Complete and exact solutions of a penny-shaped crack in a piezoelectric solid: antisymmetric shear loadings

This paper presents an exact analysis of the problem of a penny-shaped crack in a transversely isotropic piezoelectric medium subjected to arbitrary shear loading that is antisymmetric with respect to the crack plane. The analysis is based on the general solution of three-dimensional piezoelasticity, which is represented by four quasi-harmonic displacement functions. It is shown that these harmonics can be represented by one complex potential. By using the previous results in potential theory, an exact solution is obtained. In particular, for uniform shear and point shear loadings, complete expressions for the elastoelectric field are derived in terms of elementary functions.