A boundary element method for transient piezoelectric analysis

Abstract

In this paper, a boundary element (BE) formulation is developed originally which treats three-dimensional problems of transient piezoelectricity. The approach at hand uses the fundamental solution of the static piezoelectric operator instead of the transient one. This results in a domain integral appearing in the representation formula, which contains the inertia term. This domain integral can be transformed to the boundary using the dual reciprocity method (DRM), which leads to a system of ordinary differential equations in time domain, similar to the systems obtained in standard finite element methods (FEM). The DRM has been chosen because of the difficulties and big computational effort involved in a BE implementation, which makes use of the anisotropic transient piezoelectric fundamental solution. It is an approach that appears to be much too time-consuming for use in a commercial BE code, in which computational costs is an important issue. The method presented in this paper is validated by a numerical example for transient piezoelectricy, which demonstrates excellent agreement with FE computations for the generalized displacements, and an improved accuracy for the flux quantities such as electric field and elastic stresses.