General solutions for thermopiezoelectrics with various holes under thermal loading

The thermoelectroelastic problems for a hole of various shapes embedded in an in®nite matrix are considered in this paper. Using Strohʹs formalism and the technique of conformal mapping, a uni®ed solution is obtained in closed-form for an in®nite thermopiezoelectric plate with various holes induced by thermal loads. The loads may be uniform remote heat ¯ow, point heat source and temperature discontinuity. Further a detailed discussion on the critical points for the mapping function of a piezoelectric plate with polygonal holes is presented and the study shows that the transformation is nonsingle-valued. A simple approach is given to treat such a situation. As an application of the proposed solutions, a system of singular integral equations for the unknown temperature discontinuity and the dislocation of elastic displacement and electric potential de®ned on crack faces is developed and solved numerically. Numerical results are presented to illustrate the application of the proposed formulatio