Modified Green's function for a point heat source within an anisotropic thermoelastic plane

The Green's function for a homogeneous thermoelastic body usually refers to the fundamental solution for the thermoelastic field induced by a point heat source embedded in the body. However, the most typical version of such a Green's function used in the study of interactions between the heat source and nearby defects (such holes, cracks and inclusions) inevitably leads to impractical divergent thermal stresses in the region distant from the heat source, and this, in turn, would induce significant errors in predicting the local thermal stresses around the defects. To address this deficiency, we establish a modified Green's function for a homogeneous, anisotropic, thermoelastic body under plane deformations. Specifically, we consider a point heat source contained in a finite‐size anisotropic domain with a thermally permeable and traction‐free boundary, and show that the entire thermal stress field in the domain is stable as the size of the domain increases. Numerical examples are presented to validate the current results and illustrate the advantages and practicality of the modified Green's function as opposed to the classical counterpart.