Exact solutions for the plane problem in piezoelectric materials with an elliptic hole or a crack
The authors consider a plane problem for a transversely isotropic piezoelectric material. In this case the general solution to field equations can be expressed in terms of three analytical functions each of which depends solely on a single, though different, complex variable. Then the authors study the problem of elliptical hole in an infinite medium subjected to constant stresses and electric displacement vectors at infinity. The electric potential inside the hole is assumed to be a linear function of coordinates, and the standard conformal mapping technique is employed to fully determine complex potentials. The crack geometry is represented as a degenerate elliptic hole with vanishing minor axis, and the corresponding solution is obtained. Additionally, the authors evaluate intensity factors for the stress and electric displacement at crack tips.
transversely isotropic piezoelectric material
scientific article; zbMATH DE number 1340962