Boundary integral formulations for three-dimensional anisotropic piezoelectric solids

A boundary integral equation method is applied to the solutions of three dimensional piezoelectric solids. Based on the reciprocal relations, a pair of boundary integral formulae were formulated for evaluation of the fields in the medium. The Green's functions and their first partial derivatives employed in the formulations are evaluated numerically from the line integral solutions derived from the Fourier transform. By constructing some augmented matrices, we show that the topic can be treated systematically as that in the uncoupled elastic and dielectric problems. In illustration, we present results for the internal fields of a spherical cavity in an infinite piezoelectric medium loaded by a uniform traction on its boundary. Two piezoelectric ceramics, PZT-6B and gallium arsenide, are considered in the calculations. Some comparisons are made with solutions of purely elastic solids and with our recent calculations based on the finite element method.