Plane Piezoelectric Materials Virtual Boundary Element Method

Firstly, based on the fundamental solutions or Green's solutions for plane problem of piezoelectricity and the principle of superposition for linear system, a virtual boundary-equivalent collocation method was presented in this paper. Compared with direct BEM, this algorithm avoided the computation of singular integral and nearly singular integral, which are often caused when the source point lies on or closes to the integral element, respectively. At the same time, this method also has advantages of BEM, such as the reduced dimensionality of the basic process, the decreased amount of computation, continuous variables in interior point, and so on.Secondly, this paper presents the virtual boundary-least square collocation method and the virtual boundary element-integral method, for the sake of the problems of the singularity of the effective matrix and the stability of solution possibly caused in. the process of using the virtual boundary- equivalent collocation method.At the same time, some numerical examples are performed to demonstrate the performance of these algorithms, respectively. The results are found to agree well with the exact solution. So they may be one of effective computational methods to analyze the plane problem of piezoelectric media.Finally, work above is summarized and some problems are discussed, which are faced to be studied and solved in the future further, so that the use of this method can be extended to more situations.