平面电磁弹性固体的虚边界元——最小二乘配点法  

VIRTUAL BOUNDARY ELEMENT—LEAST SQUARE COLLOCATION METHOD FOR PLANE MAGNETOELECTROELASTIC SOLIDS

作　　者：姚伟岸[1] 李晓川[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《工程力学》2006年第10期61-67,60,共8页Engineering Mechanics

基　　金：国家自然科学基金(10172021)资助项目

摘　　要：从电磁弹性固体平面问题的基本方程出发,依据弹性力学虚边界元法的基本思想,利用电磁弹性固体平面问题的基本解,提出了电磁弹性固体平面问题的虚边界元——最小二乘配点法。电磁弹性固体的虚边界元法在继承传统边界元法优点的同时,有效地避免了传统边界元法的边界积分奇异性的问题。由于仅在虚实边界选取配点,此方法不需要网格剖分,并且不用进行积分计算。最后给出了一些具体算例,并和已有的解析解进行了对比,结果表明提出的虚边界元方法有很高的精度。Based on the fundamental equations of the plane magnetoelectroelastic solids and the basic idea of virtual boundary element method for elasticity, a virtual boundary element-least square collocation method （VBEM） for plane magnetoelectroelastic solids is presented. Besides all the advantages of the conventional boundary element method （BEM） over domain discretization methods, the method avoids the computation of singular integral on the boundary by introducing the virtual boundary. This method, merely using collocations technology on the real and virtual boundaries, is mesh-free and integration-free. In the end, several numerical examples are presented to demonstrate the performance of the proposed method. The results show that they agree well with the exact solutions.

关 键 词：电磁弹性固体 平面问题 虚边界元法 基本解 最小二乘配点法 

分 类 号：O242[理学—计算数学] O34[理学—数学]