to the contribution of the free space surrounding the bodies of interest.


Keywords: nonlinear electricity, nonlinear elasticity, nonlinear coupling, coupled BEM-FEM analysis.

In this paper the two-dimensional finite element with an embedded edge crack proposed by Potirniche et al. (2008) is improved further for crack depth ratios ranging up to 0.9 and for predicting the natural frequency of a cracked beam more accurately. The element is implemented in the commercial finite element code ABAQUS as user element subroutine. The accuracy of the proposed improved cracked element is verified by comparing the predicted, first natural frequency with available experimental data. Subsequently, a methodology to detect the crack's location and size in conjunction with the proposed improved cracked element is also presented.


Keywords: cracked finite element, user element, ABAQUS, natural frequency, crack fault diagnosis.

Particle swarm optimization is one of the evolutionary computations which is inspired by social behavior of bird flocking or fish schooling. This research focuses on the application of the particle swarm optimization to two-dimensional packing problem. Packing problem is a class of optimization problems which involve attempting to pack the items together inside a container, as densely as possible. In this study, when the arbitrary polygon-shaped packing region is given, the total number of items in the region is maximized. The optimization problem is defined not as the discrete-value optimization problem but as the continuous- value optimization problem. The problem is solved by two algorithms, original and improved PSOs. In the original PSO, the particle position vector is updated by the best particle position in all particles (global best particle position) and the best position in previous positions of each particle (personal best position). The improved PSO utilizes, in addition to them, the second best particle position in all particles (global second best particle position) in the stochastic way. In the numerical example, the algorithms are applied to three problems. The results show that the improved PSO can pack more items than the original PSO and therefore, number of the successful simulations is also improved.


Keywords: packing problem, particle swarm optimization, global best position, global second best position, personal best position.

A brief overview of causality analysis (CA) methods applied to MD simulations data for model biomolec ular systems is presented. A CausalMD application for postprocessing of MD data was designed and implemented. MD simulations of two model systems, porphycene (ab initio MD) and HIV-1 protease (coarse-grained MD) were carried out and analyzed. Granger's causality methodology based on a Multivariate Autoregressive (MVAR) formalism, followed by the Directed Transfer Function (DTF) analysis was applied. A novel approach based on the descriptors of local structure was also presented and preliminary results were reported. Casuality analyses are required for a better understanding of biomolecular functioning mechanisms. In particular, such analyses can link physics-based structural dynamics with functions inferred from molecular evolution processes. Current limitations and future developments of the presented methodologies are indicated.


Keywords: causality analysis, signal analysis, local descriptors, alignment, MVAR, Directed Transfer Function, molecular dynamics, porphycene, HIV-1 protease, molecular function, molecular evolution.

In this work, we discuss the role of probability in providing the most appropriate multiscale based uncertainty quantification for the inelastic nonlinear response of heterogeneous materials undergoing localized failure. Two alternative approaches are discussed: i) the uncertainty quantification in terms of constructing the localized failure models with random field as parameters of failure criterion, ii) the uncertainty quantification in terms of the corresponding Bayesian updates of the corresponding evolution equation. The detailed developments are presented for the model problem of cement-based composites, with a two- phase meso-scale representation of material microstructure, where the uncertainty stems from the random geometric arrangement of each phase. Several main ingredients of the proposed approaches are discussed in detail, including microstructure approximation with a structured mesh, random field KLE representation, and Bayesian update construction. We show that the first approach is more suitable for the general case where the loading program is not known and the best one could do is to quantify the randomness of the general failure criteria, whereas the second approach is more suitable for the case where the loading program is prescribed and one can quantify the corresponding deviations. More importantly, we also show that models of this kind can provide a more realistic prediction of localized failure phenomena including the probability based interpretation of the size effect, with failure states placed anywhere in-between the two classical bounds defined by continuum damage mechanics and linear fracture mechanics.


Keywords: multiscale analysis, inelastic behavior, uncertainty quantification, fracture, size-effect.

The paper discusses the results of laboratory experiments in which three independent measurement techniques were compared: a digital oscilloscope, phased array acquisition system, a laser vibrometer 3D. These techniques take advantage of elastic wave signals actuated and sensed by a surface-mounted piezoelectric transducers as well as non-contact measurements. In these experiments two samples of aluminum strips were investigated while the damage was modeled by drilling a hole. The structure responses recorded were then subjected to a procedure of signal processing, and features' extraction was done by Principal Components Analysis. A pattern database defined was used to train artificial neural networks for the purpose of damage detection.


Keywords: Artificial neural networks, damage detection, structural health monitoring, elastic waves, non-destructive testing.

In this paper, a time series-based damage detection algorithm is proposed using Gaussian mixture model (GMM) and expectation maximization (EM) framework. The vibration time series from the structure are modelled as the autoregressive (AR) processes. The first AR coefficients are used as a feature vector for novelty detection. To test the efficacy of the damage detection algorithm, it has been tested on the pseudo-experimental data obtained from the FEM model of the ASCE benchmark frame structure. Results suggest that the presented approach is able to detect mainly major and moderate damage patterns.


Keywords: dynamics, inverse problems, structural monitoring, damage detection, mixture model, novelty detection.

This paper presents neural networks prediction of load capacity for eccentrically loaded reinforced concrete (RC) columns. The direct modelling of the load capacity of RC columns by means of the finite element method presents several difficulties, mainly in geometry representation and handling of several nonlinearities. Properly trained neural network can provide a useful surrogate model for such columns. The paper discusses architecture and training methods of the both multi-layer perceptron (MLP) and fuzzy weights neural networks (FWNN) for this application. It also presents the performance analysis of the networks trained on data from three independent databases available in the literature.


Keywords: concrete reinforced columns, load capacity, neural networks, fuzzification.

The present paper focuses on the identification of delamination size and location in homogeneous and composite laminates. The modal analysis methods are employed to calculate the data patterns. An aggregated approach combining Haar wavelets, support vector machines (SVMs) and artificial neural networks (ANNs) is used to solve identification problems. The usability and effectiveness of the proposed technique are tested by several numerical experiments. The advantages of the proposed method lie in the ability to make fast and accurate calculations.


Keywords: delamination identification, free vibrations, Euler-Bernoulli beam theory, Haar wavelets, machine learning methods.

In the paper a proposal of using selected swarm intelligence algorithms for solving the inverse heat conduction problem is presented. The analyzed problem consists in reconstructing temperature distribution in the given domain and the form of heat transfer coefficient appearing in the boundary condition of the third kind. The investigated approaches are based on the Artificial Bee Colony algorithm and the Ant Colony Optimization algorithm, the efficiency of which are examined and compared.


Keywords: Swarm Intelligence, ACO algorithm, ABC algorithm, Inverse Heat Conduction Problem.

Validation of an experimental approach requires that both model and data errors are proved to be within acceptable ranges. In case of destructive testing none of the classic, statistically based methods can be applied for that task due to the lack of independent data series required for building data statistics. The aim of the paper is to present a non-statistical methodology for performing such validation, developed within the framework of physically based approximation (PBA). It has been developed to validate a neutron diffraction based experimental-numerical approach applied for studying 3D rail residual stress. It is for the PBA technique's capability to provide high quality physically reasonable data fits for one data set only, treated here as higher order reference fields that made it possible to develop this methodology and perform error analysis/validation. In many ways this approach is analogical to Zienkiewicz-Zhu type of error estimators, and its performance will be demonstrated for a defective RE136 rail sample that was installed in a US DOT test track.


Keywords: physically based approximation, experimental data error estimation, validation of experimental technique, residual stress in railroad rails, neutronography.

A thin metal film subjected to a laser pulse is considered. The problem is described by the system of energy equations describing the electron gas and lattice temperatures. The thermal interactions between electrons and lattice are determined by the parameter G called the electron-phonon coupling factor. To estimate the unknown parameter G the identification problem is formulated. The additional information necessary to solve an inverse problem is the knowledge of transient measurements of the reflectivity or transmissivity variation which is proportional to the variation of the electron temperature. So, at the stage of inverse problem solution, it is possible to assume the knowledge of electrons temperature on the irradiated surface of the system (x = 0). To solve the identification problem the gradient method basing on the least squares criterion and sensitivity coefficients is used. In the final part of the paper the results of computations are shown.


Keywords: microscale heat transfer, laser heating, two-temperature model, inverse problem, finite difference method.

The paper presents a solution of an inverse problem consisting in determination of boundary conditions in the process of binary alloy solidification when temperature measurements in selected points of the cast are known. In the investigated model the distribution of temperature is described using the Stefan model with the liquidus temperature varying in dependance on concentration of the alloy component. For description of the concentration we apply the model in which the immediate equalization of chemical composition of the alloy is assumed (lever arm model). Experimental verification of the developed algorithm is also presented.


