The solution to an elliptic partial differential equation for facilitating exact volume integral transformation in the 3D BEM analysis

Abstract

In the direct boundary element method (BEM), the body-force or its equivalence will reveal itself as a volume integral that shall destroy the important notion of boundary discretisation. For resolving this issue, the most elegant approach would be to analytically transform the volume integral to boundary ones. In the process of such attempt for 3D anisotropic elastostatics, the key lies in analytically formulating the fundamental solution to a partial differential equation. In this paper, the partial differential equation is presented in an elliptic form, followed by formulating its analytical solution. In the BEM analysis, the formulated solution will be a key part to the success of performing exact volume-to-surface integral transformation.