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.

H. Altenbach, K. Naumenko, S. Pylypenko. On the numerical prediction of the anisotropic elastic properties in thin-walled structures made from short-fiber reinforced plastics. CAMES 2005 (12)

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.

M. Klasztorny. Nonlinear vibrations of a moving rail-vehicle excited by snaking and lateral impacts of wheel sets. CAMES 2005 (12)

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.

A. Maciąg, J. Wauer. Wave polynomials for solving different types of two-dimensional wave equations. CAMES 2005 (12)

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.

Ł. Kaczmarczyk, Z. Waszczyszyn. Neural procedures for the hybrid FEM/NN analysis of elastoplatic plates. CAMES 2005 (12)

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.

R. Stocki. A method to improve design reliability using optimal Latin hypercube sampling. CAMES 2005 (12)

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.

M.F. Robbe, M. Lepareux, E. Treille, Y. Cariou. Numerical simulation of an explosion in a small-scale replica of a Fast Breeder Reactor. CAMES 2005 (12)

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.