Thermoelastic Green’s function for an elliptical hole in an infinite anisotropic plane

In the theory of thermoelasticity, the Green’s function is usually referred to as the fundamental solution for the elastic field induced by a point heat source in a thermoelastic medium. In terms of the thermoelastic Green’s function for a perforated medium, most of the related study in the literature have been limited to the case of isotropic materials. To remedy this deficiency, we explore in the paper the thermoelastic Green’s function for a perforated anisotropic plane with an elliptical hole under plane deformation. Using conformal mapping and Cauchy integral techniques, the heat source-induced full thermal stress field is derived explicitly and the thermal stress intensity factors in the limiting case when the elliptical hole reduces to a slender crack are also attained. Numerical examples are presented to validate the current results and to illustrate the dependence of stress intensity factors on the location of the point heat source relative to the crack.