Communication science et technologie
Volume 15, Numéro 1, Pages 104-119
2017-01-01

Analysis Of Inhomogeneous Domains And Anisotropic Inclusions By The Boundary Element Method

Authors : Yamani Sara . Sahli Ahmed . Kebdani Said . Sahli Sara .

Abstract

This paper deals with elastic 2D problems characterized by the presence of zones with different materials and anisotropic inclusions using the boundary element method. The anisotropy can be either assumed over the whole domain, or defined only over some particular inclusions, which is the most usual case. Fundamental solutions for anisotropic domains, although well-known, lead to more complex formulations and may introduce difficulties when the analysis requires more complex material models as for instance plastic behavior, finite deformations, etc. The alternative formulation proposed in this work can be applied to anisotropic bodies using the classical fundamental solutions for 2D elastic isotropic domains plus correction given by an initial stress field. The domain region with anisotropic properties or only with different isotropic elastic parameters has to be discretized into cells to allow the required corrections, while the complementary part of the body requires only boundary discretization. The initial stress tensor to be applied to the anisotropic region is defined as the isotropic material elastic stress tensor correction by introducing a local penalty matrix. This matrix is obtained by the difference between the elastic parameters between the reference values and the anisotropic material. This technique is particularly appropriate for anisotropic inclusion analysis, in which the domain discretization is required only over a small region, therefore increasing very little the number of degrees of freedom of the final algebraic system. The numerical results obtained by using the proposed formulation have demonstrated to be very accurate in comparison with either analytical solutions or the other numerical values.

Keywords

Keywords: Key words: Boundary element method, anisotropic inclusions, multi-region.