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.

Anna Stankiewicz. Imperfection sensitivity of shear banding in gradient-dependent Cam-clay plasticity model. CAMES 2015 (22)

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.

Krystyna Kuźniar, Maciej Zając. Some methods of pre-processing input data for neural networks. CAMES 2015 (22)

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.

Aleksander Matuszak. Errors of stress numerical integration for cross-sections with straight and curved boundaries. CAMES 2015 (22)

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.

Jan Jaśkowiec. Discontinuous Galerkin method on reference domain. CAMES 2015 (22)

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.

IACM and ECCOMAS. 2015- Announcements. CAMES 2015 (22)

PCM and CCM. PCM-CCM- 2015 CONGRESS. CAMES 2015 (22)

CISM Programme 2015. CAMES 2015 (22)

Polish Academy of Sciences and Institute of Fundamental Technological Research. Journals and Books. CAMES 2015 (22)