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In this paper, we present several Green’s functions of steady-state heat conduction in anisotropic plane media, including (1) an infinite plane, (2) a half-plane, (3) a bi-material plane, (4) an infinite plane with an elliptical hole or a straight crack, and (5) an infinite plane with an elliptical elastic inclusion. These solutions are obtained by using the link between anisotropic elasticity and heat conduction. We start with reducing the Stroh formalism for two-dimensional anisotropic elasticity to anti-plane deformation and then use the analogy between anti-plane deformation and heat conduction. These Green’s functions serve as fundamental solutions of boundary element method, and the derived temperature field and gradients on the boundary are used as input for thermoelastic analysis. The results of heat conduction and thermoelasticity are verified with analytical solutions or finite element solutions.

Some Green’s functions for steady-state heat conduction in anisotropic plane media and their application to thermoelastic boundary element analysis