A further study of two-dimensional boundary element crack analysis in anisotropic or orthotropic materials

Abstract

In two-dimensional problems, composite materials can generally be treated as anisotropic or orthotropic materials. When composite materials are analysed by BEM, the fundamental solutions with characteristic roots are used in the BEM differently from FEM, so that some problems related to the characteristic roots occur in anisotropic or orthotropic materials. In this paper, the fundamental solutions of BEM are systematically classified and analysed according to the kind of characteristic roots for anisotropic or orthotropic materials. In particular, when the characteristic roots of orthotropic materials are equal, we call these materials pseudo-isotropic materials. The fundamental solutions of BEM and the stress and displacement fields of a crack for pseudo-isotropic materials are analysed by the analogous method of isotropic materials. Also, because there is a risk of analysing non-existent anisotropic or orthotropic materials by numerical methods for some types of characteristic roots, the range of existing orthotropic materials is clarified by the positive definiteness of strain energy density. The BEM results of cracks or other problems are shown and discussed.