Electro-elastic fields in an elliptic piezoelectric plane with an elliptic hole or a crack of arbitrary location

Electro-elastic fields in an elliptic piezoelectric plane with an elliptic hole or a crack of arbitrary location are studied based on the complex variable method and the assumption that the elliptic hole or the crack is impermeable to an electric field. The novel feature of the present work is to construct the complex potentials in a finite piezoelectric body with Faber series containing unknown coefficients. Using the given boundary conditions, the coefficients can be solved, and then the electro-elastic fields in the plane can be calculated. Finally, numerical examples are given for the electro-elastic fields in the plane and the electro-elastic intensity factors at the crack tips when the hole degenerates into a crack. It is found that the sizes of the elliptic plane and the elliptic hole (or the crack) have a great influence on electro-elastic fields (or the intensity factors of the crack).