Internal Point Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids Using the Boundary Element Method

In this paper, fully explicit, algebraic expressions are derived for the first and second derivatives of the Green's function for the displacements in a three dimensional anisotropic, linear elastic body. These quantities are required in the direct formulation of the boundary element method (BEM) for determining the stresses at internal points in the body. To the authors' knowledge, similar quantities have never previously been presented in the literature because of their mathematical complexity. Although the BEM is a boundary solution numerical technique, solutions for the displacements and stresses at internal points are sometimes required for some engineering applications. To this end, the availability of the derivatives of the fundamental solution in closed, algebraic form enables their implementation into an existing BEM code in a relatively straightforward manner. Some examples are presented to demonstrate the veracity of these expressions and their successful implementation for determining interior point solutions in 3D general anisotropic elastostatics in BEM.