Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids

Two-dimensional electroelastic analyses have been performed theoretically on a transversely isotropic piezoelectric material containing an elliptic hole, subjected to a uniform stress field and a uniform electric displacement field at infinity while the surface of the hole is free of traction and electrically open. Solutions are obtained by using the exact electric boundary condition based on the complex variation method. Explicit solutions for the distributions of the mechanical and electrical components on the rim of the elliptic hole are obtained. An interesting relationship between the stress concentration factor of an elliptic hole (K_t) and that of a circular hole (K _t|t=1), K_t=1+K_t|t=1-1/t, is found in both elastic and piezoelectric materials. It is shown that the electromechanical coupling effect is helpful to reduce the stress concentration. And the influence of the dielectric parameter of the medium inside the hole on the stresses and the concerned stress concentration factor at the surface of the hole is weak in a wide range of the dielectric parameter. Comparisons with available results show good coincidence.