A new solution for thermopiezoelectric solid with an insulated elliptic hole

Abstract

A new solution is obtained for thermal analysis of insulated elliptic hole embedded in an infinite thermopiezoelectric plate. In contrast to our previous results, the present formulation is based on the use of exact electric boundary conditions at the rim of the hole, thus avoiding the common assumption of electric impermeability. Using Lekhnitskii's formulation and conformal mapping, the elastic and electric fields can be expressed in a closed form in terms of complex potentials. The solutions for the crack problem are obtained by setting the minor axis of the ellipse approach to zero. As a consequence, the stress and electric displacement (SED) intensity factors and strain energy release rate can be derived analytically. One numerical example is considered to illustrate the application of the proposed formulation and compare with those obtained from impermeable model.