ANISOTROPIC THERMOPIEZOELECTRIC SOLIDS WITH AN ELLIPTIC INCLUSION OR A HOLE UNDER UNIFORM HEAT FLOW

The two-dimensional problem of a thermopiezoelectric material con-taining an elliptic inclusion or a hole subjected to a remote uniform heat. flow isstudied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity,conformal mapping and Laurent series expansion, the explicit and closed-form solu-tions are obtained both inside and outside the inclusion (or hole). For a hole problem,the exact electric boundary conditions on the hole surface arc used. The results showthat the electroelastic fields inside the inclusion or the electric field inside the holeare linear functions of the coordinates. When the elliptic hole degenerates into a slitcrack, the electroelastic fields and the intensity factors are obtained. The effect of theheat flow direction and the dielectric constant of air inside the crack on the thermalelectroelastic fields are discussed. Comparison is made with two special cases of whichthe closed solutions exist and it is shown that our results are valid.