Keywords: solidification, segregation, binary alloy, genetic algorithm.

Grammatical evolution (GE), which is a kind of evolutionary algorithms, is designed to find a function, an executable program or program fragment that will achieve a good fitness value for the given objective function to be minimized. In this study, GE is applied for the coefficient identification problem of the stiffness matrix in the two-dimensional elastic problem. Finite element analysis of the plate with a circular hole is performed for determining the set of the stress and the strain components. Grammatical evolution determines the coefficient matrix of the relationship between the stress and strain components. The coefficient matrix is compared with Hooke's law in order to confirm the validity of the algorithm. After that, three algorithms are shown for improving the convergence speed of the original GE algorithm.


Keywords: grammatical evolution, Backus-Naur form (BNF), coefficient matrix, plane strain state.

This paper presents the out-of-core solver for three-dimensional multiphysics problems. In particular, our study focuses on the three-dimensional simulations of the linear elasticity coupled with acoustics. The out-of-core solver is designed with three principles in mind. First, to store the dense matrices associated with the nodes of the elimination tree with blocks related to nodes of the mesh, where many degrees of freedom may be located in the case of multiphysics computations with high order polynomials. The second principle is to minimize the memory usage. This is obtained by dumping out all local systems from the entire elimination tree to the disk during the elimination stage. The local systems are reutilized later during the backward substitution stage. The third principle is that the communication in the parallel version of the out-of-core solver occurs through the parallel file system. The memory usage of the solver is compared against the state-of-the-art MUMPS solver.


Keywords: multi-frontal direct solver, finite element method, out-of-core, parallel simulations, multiphysics.

We present a layered architecture for iterative solvers of linear equations, designed to allow for easy integration with existing hp-adaptive FEM codes. We discuss interfaces between a solver and an external FEM code and requirements for the FEM code that must be met in order to work with the solver. Our solution is suited to work effectively with stationary as well as time-dependent problems. In this article, we provide an overview of the layered solver's structure and modules of each layer. In subsequent articles, we will present specific implementations of particular layers.


Keywords: solver, FEM, higher-order.

Mesh smoothing improves mesh quality by node relocation without altering mesh topology. Such methods play a vital role in finite element mesh improvement with a direct consequence on the quality of the discretized solution. In this work, an improved version of the recently proposed geometric element transformation method (GETMe) for mesh smoothing is presented. Key feature is the introduction of adaptive concepts, which improve the resulting mesh quality, reduce the number of parameters, and enhance the parallelization capabilities. Implementational aspects are discussed and results of a more efficient version are presented, which demonstrate that GETMe adaptive smoothing yields high quality meshes, is particularly fast, and has a comparably low memory profile. Furthermore, results are compared to those of other state-of-the-art smoothing methods.


Keywords: mesh smoothing, GETMe adaptive, parallel smoothing, finite element mesh, mesh quality, mesh generation.

We proposed a method to analyze the galloping, a vibration by wind force, of transmission conductors. The Cosserat rod model was introduced to describe the motion of the conductor line. The deformation was tracked using the intrinsic framework of material coordinates which are able to handle the large motion in galloping phenomena. The Cosserat model provided a theory framework to simulate the non-linear coupling of the torsional motion and the translational motion. Such non-linear coupling was reported as one of the main causes for the galloping phenomena.


Keywords: galloping, numerical simulation, conductor, Cosserat rod.

We conducted thermal conductivity investigations by homogenization. This method can effectively model structural features such as pores within dispersed particle architectures via a finite element mesh. We investigated the factors that determine the effective thermal conductivity of porous structures and composites, such as the volume ratio of the continuous and dispersed phases, conductivity ratio, Biot number and particle packing model.


Keywords: homogenization method, effective thermal conductivity, multi-scale.

The robust and simple optimization method of functionally graded material (FGM) for combined cyclic thermal and mechanical loading with application to valve design is proposed. The optimization procedure starts from the homogeneous ceramic material distribution and after thermomechanical analysis of the whole process, the new distribution of material is determined by reducing concentration of the ceramic phase at places of high tensile stresses and by increasing ceramic contents at places of high effective stresses. The optimal distribution of ceramic phase is found through iterations. We have shown the numerical example of the proposed method for optimization of a composite exhaust valve of combustion engine. The example illustrates the optimal density distribution of ceramic phase of Al₂O₃ within NiAl matrix. In the design study we have used the transient analysis of stress and temperature fields. The proposed method shares merits of standard optimization and topology optimization, it allows for creating one phase of material inside the other. It can be especially useful to problems of structural elements subjected to thermomechanical loading histories.


Keywords: thermomechanical analysis, high frequency cyclic loading, coating, design, FGM, optimization.

In the paper, the thin metal film subjected to the ultrashort laser pulse has been analyzed. The heat conduction in the domain considered has been described by two-temperature model consisting of the system of two coupled parabolic equations determining the electron and lattice temperatures. The sensitivity analysis of electron and lattice temperatures with respect to the parameters appearing in mathematical description has been discussed. In particular, the changes of temperatures due to the changes of coupling factor G and the film thickness L have been estimated. At the stage of numerical computations in a case of basic as well as sensitivity problems solutions the explicit scheme of finite difference method has been used. In the final part of the paper the results of computations have been shown.


Keywords: microscale heat transfer, two-temperature model, sensitivity analysis, finite difference method.

The paper concerns the modelling of artificial hyperthermia. The 3D domain including healthy tissue and tumor region is considered. Heat transfer processes proceeding in this domain are described by the Pennes model and next by the porous one. The external heating of tissue is taken into account by the introduction of internal source function to the equation considered. Both models are supplemented by the same geometrical, physical, boundary and initial conditions. At the stage of numerical simulation the explicit scheme of finite difference method is used. The examples of computations show the similarities and differences of solutions and allow to formulate the conclusions connected with the applications of the results obtained in the hyperthermia therapy.


Keywords: bioheat transfer, heating of tissue, hyperthermia therapy, porous model, Pennes' equation.

This paper describes results of the mathematical modelling of the steady-state thermal phenomena taking place in a Fracmo 240 W DC electric motor. The model of the motor was defined in the ANSYS Fluent software to predict flow and temperature fields inside the machine. The thermal model was coupled with an electromagnetic solver to determine power losses occurring in different parts of the unit. In order to validate the proposed numerical model, a test rig was set up to measure temperatures at points located inside the motor housing and on its external wall. Additionally, the temperature field was captured by an infrared camera. The results obtained from the coupled analysis are comparable with the measurement data.


Keywords: computational fluid dynamics, coupled thermal problems, electric motor, validation.

In the paper, the numerical model of the flow phenomena in the flotation machine is presented. The process of flotation consists of a number of phenomena which provide serious numerical difficulties. One can enumerate rotation, two phase flow, foam formation etc. To the knowledge of authors there is no complete numerical model available for the flotation machine. The long-term task of the project is to create a complete model of the machine. Such a model would be very helpful in the process of construction and modernization of the flotation machine. As it was mentioned, due to difficulties connected with modelling the flotation phenomena, only a few aspects of the process were taken under consideration. In the paper, a single phase flow of water is considered. The efficiency of the flotation process strongly depends on the fluid flow field in the machine. The level of mixing the fractions and air bubbles strongly depends on the velocity field of the water, so the proper model of fluid flow is of great practical importance. This paper presents preliminary results of mathematical modelling. The commercial package ANSYS Fluent was utilized for the analysis. The results were compared with the measurements performed on the small scale model of the machine. Obtained results are satisfying and encouraging for further development.


Keywords: flotation, multiphase flow, numerical analysis, CFD, experiments, PIV measurements.

A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed particle finite element method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved using the FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including radiation, loss of mass by gasification and combustion is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting, burning and flame spread of polymers under different fire conditions are described.


Keywords: melting, dripping, polymers, particle finite element method (PFEM).

Knowledge of a material thermal conductivity is essential in several engineering applications. This material property serves also as a measure of the quality of manufactured materials. Nowadays, a lot of effort is directed into development of non-destructive, fast and reliable measurement techniques. In the works of Adamczyk et al. [1] and Kruczek et al. [10], a new in situ conductivity measurement technique for an anisotropic material was developed. This method, due to its rapidity and nondestructive character, can be embedded in a manufacturing process. However, despite many advantages, the developed measuring technique has some drawbacks corresponding to the applied mathematical model, which is used for determining the material thermal conductivities. It neglects the effect of heat losses due to radiation and convection phenomena on the calculated values of thermal conductivities. In this work, the computational fluid dynamic (CFD) modeling was applied to estimate heat losses due to radiation and convection. The influence of omitting the radiative and convective heat transfer on the predicted temperature field and calculated thermal conductivities was investigated. Evaluated numerical results were compared against experimental data by using the developed in situ measurement technique for the thermal conductivity of anisotropic materials.


