Analytical transformation of the volume integral in the boundary integral equation for 3D anisotropic elastostatics involving body force
In the boundary element method (BEM), it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations. To restore the BEMs distinctive notion of boundary discretization, the present work analytically transforms the volume integral to surface ones for the body-force effect in the 3D anisotropic elasticity. On applying Greens Theorem, new fundamental solutions with explicit forms of Fourier series are introduced to facilitate the volume-to-surface transformation. The coefficients of the Fourier-series representations are determined by solving a banded matrix formulated from integrations of the constrained equation. Of no doubt, such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3D anisotropic elasticity involving body force. At the end, numerical verifications of the volume-to-surface integral transformation are presented. Also, such an approach has been implemented in an existing BEM code. For demonstrating the implementation, numerical examples are presented with comparisons with ANSYS analysis. To the authors knowledge, this is the first work in the open literature that reports the successful transformation for 3D anisotropic elasticity.
3d anisotropic elasticity body force boundary element method volume-to-surface integral transformation