Green's Functions for Anisotropic/Piezoelectric Bimaterials and Their Applications to Boundary Element Analysis

Abstract

The Green’s function for anisotropic bimaterials has been investigated around three decades ago. Since the mathematical formulation of piezoelectric elasticity can be organized into the same form as that of anisotropic elasticity by just expanding the dimension of the corresponding matrix to include the piezoelectric effects, the extension of the Green’s function to piezoelectric bimaterials can be obtained immediately through the associated anisotropic bimaterials. In this paper, the Green’s function for the bimaterials bonded together with one anisotropic material and one piezoelectric material is derived by applying Stroh’s complex variable formalism with the aid of analytical continuation method. For this problem, the interfacial condition of electric field depends on the electric conductivity of anisotropic elastic materials. Employing these Green’s functions, a special boundary element satisfying the interfacial continuity conditions of anisotropic/piezoelectric bimaterials is developed. With the embedded Green’s functions, this special boundary element preserves two special features: (1) the interface continuity conditions are satisfied exactly and no meshes are needed along the interface; (2) the materials below and above the interface can be any kinds of piezoelectric or anisotropic elastic materials. To show the advantages of the present special boundary element, several numerical examples such as orthotropic/isotropic bimaterials, PZT-7A/PZT-5H bimaterials and anisotropic/piezoelectric bimaterials are illustrated and compared with the solutions calculated by other numerical methods. The numerical results show that the present special boundary element is not only accurate but also efficient.