Keywords: thermal conductivity, in-situ method, CFD, radiation, natural convection.

The work deals with thermal-hydraulic analyses of a pressurized water reactor containment response to accidents caused by a rupture of primary circuit. The in-house system computer code HEPCAL-AD and CFD ANSYS Fluent have been coupled for these simulations. The aim of this work is verification of possible ways of the codes coupling. The assessment of each method has been done by comparing the computational results with experimental data obtained from testing rigs of the AP-600 reactor containment cooling system. Additional simulations of a loss-of-coolant accident (LOCA) have been carried out as well, and compared with outcomes of the AP-600 reactor simulator.


Keywords: reactor containment, thermal-hydraulic analysis, lumped parameter code, CFD code, coupling.

A model integrated meshless solver (MIMS) tailored to solve practical large-scale industrial problems is based on robust meshless methods strategies that integrate a native model-based point generation procedures. The MIMS approach fully exploits strengths of meshless methods to achieve automation, stability, and accuracy by blending meshless solution strategies based on a variety of shape functions to achieve stable and accurate iteration process that is integrated with a newly developed, highly adaptive model generation employing quaternary triangular surface discretization for the boundary, a binary-subdivision discretization for the interior, and a unique shadow layer discretization for near-boundary regions. Together, these discretization techniques provide directionally independent, automatic refinement of the underlying native problem model to generate accurate adaptive solutions without need for intermediate user intervention. By coupling the model generation with the solution process, MIMS addresses issues posed by ill-constructed geometric input and pathologies often generated from solid models in the course of CAD design.


Keywords: meshless methods, heat transfer, large-scale problems.

The key issue in designing borehole heat exchangers (BHE) is the long-term performance of the ground source heat pump (GSHP) systems. The performance directly reflects economic profitability and depends on a large number of parameters including rock formation, the construction of the borehole heat exchangers, working parameters (circulation rates) and thermal load. The objective of the paper is to perform a realistic long-term (up to 10 years) analysis of the ground system to show possible degradation of efficiency over time. A mathematical model of the heat transfer in a borehole heat exchanger and the surrounding area has been constructed for parameters of the currently running experimental system. The long-term performance of the ground source heat pump system is evaluated.


Keywords: borehole heat exchangers, reservoir engineering, heat pumps systems, geoenergetics.

The main objective of this paper is to recognise the heat transfer phenomena between an infant placed in a radiant warmer and the surrounding environment. The influence of the parameters in the computational time during different physical phenomena in heat transfer is studied. This model can be also used in future work to improve radiant warmer efficiency. A complete 2D and 3D numerical simulation was carried out using commercial code ANSYS Workbench- ANSYS Fluent. The analysis involved the fluid flow, convection and radiation heat transfer as well as turbulence modeling, although moisture phenomena were omitted. The experiments were completed to validate a numerical solution.


Keywords: numerical analysis, radiant warmer, radiation, premature infant, CFD, heat transfer, fluid mechanics.

A CORDIC- based shift-add algorithm for generating B-spline curves is presented in this paper. This algorithm can be realized by hardware without multiplier, or coded with assembly language and run in the basic computing system which exists in many application systems. Convergence of the algorithm was proved. Errors were estimated and well controlled in the algorithm. A numerical experiment was carried out to validate algorithm. This algorithm can be used for adding complex curve plotting functions in embedded systems.


Keywords: B-spline, CORDIC, shift-add algorithm, basic computing system.

The main interest of pharmacokinetics is the study of the fate of drugs in the living organism. This work proposes the system of the conservation laws that describes time-dependent concentrations of a drug, after a single intravenous administration. Compared with others, the proposed model considers both free and protein-bound drug concentrations at the same time. Plasma protein binding captured in the model enters the nonlinearity arising from the Guldberg-Waage law. According to our best knowledge, the analytical solution for our system does not exist. Our model allows the calculation of the free and bound-drug protein concentrations at any time point and at any dose after single intravenous bolus dose administration. In order to compare the empirical with simulated data, a numerical approach has been proposed. On the basis of published experimental data the model validation has been carried out. The goodness of fit was satisfactory (R² = 0.99) and the experimental and simulated AUC (area under the curve) values, as the measure of the bioavailability of drug, were similar (150 M/hxh^-¹). The preliminary assessment of the model credibility was positive and encouraged further studies.


Keywords: evolution equations, non-linear model, drug protein binding.

The paper contains some estimates of an approximation to the solution of the problem of acoustic waves's scattering by an elastic obstacle in two dimensions. The problem is approximated by the isogeometric adaptive method based on the known NURBS functions. The estimates show how the error of an approximation depends on the size of intervals and the degree of functions.


Keywords: NURBS, adaptive methods, error estimates, acoustic scattering.

The effective mechanical properties and the stress-strain relations of the eight types of the graphene allotropes are presented in this paper. Series of the tensile and shear tests are performed using the non-equilibrium molecular dynamics (NEMD) and the adaptive intermolecular reactive bond order (AIREBO) potential. The methodology of the investigation as well as obtained results are explained and discussed in detail. Where possible, the achieved results are compared with the data available in the scientific literature in order to validate our molecular dynamics models and simulations. In other cases, i.e., where only information about structural or electronic properties is available, presented results can complement the knowledge about these particular planar carbon networks.


Keywords: graphene, nanomechanics, molecular dynamics, mechanical properties.

The paper deals with the identification in multiscale analysis of structures under thermal and mechanical loads. A two-scale model of porous materials is examined. Direct thermoelastic analyses with representative volume element (RVE) and finite element method (FEM) are taken into account. Identification of material constants of the microstructure and identification of the shape of the voids in the microstructure are considered. Identification functional is formulated on the basis of information obtained from measurements in mechanical and thermal fields. Evolutionary algorithm is used for the identification as the optimization technique. Numerical examples of identification for porous aluminum models are enclosed.


Keywords: multiscale modeling, numerical homogenization, thermoelasticity, evolutionary algorithms, identification, coupled problems, finite element method.

Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that is obtained after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal material configuration, a subsequent FEM computation then has to result exactly in the nodal coordinates of the desired deformed workpiece. Germain et al. [1] recently presented a new form finding strategy for isotropic elastoplasticity. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. In this contribution, the developed recursive algorithm is extended to anisotropic plasticity. In particular the orthotropic Hill yield function is considered. A load and a displacement-controlled example demonstrate that this new strategy requires only a few iterations to determine the optimal initial design whereby an almost linear convergence rate is obtained.


Keywords: inverse FEM, inverse form finding, orthotropic Hill's yield criterion, logarithmic strain space, optimum blank design.

A new semi-analytical method, discussed in the presented paper, is composed of two stages. Stage A corresponds to the direct analysis, in which the Lamb Waves Measurements (LWM) technique enables obtaining an experimental set of points , where f and k are frequency and wavenumber, respectively. After the preprocessing in the transform space an experimental approximate curve can be formulated. In Stage B the identification procedure is simulated as a sequence of direct analyses. The dimensionless Lamb Dispersion curves are computed by means of the dimensionless simulation curve k_sim ( f | par), where the vector of plate parameters par = {E, v, d, p} is adopted, in which Young's modulus E , Poisson ratio v , plate thickness d and density p are used. The main idea of the proposed approach is similar to that in the classical method of error minimization. In our paper we propose to apply the zero error value of relative criterion Reky = 0, cf. formula (15). The formula can be applied for the identification of a single plate parameter, assuming a fixed value of the other plate parameters. This approach was used in a case study, in which Stages A and B were analysed for an aluminum plate.


Keywords: Structure Health Monitoring, non-destructive method, Lamb waves, dispersion curve, modes of vibration, elastic isotropic and homogenous plate, identification of plate parameters.

Sequential stochastic identification of elastic parameters of thin aluminum plates using Lamb waves is proposed. The identification process is formulated as a Bayesian state estimation problem in which the elastic constants are the unknown state variables. The comparison of a sequence of numerical and pseudo-experimental fundamental dispersion curves is used for an inverse analysis based on particle filter to obtain sequentially the elastic constants. The proposed identification procedure is illustrated by numerical experiments in which the elastic parameters of an aluminum thin plate are estimated. The results show that the proposed approach is able to identify the unknown elastic constants sequentially and that this approach can be also useful for the quantification of uncertainty with respect to the identified parameters.


Keywords: Bayesian state estimation, particle filter, guided Lamb waves, dispersion curves, thin plate.

