Two-dimensional BEM thermoelastic analysis of anisotropic media with concentrated heat sources

It is well known in elastic stress analysis using the boundary element method (BEM) that an additional volume integral appears in the basic form of the boundary integral equation if thermal effects are considered. In order to restore this general numerical tool as a truly boundary solution technique, it is perhaps most desirable to transform this volume integral exactly into boundary ones. For general 2D anisotropic thermoelastostatics without heat sources, this was only achieved very recently. The presence of concentrated heat sources in the domain, however, leads to singularities at these points that pose additional difficulties in the volume-to-surface integral transformation. In this paper, the steps to overcome these difficulties are described and the integral transformation is successfully achieved for BEM implementation in a mapped plane. Three numerical examples are presented to demonstrate the veracity of the analytical and numerical formulations.