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.