The paper presents the results of research on the effectiveness of the PIES method developed by the authors, applied to modeling and solving complex 3D problems of elasticity. The results were compared with those obtained using classical element methods FEM and BEM. For the calculation in mentioned methods we have used professional programs ANSYS (FEM), BEASY (BEM) and our own software in the c...

This paper describes the application of a two-parameters crack growth model, based on the usage of two threshold material parameters (DKth and Kmax,th) and on the allowance for residual stresses, introduced at the crack tip by a fatigue load spectrum or by material plastic deformations. The coupled usage of finite element method (FEM) and dual boundary element method (DBEM) is proposed in order...

In this paper we prove the L2 convergence rates for a fully discrete finite element procedure for approximating minimal, possibly unstable, surfaces. Originally this problem was studied by G. Dziuk and J. Hutchinson. First they provided convergence rates in the H1 and L2 norms for the boundary integral method. Subsequently they obtained the H1 convergence estimates using a fully discrete finite...

This paper analyzes the limits of applicability of the time domain surface impedance concept. Numerical results obtained by the boundary element formulation employing time domain surface impedance boundary conditions (SIBCs) of different orders of approximation are compared with experimental data and numerical results obtained using the finite element method. An analytical formula for evaluatio...

We reformulate the discretization of the Johnson–Nedelec method [11] of coupling boundary elements and finite elements for an exterior bidimensional Laplacian. This new formulation leads to optimal error estimates and allows the use of simple quadrature formulas for calculation of the boundary element matrix. We show that if the parameter of discretization is sufficiently small, the fully discr...

The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in analysis pipeline standard (FEM). In this paper, we implement based on SBFEM into commercial software ABAQUS. To end, user are provided through subroutine UEL. Detailed explanation...

This paper deals with the coupled procedure of the boundary element method (BEM) and the finite element method (FEM) for the exterior boundary value problems for the Helmholtz equation. A circle is selected as the common boundary on which the integral equation is set up with Fourier expansion. As a result, the exterior problems are transformed into nonlocal boundary value problems in a bounded ...