In this paper an evolutionary algorithms (EA) application to the physically based approximation (PBA) of experimental and/or numerical data is considered. Such an approximation may simultaneously use the whole experimental, theoretical and heuristic knowledge about the analyzed problems. The PBA may be also applied for smoothing discrete data obtained from any rough numerical solution of the boundary value problem, and for solving inverse problems as well, like reconstruction of residual stresses based on experimental data. The PBA presents a very general approach formulated as a large non-linear constrained optimization problem. Its solution is usually complex and troublesome, especially in the case of non-convex problems. Here, considered is a solution approach of such problems based on the EA. However, the standard EA are rather slow methods, especially in the final stage of optimization process. In order to increase their solution efficiency, several acceleration techniques were introduced. Various benchmark problems were analyzed using the improved EA. The intended application of this research is reconstruction of residual stresses in railroads rails and vehicle wheels based on neutronography measurements.


Keywords: evolutionary algorithms, solution efficiency increase, experimental data smoothing, large non-linear constrained optimization problems.

In this paper we present a new approach for solving identification problems based on a novel combination of computer vision techniques, Bayesian state estimation and finite element method. Using our approach we solved two identification problems for a laboratory-scale aluminum frame. In the first problem, we recursively estimated the elastic modulus of the frame material. In the second problem, for the known elastic constant, we identified sequentially the position of a quasi-static concentrated load.


Keywords: identification problems, Bayesian state estimation, particle filtering, computer vision, digital image correlation, finite element method.

The paper presents the application of artificial neural networks (ANN) for description of the Ramberg- Osgood (RO) material model, representing the non linear strain-stress relationship of ε (σ). A neural model of material (NMM) is a feed-forward layered neural network (FLNN) whose parameters were determined using the penalized least squares (PLS) method. A FLNN performing the inverse problem: σ(ε), using pseudo empirical patterns, was developed. Two models of NMM were developed, i.e. a standard model (SNN) and a model based on Bayesian inference (BNN). The properties of the models were compared on the example of a reference truss structure. The computations were performed by means of the hybrid FEM/NMM program, in which NMM developed previously described the current model of the material, and made it possible to explicitly build a tangent operator E_t = dσ/dε. The neural model of material was applied to the analysis of the shakedown of load carrying capacity of an aluminum truss.


Keywords: artificial neural network, inverse problem, material modeling, finite element method, hybrid program, shakedown analysis.

Two problems are presented in the paper concerning axial loading of R/C columns: I) prediction of critical loads, II) identification of concrete strength. The problems were analyzed by two methods: A) Gaussian Processes Method, B) Advanced Back-Propagation Neural Network. The results of the numerical analysis are discussed with respect to numerical efficiency of the applied methods.


Keywords: Gauss Processes Method (GPM), Advanced Back-Propagation Neural Network (ABPNN), Reinforced Concrete (R/C), axial loading, Success Ratio (SR).

This paper presents application of artificial neural networks (ANNs) for prediction of consistency parameters (plastic limit, liquid limit) of fen soils in comparison with the standard regression analysis. All samples of cohesive soils were retrieved from the Wisłok river floodplain, in the vicinity of Rzeszów, near Lisia Góra (Fox Mountain) reserve. Basic fractions (clay, silt, sand) of fen soils are independent variables in modeling of soil properties. Two regression models and a standard multi-layer back-propagation net have been used.


Keywords: fen soils, granulation, plastic limit, liquid limit, regression, artificial neural networks.

The article presents basic rules for constructing and training neural networks, called the Support Vector Machine technique. SVM networks can mainly be used for solving tasks of classification of linearly and nonlinearly separable data and regression as well as identifying signals and recognising increases. In this paper SVM networks have been used for classifying linearly separable data in order to formulate a model of displacements of points representing a monitored object. The problem of learning networks requires the use of quadratic programming in search of an optimum point of a Lagrange function with respect to optimised parameters. Estimated parameters determine the location of the hyperplane which maximises the separation margin of both classes.


Keywords: linear SVM network, classification, displacements.

Beveloid gears, also known as conical involute gears with very complex tooth shapes, gain more and more importance in industrial practice due to their ability to realize gear stages with crossed axes. This is why they are frequently found in power transmissions. The most familiar application of beveloid gears is the reduction gear used in marine transmissions, but in the last few years they have also been used increasingly often in the automotive industry. In the last decade many studies on beveloid gears were published, however, the meshing between teeth and the contact characteristics during meshing of beveloid gears still have not been studied in detail using fully elastic models. In this work, the fully elastic multibody approach will be applied to study contact forces and contact characteristics including contact patterns during meshing of straight beveloid gears. To validate the fully elastic approach, simulation results of a beveloid gear pair by finite element method and by the fully elastic multibody system are compared. The comparison shows very good agreement.


Keywords: multibody dynamics, gears, involute gears, beveloid gears, contact forces, contact patterns, elastic multibody system.

The paper is devoted to calculation of effective orthotropic material parameters for trabecular bone tissue. The finite element method (FEM) numerical model of bone sample was created on the basis of micro-computed tomography (µCT) data. The buffer zone surrounding the tissue was created to apply the periodic boundary conditions. Numerical homogenization algorithm was implemented in FEM software and used to calculate the elasticity matrix coefficients of the considered bone sample.


Keywords: trabecular bone, numerical homogenization, multiscale modeling, FEM.

This paper uses artificial neural network (ANN) technique for the identification of structural parameters of multistorey shear buildings. First, the identification has been done using response of the structure subject to ambient vibration with interval initial condition. Then, forced vibration with horizontal displacement in interval form has been used to investigate the identification procedure. The neural network has been trained by a methodology so as to handle interval data. This is because, in general we may not get the corresponding input and output values exactly (in crisp form) but we may only have the uncertain information of the data. These uncertain data are assumed in term of interval and the corresponding problem of system identification is investigated. The model has been developed for multistorey shear structure and the procedure is tested for the identification of the stiffness parameters of simple example problem using the prior values of the design parameters.


Keywords: identification, inverse vibration, modeling, interval neural network, shear buildings, structures.

Finding a solution of nonlinear constrained optimization problem may be very computer resources consuming, regardless of solution method adopted. A conceptually simple preconditioning procedure, based on singular value decomposition (SVD), is proposed in the current paper in order to speed up the convergence of a gradient based algorithm to solve constrained minimization problem having quadratic objective function. The efficiency of the proposed procedure is tested on a constrained minimization problem with quadratic objective function and quadratic constraints. Accuracy of the results obtained using proposed preconditioning method is checked and verified against the results determined without the preconditioning procedure. Results obtained so far seem to indicate a significant speedup of the calculations at the expense of, negligible from the engineering point of view, loss of accuracy.


Keywords: numerical method, nonlinear optimization, singular value decomposition.

In the paper the aerodynamic forces acting on a part of a water slide or other object with curved, tubular shape, depending on the section of a torus and value of the wind velocity, were obtained. This was done by means of finite element method (FEM) and finite volume method (FVM) computer simulations, using modules: computational fluid dynamics (CFD) and fluid-structure interaction (FSI) and taking into account the Eurocode EN 1991-1-4.


Keywords: fluid-structure interaction, water slide, wind action, CFD, FSI, FEM, FVM.

In recent years, Trefftz methods have received increasing attention, as being alternatives of the already well-established element-based simulation methods (e.g., finite element and boundary element methods). The wave-based technique is based on the indirect Trefftz approach for the solution of steady-state, time-harmonic acoustic problems. The dynamic field variables are expanded in terms of wave functions, which satisfy the governing partial differential equation, but do not necessarily satisfy the imposed boundary conditions. Therefore, the approximation error of the method is exclusively caused by the error on the boundary, since there is no additional error present in the domain. The authors investigate the potentials of a novel boundary error indicator-controlled adaptive local refinement strategy. Practical, industrial-oriented application of the method is presented on the 3D free-field sound radiation model of a simplified combustion engine. Results and efficiency of the approach are compared to a priori, frequency-dependent global refinement strategies.


Keywords: Trefftz method, adaptivity, error indicator, boundary error, Wave Based Technique, engine sound, numerical acoustics.

Several optimization techniques are proposed both to identify the aerodynamic coefficients and to reconstruct the trajectory of a fin-stabilized projectile from partial flight data. A reduced ballistic model is used instead of a more general six degree of freedom (6DOF) ballistic model to represent the flight of the projectile. Optimization techniques are proposed in order to identify the set of aerodynamic coefficients. These techniques are compared when identifying the aerodynamic coefficients from both exact and noisy simulated partial flight data.


Keywords: aerodynamic coefficients, identification, free flight data, regularization.

This paper is devoted to a theoretical and numerical study of different ways of calculating the Fourier transform of a noisy signal where the boundary conditions at the lateral boundaries of the measurement interval are not precisely known. This happens in different characterization problems where infrared camera is used for temperature measurements. In order to overcome this difficulty, the interval where the Fourier transform (its support) is supposed to be larger than the measurement domain is defined. Thus, this virtual interval larger than the measurement interval is used. We show that regularization by truncated singular value decomposition is able to yield good estimates to this very ill-posed inverse problem.


Keywords: integral transforms, thermal quadrupoles, heat transfer in mini-channel, inverse heat conduction and convection.

