A new thermoelectroelastic solution for piezoelectric materials with various openings

A new solution is obtained for thermoelectroeiastic analysis of an insulated hole of various shapes embedded in an infinite piezoelectric plate. Based on the exact electric boundary conditions on the hole boudnary, Lekhnitskii's formulation and conformal mapping, the solution for elastic and electric fields has been obtained in closed form in terms of complex potential. The solution has a simple unified form for various holes such as ellipse, circle, triangle and square openings. As an application of the solution, the hoop stress and electric displacement (SED) and the solution for crack problems are discussed. Using the above results, the SED intensity factor and strain energy release rate can be obtained analytically. One numerical example is considered to illustrate the application of the proposed formulation and compared with those obtained from impermeable model.