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.