压电介质二维边界积分方程中的基本解

由于压电介质的变形－电场耦合效应及压电响应的各向异性，使解析求解压电介质问题的工作变量十分复杂，若采用边界元数值方法求解，必须具备积分方程中的基本解，本文根据电磁场方程及连续介质力学的耦合性质论层出了二维无限域中分别在单位力及单位电荷载作用下的位移场，电势场、应力场和电位移场的解，从而确立了边界积分方程中所必需的八个基本解。

THE FUNDAMENTAL SOLUTIONS OF BOUNDARY INTEGRAL EQUATION FOR A TWO-DIMENSIONAL PIEZOELECTRIC MEDIUM

It is extremely difficult to obtain the analytical solution of general piezoelectric Problem due to the deformation-electric field coupling affects and anisotropy of piezoelectric properties.It is hopeful to obtain the solution by using the boundary element method. However,the fundamental solutions of the boundary integral equation must be provided beforehand. In this paper,the solutions of displacement,potential,stress and electric displacement field effected by a unit mechanical force and a unit electric charge individually applied at a point in a two-dimensional infinite domain are derived based on the coupling theory of electromagnetics and continuum mechanics.Hence,the eight indispensable fundamental solutions for BEM are established.