Unified and explicit expressions of three-dimensional Green’s functions and their first derivatives for piezoelectric solids with general anisotropy

Abstract

Unified and explicit expressions of static three-dimensional generally anisotropic Green’s functions and their first derivatives are presented. The application of residue calculus to the line integral form of the Green’s functions and their derivatives yields the conventional explicit expressions. The numerical evaluations of these expressions become unstable in the nearly degenerate case. In contrast to the conventional explicit expressions, the novel unified explicit expressions have no factors like (pi−pj) in any denominator. The novel expressions remain valid for all cases. Their numerical evaluations, therefore, possess very high accuracy and efficiency. Following our previous works in generally anisotropic elasticity, the unified explicit expressions of the Green’s functions and their derivatives for anisotropic piezoelectric materials are presented for the first time. The accuracy and stability of novel unified and explicit expressions are verified numerically. Furthermore, the newly derived explicit expressions are used to investigate the influences of the material anisotropy on the displacements and electrical potential in a piezoelectric solid, when a point force or an electrical charge is imposed. The numerical results suggest that the field quantities can be tuned by the proper choose of the material anisotropy or the orientation of the principal material axes.