Thermoelastic Problems for the Anisotropic Elastic Half-Plane

Abstract

By applying the extended version of Stroh’s formalism, the two-dimensional thermoelastic problem for a semi-infinite anisotropic elastic half-plane is formulated. The steady-state heat transfer condition is assumed and the technique of analytical continuation is employed; the formulation leads to the Hilbert problem, which can be solved in closed form. The general solutions due to different kinds of thermal and mechanical boundary conditions are obtained. The results show that unlike the two-dimensional thermoelastic problem for an isotropic media, where a simply-connected elastic body in a state of plane strain or plane stress remains stress free if the temperature distribution is harmonic and the boundaries are free of traction, the stress within the semi-infinite anisotropic media will generally not equal zero even if the boundary is free of traction.