A 3-D boundary element formulation of anisotropic elasticity with gravity

Abstract

This paper presents a new boundary element formulation for three-dimensional (3-D) linear elastic bodies with anisotropic properties (transverse isotropy with any orientation) subject to gravity. Green's functions for such anisotropic media are derived in exact closed-form. Particular stresses and displacements related to the gravity body force are also presented in exact closed-form for generalized anisotropic media. The boundary integral equation with only weak singularities is formulated based on the principle of superposition and is such that no numerical integration associated either with the Green's functions for anisotropic media or with body forces is necessary. This new 3-D boundary element formulation has been programmed, and several numerical examples are presented and checked with existing closed-form solutions. It is found that even with a very coarse discretization, excellent results can be obtained with the proposed method.