This paper presents the research results of milling process optimization in the electromagnetic mill to obtain the predetermined particle size distribution of brown coal. Because of an important role of brown coal in Polish energy industry (power plants produce 9433 MW of electrical power from brown coal, which corresponds to about 34% share in total fuel usage structure of energy industry in Poland-2nd quarter 2013 [1]), there is a great need to look for and develop highly efficient methods of its mining, valorisation and low-emission combustion alongside with CO₂ capture technology. This paper proposes, as one of the methods of adapting low-rank coal to being utilized in modernized and newly built plants, the process of simultaneous grinding and drying in an electromagnetic mill system. This method is energy efficient and what is more significant it reduces the space required for its adaptation, thanks to electromagnetic mill's compact installation design. It is essential to obtain the desired characteristics of the product through the adequate control of the processes. Major concern of this case study was focused on determination of optimal grinding parameters in the electromagnetic mill in order to obtain two products of a desired size distribution (1-6.3 mm for application in fluidized bed boilers and 0-315 µm for boiler burners). The authors presented some theoretical considerations of the mechanisms and physical phenomena occurring during a fragmentation of solid particles as well as the literature review of the subject. The process complexity level, taking place in the active area of electromagnetic mill, involves the influence of particle-milling rod and particle-particle interactions as well as the volume of milling rods or coal particle residence time on the size distribution of the product. All of the mentioned factors account for nonlinearity of the problem and make the conditions difficult to rescale. Hence, a heuristic approach to inverse problem was chosen to analyse the differences between the desired and obtained particle size distributions. The examinations concerned grinding parameters such as total amount of rods (volume-based) and rod sizes (single and multi-size combinations of milling elements) were conducted. Equivalent samples of Polish brown coal with a particle diameter size ranging from 0 to 10 mm were chosen as an investigated material. Influence of the total volume of rods was examined using three amounts: 100 ml, 150 ml and 200 ml. Two grinding aid sizes were chosen in the form of ferromagnetic rods: fine rods of the size of 10 x 1 mm and coarse rods of the size of 20 x 2 mm.


Keywords: milling, brown coal, particle size distribution, optimization, electromagnetic mill.

Microwave imaging is considered as a nonlinear inverse scattering problem and tackled in a Bayesian estimation framework. The object under test (a breast affected by a tumor) is assumed to be composed of compact regions made of a restricted number of different homogeneous materials. This a priori knowledge is defined by a Gauss-Markov-Potts distribution. First, we express the joint posterior of all the unknowns; then, we present in detail the variational Bayesian approximation used to compute the estimators and reconstruct both permittivity and conductivity maps. This approximation consists of the best separable probability law that approximates the true posterior distribution in the Kullback-Leibler sense. This leads to an implicit parametric optimization scheme which is solved iteratively. Some preliminary results, obtained by applying the proposed method to synthetic data, are presented and compared with those obtained by means of the classical contrast source inversion method.


Keywords: inverse scattering, microwave imaging, breast cancer detection, Gauss-Markov-Potts prior,variational Bayesian approximation.

Braess pointed out that adding a new road to overcome a traffic congestion could cause a new traffic congestion leading to the reduction of the traffic flow in the whole traffic network, which is called Braess' paradox. The aim of this study is to formulate a traffic network design algorithm to increase the traffic flow in a traffic network. The objective function is the traffic flow of the whole traffic network and the route selection at the corners is considered as design variable. The traffic flow is estimated by a traffic flow simulator based on the cellular automaton model. A simple traffic network is considered as a numerical example. At different traffic densities, the traffic network is optimized to maximize the traffic flow. The results show that the optimized traffic network depends on traffic density. The situation presented by Braess' paradox could disappear at high traffic density.


Keywords: traffic network design, cellular automaton, optimization, Braess' paradox.

This paper studies electrical impedance tomography (EIT) using Bayesian inference [1]. The resulting posterior distribution is sampled by Markov chain Monte Carlo (MCMC) [2]. This paper studies a toy model of EIT as the one presented in [3], and focuses on efficient MCMC sampling for this model. First, this paper analyses the computation of forward map of EIT which is the bottleneck of each MCMC update. The forward map is computed by the finite element method [4]. Here its exact computation was conducted up to five times more efficient, by updating the Cholesky factor of the stiffness matrix [5]. Since the forward map computation takes up nearly all the CPU time in each MCMC update, the overall efficiency of MCMC algorithms can be improved almost to the same amount. The forward map can also be computed approximately by local linearisation, and this approximate computation is much more efficient than the exact one. Without loss of efficiency, this approximate computation is more accurate here, after a log transformation is introduced into the local linearisation process. Later on, this improvement of accuracy will play an important role when the approximate computation of forward map will be employed for devising efficient MCMC algorithms. Second, the paper presents two novel MCMC algorithms for sampling the posterior distribution in the toy model of EIT. The two algorithms are made within the 'multiple prior update' [6] and 'the delayed-acceptance Metropolis-Hastings' [7] schemes respectively. Both of them have MCMC proposals that are made of localized updates, so that the forward map computation in each MCMC update can be made efficient by updating the Cholesky factor of the stiffness matrix. Both algorithms' performances are compared to that of the standard single-site Metropolis [8], which is considered hard to surpass [3]. The algorithm of 'multiple prior update' is found to be six times more efficient, while 'the delayed-acceptance Metropolis-Hastings' with single-site update is at least twice more efficient.


Keywords: electrical impedance tomography, Bayesian inference, Markov chain Monte Carlo.

An efficient, global meshless method has been developed for creating 3-D wind fields utilizing sparse meteorological tower data. Meshless methods do not require the need for a mesh in order to connect node points. In this study, node points are placed within the computational domain based on topological features. Wind speeds and directions are obtained from a set of instrumented meteorological towers. Inverse weighting is used to initially establish wind vectors at all nodal points. The Kansa technique, employing global basis functions, is then used to create a mass-consistent, 3-D wind field. The meshless method yields close approximations to results obtained with a high-order finite element technique. The method was implemented using MATLAB.


Keywords: mesh-free method, 3-D wind field, mass-consistent.

Recently, Bevilacqua, Galeão and co-workers have developed a new analytical formulation for the simulation of diffusion with retention phenomena. This new formulation aims at the reduction of all diffusion processes with retention to a unifying model that can adequately simulate the retention effect. This model may have relevant applications in a number of different areas such as population spreading with partial hold up of the population to guarantee territorial domain chemical reactions inducing adsorption processes and multiphase flow through porous media. In this new formulation a discrete approach is firstly formulated taking into account a control parameter which represents the fraction of particles that are able to diffuse. The resulting governing equation for the modelling of diffusion with retention in a continuum medium requires a fourth-order differential term. Specific experimental techniques, together with an appropriate inverse analysis, need to be determined to characterize complementary parameters. The present work investigates an inverse problem which does not allow for simultaneous estimation of all model parameter. In addition a two-step characterization procedure is proposed: in the first step the diffusion coefficient is estimated and in the second one the complementary parameters are estimated. In this paper, it is assumed that the first step is already completed and the diffusion coefficient is known with a certain degree of reliability. Therefore, this work is aimed at investigating the confidence intervals of the complementary parameters estimates considering both the uncertainties due to measurement errors in the experimental data and due to the uncertainty propagation of the estimated value of the diffusion coefficient. The inverse problem solution is carried out through the maximum likelihood approach, with the minimization problem solved with the Levenberg-Marquardt method, and the estimation of the confidence intervals is carried out through the Monte Carlo analysis.


Keywords: diffusion, inverse problems, uncertainty propagation, Monte Carlo method.

Aircraft have become increasingly costly and complex. Military and civil pilots and engineers have used flight simulators in order to increase safety of flight through the training of crew. It is necessary to calibrate the simulation for simulators to have good adherence to reality, that is, to identify the parameters that make the simulation as close as possible to the actual dynamics. After determining these parameters, the simulator will be ready to be used in human resources training or assessing the aircraft. Parameter identification characterizes the aerodynamic performance of the aircraft and can be formulated as a problem optimization. The calibration of a dynamic flight simulator is achieved by a new meta-heuristic called multiple particle collision algorithm (MPCA). Preliminary results show a good performance of the employed approach.


Keywords: flight dynamic, parameter identification, multiple particle collision algorithm (MPCA).

Effective thermal conductivity with radiation is analyzed by a homogenization method. The method used can precisely represent the conditions around particles in a packed bed. In this study, the effects of variation in parameters such as heat transfer coefficient distribution around spherical particles in a packed bed, Reynolds number, temperature and particle size on the conductivity were estimated in order to elucidate the heat transfer mechanism of complex packed structures. The results show that it is unnecessary in heat transfer analysis to consider the anisotropic behavior of the flow direction for larger particles, high Reynolds numbers and high temperatures. However, the heat transfer was anisotropic for smaller particle sizes.


