3D BEM for the general piezoelectric solids

Abstract

In this paper we present a new scheme of three-dimensional boundary element method for the general anisotropic piezoelectric solids. We use the Radon transform representation of the three-dimensional fundamental solutions of piezoelectricity and integrate them analytically over the triangular boundary element with the linear interpolation. This reduces the computation for the system matrices G and H from the standard singular surface integrations to the simple regular line integrations and enables a drastic reduction of the computation time. The integrand of the line integral consists of the product of a function dependent and another function independent on the location vectors representing the source and observation points. The latter function depends only on the material and element properties and thus calculated only once for each element and saved for a repeated use in the calculation of G and H matrices and in the post-processing. Exploitation of this favorable structure results in the further reduction of the computation time for very large systems. The implementation of the proposed method with numerical examples will be presented.