Keywords: effective thermal conductivity homogenization method, multi-scale analysis microstructure, thermal radiation, packed bed.

The numerical modeling of plates with periodic corrugation requires some efforts to be made in terms of careful and precise discretization of the complicated structure. This automatically generates very computationally expensive models. One of the most popular methods of model simplification is analytical or numerical homogenization. The main goal of this paper is to present the homogenization techniques that can be used to effectively model sandwich panels such as corrugated plates in an elastic phase. Two methods of different complexity are described: homogenization through application of the classical laminated plate theory and homogenization through the deformation energy-equivalence method. The accuracy of these methods is compared with the literature data and the results of a structural sample in two basic tests, i.e., the four-point bending test and the uniaxial tensile test. The results show that each method provides similar effective parameters which proves the robustness of the presented methods.


Keywords: homogenization, finite element method, corrugated cardboard.

In this work, we propose a methodology to estimate the profile of chlorophyll concentration from the upwelling radiation at the ocean surface, using a system of artificial neural networks (ANNs). The input patterns to train the networks are obtained from the resolution of the radiative transfer equation, where the absorption and scattering coefficients are represented by bio-optical models, with the profile of chlorophyll concentrations based on a shifted-Gaussian model. In the performed analysis, we used 14 720 profiles of chlorophyll that were generated by attributing two values to the biomass quantity, and by considering two sets of wavelengths and three sets containing the directions in which the radiation emitted at the surface is measured. To be able to recover the chlorophyll profile, we need to use a system of networks that works in a "cascade mode". The first one performs an analysis on the features of the chlorophyll profile from the upwelling radiation and determines which profiles can be recovered. The second and third ANNs act only on those profiles that can be recovered. The second ANN performs estimation of the standard deviation from the upwelling radiation and the chlorophyll concentration at the surface. Finally, the third ANN performs an estimation of the peak depth from the upwelling radiation, the chlorophyll concentration at the surface and the standard deviation estimated by second network. The stopping criteria we adopted was the cross-validation process. The obtained results show that the proposed methodology is quite promising.


Keywords: radiative transfer equation, inverse problems, artificial neural networks, chlorophyll profile concentration, bio-optics, phytoplankton.

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the first-order shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive time-integration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.


Keywords: Mindlin plate, two-parameter elastic foundation, Lobatto integration, bending and eigenvalue analysis.

The paper deals with the numerical simulation of strain localization in granular two-phase material. A gradient enhancement of modified Cam-clay model is introduced to overcome the problem of spurious discretization sensitivity of finite element solution. Two- and three-field finite elements implemented in the finite element analysis program (FEAP) are used in numerical simulations. The attention is focused on imperfection sensitivity of shear banding simulations. An application of the modelling framework to the slope stability problem is also included.


Keywords: two-phase medium, finite element method, plasticity, Cam-clay model, gradient regularization, localization, imperfection sensitivity.

Two techniques of data pre-processing for neural networks are considered in this paper: (i) data compression with the application of the principal component analysis method, and (ii) various forms of data scaling. The novelty of this paper is associated with compressed input data scaling by the rotation (by the "stretching") in neural network. This approach can be treated as the new proposition for data pre-processing techniques. The influence of various types of input data pre-processing on the accuracy of neural network results is discussed by using numerical examples for the cases of natural frequency predictions of horizontal vibrations of load-bearing walls. It is concluded that a significant reduction in the neural network prediction errors is possible by conducting the appropriate input data transformation.


Keywords: neural networks, data pre-processing, input data, principal component analysis method, data scaling.

Internal forces are integrals of stress in a section area. Integrating the stress for an arbitrary cross-section shape and for the nonlinear stress-strain law σ (ε) is tedious and the use of the boundary integral approach can simplify computations. Numerical integration when applied to the computations of such integrals introduces errors in many cases. Errors of numerical integration depend on the adopted integration scheme, the type of σ (ε) and the shape of the cross-section boundary. In the case of adaptive numerical integration what is very important are the properties of the sequence of errors produced by a given integration scheme in the increasing order of the numerical quadrature or the increasing number of subdivisions. This paper analyses errors caused by different integration schemes for the typical σ (ε) either for a straight or curved boundary. Special attention is paid to the properties of the error sequence in each case. The outcome of this paper is important from the viewpoint of the reliability and robustness of the software developed for nonlinear simulations of bar structures.


Keywords: computational mechanics, section forces, stress integration, biaxial bending, numerical integration, frame structures, nonlinear material, reinforced concrete.

A reference domain is chosen to formulate numerical model using the discontinuous Galerkin with finite difference (DGFD) method. The differential problem, which is defined for the real domain, is transformed in a weak form to the reference domain. The shape of the real domain results from a considered problem which can be complex. On the other hand, a reference domain can be chosen to be, for example, cube or square, which is convenient for meshing and calculations. Transformation from the reference domain into the real one has to be defined. In this paper, the algorithm for such a transformation is proposed, which is based on second-order differential equations. The paper presents a series of benchmark examples that show both the correctness and flexibility of the proposed algorithms. In the majority of the examples, the reference domain is square when the real domains are, for example, quarter of annulus, circle or full annulus.


Keywords: discontinuous Galerkin method, domain transformation, reference domain.

The computational fluid dynamics (CFD) analysis of the indoor environment in buildings requires numerical modelling of a human being (computer simulated person - CSP). There are two crucial aspects in developing reliable CSP models: the CSP geometry and the breathing model. This paper focuses on the analysis of different breathing models for application in the CFD modelling. Three breathing models were analysed: first model was restricted to constant exhalation, second model, the so-called full breathing, included constant rate inhalation, constant rate exhalation and pause period, and in the third model temporal variation of flow rate was represented by sinusoidal function. The main findings from this work show that all three models compared with experimental data gave reliable results. The spatial distribution of CO₂ concentration and velocity showed only small differences among the models in the vicinity of the mouth and above the person. It was shown that a simplified constant exhalation model can be effectively used for the CFD analysis of the indoor air quality (IAQ). However, a detailed simulation of micro-environment in the room and transport of contaminants should include complete breathing.


Keywords: breathing models, metabolic carbon dioxide, indoor air quality (IAQ), computer simulated person (CSP), CFD.

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high conditioning number for the interpolation matrix, rendering the RBF smooth [1-10]. However, this strategy fails for a problem with a shock or sharp discontinuity. Instead, in such cases the conditioning number must be kept small. The focus of this work is then to demonstrate the use of RBF interpolation in the approximation of sharp gradients or shocks by use of a RBF blending interpolation approach. This RBF blending interpolation approach is used to maintain the optimum shape parameter depending on the field. The approach is able to sense gradients or shocks in the field and adjust the shape parameter accordingly to keep excellent accuracy. Presented in this work, is an explanation of the RBF blending interpolation methodology and testing of the RBF blending interpolation approach by solving the Burger's equation using the virtual finite difference method.


Keywords: meshless methods, radial basis functions, multiquadrics, shape parameter, shocks.

In this work, the influence of boundary conditions model (environmental model) on the ground temperature profile is analyzed. A numerical model for transport phenomena in the area above the top ground surface and below in the ground is presented. The results of simulation- ground temperature profile and mean seasonal temperature which estimate the energy potential of the ground are presented. In addition, the results of implementation of five different environmental models for the area above the top ground surface are presented. It is found that none of the models is able to reproduce the temperature variation similar to the reference (most complex) model accuracy. On the other hand, it is found that with a slight error a similar result for low ground depth can be obtained using the simplest Model 1.


Keywords: heat transfer, ground heat transport, ground temperature profile, ground source heat pump.

This paper presents a population-based heuristic method - a real ant colony optimization (RACO) as a tool for multi-criteria optimization problems. The idea of multi-criteria optimization is discussed and the necessary modifications of RACO are proposed. These modifications made possible to use the method to simultaneously search many Pareto-optimal solutions. The method was numerically tested in problems of benchmark-type and used for solving simple engineering problems. This article presents and discusses all results obtained in tests, and two different approaches to multi-criteria optimization are additionally compared (search then decision and decision then search).


Keywords: multi-objective optimization.

The development of steam power units aims to increase the working steam parameters as they are the main factors that determine the efficiency of energy conversion. Most state of the art units are designed for supercritical steam parameters. However, the temperature level of steam feeding the turbine is limited by thermal strength of the material used to make the machine components. In this situation, using nickel alloys or cooling the elements exposed to the impact of high temperatures could be the appropriate solution. The former is rather expensive and the latter - technically difficult. The cooling option would require that the cooled element should be fed by a steam with a very high pressure and with a lower temperature than the temperature in the machine flow system. This paper presents the concept of using working steam as the cooling medium after it is expanded in a convergent-divergent nozzle. In such a case, the cooling system is very simple and the performed simulations indicate, for example, that the turbine blades may be cooled in this way.


Keywords: blade cooling, convergent-divergent nozzle, Laval nozzle, shock wave.

In this paper, the methodology for determination of the out-of-plane thermal diffusivity (TD) of a thin graphite layer deposited onto a substrate of known properties is presented. The developed methodology resulted in combined experimental-numerical procedure enabling investigation of the properties of thin layer deposits. The procedure involves the experimental data acquisition during the laser flash tests, and next the numerical processing of the collected data using the heat conduction problem solution and the nonlinear least square parameter identification approach. Two last steps produce a certain inverse heat conduction problem that is formulated and numerically solved for a three-layer specimen. The procedure has been successfully tested while processing the real experimental data from investigation of flake graphite layers. This proved the effectiveness of the methodology in providing quantitative data on the TD of thin layers of relatively poor conductors deposited onto a highly conductive substrate.


Keywords: inverse analysis, finite element method (FEM), multilayer heat transfer, thin layer diffusivity, laser flash data processing.

The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular method of fundamental solutions (MFS) which does not require artificial boundary, i.e., source points of fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity is obtained from the analytical solution due to the action of the Dirac delta- type force. Instead of Dirac delta force, a non-singular function called blob, with a free parameter epsilon is employed, which is limited to Dirac delta function when epsilon is limited to zero. The analytical expressions for related Stokes flow pressure and velocity around such regularized sources have been derived for rational and exponential blobs in an ordered way. The solution of the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary and with their intensities chosen in such a way that the solution complies with the boundary conditions.A numerical example for two-dimensional (2D) driven cavity and a flow between parallel plates are chosen to assess the properties of the method. The results of the posed method of regularized sources (MRS) have been compared with the results obtained by the fine-grid second-order classical finite difference method (FDM) and analytical solution. The results converge with finer discretisation; however, they depend on the value of epsilon. The method gives reasonably accurate results for the range of epsilon between 0.1 and 0.5 of the typical nodal distance on the boundary. Exponential blobs give slightly better results than the rational blobs; however, they require slightly more computing time. A robust and efficient strategy to find the optimal value of epsilon is needed in the perspective.


Keywords: Stokes flow, regularized sources, rational blobs, exponential blobs, meshless method, driven cavity problem, convergence study.

Measurements of heat transfer and temporal temperature distribution can be used as input in the diagnostic tools and methods of skin lesions, with special attention paid to malignant melanoma identification. Such approach requires mutual use of skin temperature and heat flux measurements combined with numerical simulation. A mild skin cooling process by a brass compress is considered in this paper. The temperature distribution on the skin and the heat flux between metal and tissues are measured. They are used in the course of validation study of the proposed numerical model. A numerical model of heat transfer in living tissues is described by Pennes' bioheat equation augmented with additional models of passive thermoregulation and vasoconstriction effects. The information regarding material properties of tissues and cooling compress involved in the simulation is essential to accurately solve this problem. Therefore, the main purpose of this work is to determine the accurate material property information by means of laboratory experiments.


Keywords: bioheat transfer, LFA, melanoma, thermal conductivity, thermal diffusivity.

The high (HTGR) and very high (VHTR) temperature nuclear reactors are the most innovative designs and belong to the most advanced fourth generation gas-cooled reactor technology. These types of reactors are designed to have an outlet temperature between 800-1000° C for the HTGR and the VHTR respectively. Such systems are able to generate electrical energy and supply process heat in a broad spectrum of high-temperature and energy-intensive non-electric and thermal processes. In this paper, a numerical analysis of the high temperature HTGR/VHTR combined cycle with co-production of hydrogen and electricity is conducted. The presented cycle consists of three subsidiary circuits with gas turbine and two steam turbines for electric energy generation, and two heat exchangers for hydrogen production at high or medium temperature. The results show that such a combination allows a significant increase of thermal efficiency to about 50% at the reactor outlet temperature of 1273 K and a decrease in cost of hydrogen production.


Keywords: high temperature nuclear reactor, HTR, VHTR, hydrogen production, combined cycle.

There are two main topics of this research: (i) one topic considers overall properties of a nonlinear cellular composite, treated as a model of the liver tissue, and (ii) the other topic concerns the propagation of heat in the nonlinear medium described by the homogenised coefficient of thermal conductivity. For (i) we give a method and find the effective thermal conductivity for the model of the liver tissue, and for the point (ii) we present numerical and analytical treatment of the problem, and indicate the principal difference of heat propagation in linear and nonlinear media. In linear media, as it is well known, the range of the heat field is infinite for all times t > 0, and in nonlinear media it is finite. Pennes' equation, which should characterize the heat propagation in the living tissue, is in general a quasi-nonlinear partial differential equation, and consists of three terms, one of which describes Fourier's heat diffusion with conductivity being a function of temperature T . This term is just a point of our analysis. We show that a nonlinear character of the medium (heat conductivity dependent on the temperature) changes in qualitative manner the nature of heat transfer. It is proved that for the heat source concentrated initially (t = 0) at the space point, the range of heated region (for t > 0) is finite. The proof is analytical, and illustrated by a numerical experiment.


Keywords: heat transport, asymptotic homogenisation, effective heat conductivity.

The paper presents numerical analysis of heat transfer in the human forearm and influence of its internal structure on the temperature distribution inside. For this purpose three geometrical models of a human forearm were developed: model containing continuous muscle tissue only, model in which muscle tissue and bones were considered and model which contained muscle tissue bones and main blood vessels. In those models heat transfer in the muscle tissues and bones were described by Pennes' bioheat equation, while for blood flowing through main vessels (artery and vein) full set of governing equations were solved. Moreover, simplified one-dimensional description of skin was developed in order to reduce model complexity. Results obtained with all models were confronted against each other to reveal influence of the main blood vessels on the temperature distribution in a forearm.


Keywords: bioheat transfer, Pennes' equation, human forearm, temperature distribution, simplified skin model.

In this work, we applied the Markov chain Monte Carlo (MCMC) method for the estimation of parameters appearing in the Pennes' formulation of the bioheat transfer equation. The inverse problem of parameter estimation was solved with the simulated transient temperature measurements. A one-dimensional (1D) test case was used to explore the capabilities of using the MCMC method in bioheat transfer problems, specifically for the detection of skin tumors by using surface temperature measurements. The analysis of the sensitivity coefficients was performed in order to examine linear dependence and low sensitivity of the model parameters. The solution of the direct problem was verified with a commercial code. The results obtained in this work show the ability of using inverse heat transfer analysis for the detection of skin tumors.


Keywords: inverse problems, Bayesian framework, Markov chain Monte Carlo method, Pennes' equation, skin tumor.

Among numerous applications of numerical modeling in many different fields of science, there is numerical modeling applied to the issues related to geothermal investments [1]. A number of important parameters and properties can be estimated based on numerical modeling. In the case of geothermal investments, we can determine several factors, which may influence operation of the heating plants, e.g.: exploitation and size of extraction and/or injection of groundwaters, selection of an optimal spacing of boreholes (in the case of geothermal doublets), and water temperature or pressure [2]. This paper presents the issues related to the numerical modeling of geothermal reservoirs as well as a variety of computer software packages commonly used in creation of static and dynamic models, such as: Visual MODFLOW, TOUGH, FEFLOWor Petrel [3, 4]. The process of numerical modeling is presented in four general steps: (1) archival data collection and analysis (often using statistical methods), (2) creation of the static and (3) dynamic numerical models of a reservoir, and (4) environmental, financial and technical assessments based on a mathematical model of surface installation [5]. Each step is presented in details and the most important reservoir parameters, which influence the utilization of geothermal energy, are discussed. At the end, the main directions in current utilization of geothermal waters in Poland and the future opportunities of geothermal heat generation, including the financial aspects related to geothermal investments, are discussed.


Keywords: numerical modeling, geothermal investments, geothermal heating plants.

This paper presents the design of flexible interfaces between finite element (FE) codes and solvers of linear equations. The main goal of the design is to allow for coupling FE codes that use different formulations (linear, non-linear, time dependent, stationary, scalar, vector) and different approximation techniques (different element types, different approximation spaces - linear, higher order, continuous, discontinuous, h- and hp-adaptive) with solvers of linear equations that use different storage formats for sparse system matrices and different solution strategies (such as, e.g., reordering of degrees of freedom (DOFs), multigrid solution or preconditioning for iterative solvers, frontal and multi-frontal strategies for direct solvers). Suitable data structures associated with the design are presented and examples of algorithms related to the interface between the FEM codes and linear solvers, together with their execution time and performance estimates, are described.


Keywords: finite element method, solvers of linear equations, hp-adaptivity, multigrid, multi-frontal strategies.

In this paper, the two-dimensional linear and nonlinear integral equations of the second kind is analyzed. The homotopy analysis method (HAM) is used for determining the solution of the investigated equation. In this method, a solution is sought in the series form. It is shown that if this series is convergent, its sum gives the solution of the considered equation. The sufficient condition for the convergence of the series is also presented. Additionally, the error of approximate solution, obtained as partial sum of the series, is estimated. Application of the HAM is illustrated by examples.


Keywords: homotopy analysis method, convergence, error estimation, nonlinear integral equation, linear integral equation.

This paper deals with hp-type adaptation in the discontinuous Galerkin (DG) method. The DG method is formulated in this paper with a non-zero mesh skeleton width, which leads to a version of the method called in this paper the interface discontinuous Galerkin (IDG) method. In this formulation, the mesh skeleton has a finite volume and special finite elements are used for discretization. The skeleton spatial calculations are performed using the finite difference or mid-values formulas which are based on the shape functions of the neighbouring finite elements. The Dirichlet boundary conditions are applied using a non-zero width of the material between the outer boundary and a finite element aligned with the boundary. Next, the paper discusses the mesh refinement of hp type. In the IDG method, the mesh does not have to be conforming. The Zienkiewicz-Zhu (ZZ) error indicator is adapted in the IDG method for the purpose of mesh refinement. The paper is illustrated with two-dimensional examples, in which the mesh refinement for an elliptic problem is performed.


Keywords: discontinuous Galerkin method, hp refinement, Zienkiewicz-Zhu error estimation.

The purpose of this paper is the analysis of numerical approaches obtained by describing the Dirichlet boundary conditions on different connected components of the computational domain boundary for potential flow, provided that the domain is a rectangle. The considered problem is a potential flow around an airfoil profile. It is shown that in the case of a rectangular computational domain with two sides perpendicular to the speed direction, the potential function is constant on the connected components of these sides. This allows to state the Dirichlet conditions on the considered parts of the boundary instead of the potential jump on the slice connecting the trail edge with the external boundary. Furthermore, the adaptive remeshing method is applied to the solution of the considered problem.


Keywords: adaptation, rate of convergence, remeshing, Delaunay triangulation, finite element method, potential flow, Kutta-Joukovsky condition, Dirichlet condition.

This paper focuses on the discontinuous Galerkin (DG) method in which the compatibility condition on the mesh skeleton and Dirichlet boundary condition on the outer boundary are enforced with the help of one-dimensional finite difference (FD) rules, while in the standard approach those conditions are satisfied by the penalty constraints. The FD rules can be of arbitrary degree and in this paper the rules are applied up to fourth degree. It is shown that the method presented in this paper gives better results in comparison to the standard version of the DG method. The method is based on discontinuous approximation, which means that it can be constructed using arbitrary local basis functions in each finite element. It is quite easy to incorporate some global basis functions in the approximation field and this is also shown in the paper. The paper is illustrated with a couple of two-dimensional examples.


Keywords: discontinuous Galerkin method, finite difference, compatibility condition, approximation basis.

In this paper, a comparison between the improved element-free Galerkin (IEFG) method, based on the improved moving least square (IMLS) approximation, and the element-free Galerkin (EFG) method, based on the moving least square (MLS) approximation, is presented. The IMLS approximation is obtained when an orthogonal basis function with a weight function is used. The IMLS approximation has a greater computational efficiency than the existing MLS approximation and does not lead to an ill-conditioned system of equations. The comparison is made for two-dimensional (2D) potential problems and 2D elastic problems. From these problems, the efficiency of the IEFG method is validated by comparing the results obtained with the IEFG method and EFG method with those obtained analytically.


Keywords: EFG method, potential problems, elasticity problems, IMLS approximation.

In this paper a comparison of the performance of two ways of discretizing the nonlinear convection-diffusion equation in a one-dimensional (1D) domain is performed. The two approaches can be considered within the class of high-order methods. The first one is the discontinuous Galerkin method, which has been profusely used to solve general transport equations, either coupled as the Navier-Stokes equations, or on their own. On the other hand, the ENATE procedure (Enhanced Numerical Approximation of a Transport Equation), uses the exact solution to obtain an exact algebraic equation with integral coefficients that link nodal values with a three-point stencil. This paper is the first of thorough assessments of ENATE by comparing it with well-established high-order methods. Several test cases of the steady Burgers' equation with and without source have been chosen for comparison.


Keywords: one-dimensional transport equation, high-order methods.

This paper presents the multi-objective optimization process of a hydraulic damper design based on its interdisciplinary meta-model considering both the properties of a damper and of the testing equipment used for the purpose of design criteria verification, and in particular the tolerance band criterion of damping force characteristics, the criterion of maximum permissible vibration level expressed with the piston rod acceleration and the criterion of fatigue durability for the damper's hydraulic valve system. The meta-model of a damper and a testing bench include the following models: mechanical model, hydraulic model, electro-hydraulic model and valve system fatigue durability model. The multi-objective optimization method provides an optimal solution by means of Pareto frontier. Furthermore, all potential feasible solutions are ranked according to additional customer preferences to select the most suitable ones. The proposed method is intended to be used to determine the best starting point in a new shock absorber design process.


Keywords: multi-objective optimization, model-based design, shock absorber model.

In this study, the authors developed the numerical model of brain structure to assess brain injury of a person in military conditions. The numerical model aimed at analyzing changes in the mechanical parameters of brain structure in the conditions of rapid overload. The results of our investigation are intended to contribute to the explanation of the phenomena of degradation of brain structures among soldiers.


Keywords: FEM, biomechanics of brain injury, combat conditions.

This paper presents a fluid-structure interaction simulation applicable for evaluating and optimizing hydraulic valve designs. A special emphasis is placed on shim stack valve commonly used in automotive and railway shock absorbers. For simplicity, the problem was effectively reduced to a two-dimensional (2D) problem. This was accomplished by introducing section-lines along which the pressure profile was computed to find and evaluate the global minimum. The global minimum was then treated as the design ranking measure. This ranking function provided a means to choose an optimal design from a set of available design variants. In the presented results, the ranking is problem-specific as it identifies and localizes low pressure zones that are the root causes of both aeration and cavitation effects. The damping force performance was experimentally evaluated for both the baseline and optimized valve design using a shock absorber level test on a servo-hydraulic test rig.


Keywords: valve system, aeration, cavitation, computational fluid dynamics, fluid-structure interactions, simulation, optimization.

This paper presents an approach to optimize the structure of a micro-drill for reducing its lateral vibration, which has a strong effect on the quality of drilled holes during the cutting process. The micro-drill and the spindle of a micro-drilling spindle system are modeled as Timoshenko's beam elements. Each element with five degrees of freedom at each node comprehensively includes the effects of continuous mass eccentricity, shear deformation, gyroscopic moments, rotational inertia with external thrust force and torque, and coupling torsional and lateral effect. The finite element method is used to determine the lateral amplitude response at the micro-drill point, which is considering the objective function during the optimization of the micro-drill by the interior-point approach. The diameters and the lengths of drill segments are chosen as the design variables with nonlinear constraints in the constant mass, mass center location, and torsional deformation of the drill. The in-house finite element code-integrated optimization environment is implemented in MATLAB to solve the optimal problem. The results showed that compared with the original micro-drill, the lateral amplitude response at the drill point of the optimal one is reduced by 91.89% at an operating speed of 50 000 rounds per minute (r/min), and its first critical speed and the corresponding amplitude response exceed those of the original one.


Keywords: nonlinear constrained optimization, finite element analysis, micro-drilling spindle, continuous eccentricity.

A significant influence of explosive charge geometry is frequently observed during experimental testing. In this paper, the effect of explosive charge shape, along with its material properties, on the generated blast waves is studied. The FEM analysis was conducted for six different explosive materials and three different cylindrical shapes, with geometrical proportions of length L to diameter D varying between 2, 1 and 0.25 and constant charge mass. We found that the blast wave generated by detonation is susceptible to shape changes. However, the different explosive materials were influenced by the charge shape in almost the same way, with only insignificant differences resulting from the material properties.


Keywords: blast wave, FEM, ALE.

This article presents possibilities of using one of network analysis tools for public transport optimization. The work focuses on presenting the transport system as a research polygon for analysis of its geographical information system (GIS). The article covers both a cognitive and methodological application approach. The first is achieved on a wider scope through discussing research regarding public transport in the GIS environment and in a narrower focus on the methodology where the vehicle routing problem (VRP) tool is referred to in detail. The city of Łódz, Poland and its system of night bus connections were used as a case study to illustrate how GIS solutions may be used to manage public transport. The simulation using the VRP tool conducted on a large urban center meets the work's methodological assumptions and may present an indication for local transport managers of how the spatial information systems can boost their organizational operations.


Keywords: vehicle routing problem, network analyst, accessibility, public transport, city.