各向异性位势平面问题的规则化边界元法  

A REGULARIZED BOUNDARY ELEMENT METHOD FOR ANISOTROPIC POTENTIAL PROBLEMS

作　　者：张耀明[1,2] 刘召颜[1] 李功胜[1] 屈文镇[1] 

机构地区：[1]山东理工大学理学院应用数学所,淄博255049 [2]大连理工大学 工业装备结构分析国家重点实验室,大连116024

出　　处：《力学学报》2011年第4期785-789,共5页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10571110,11071148);山东省自然科学基金重点项目(ZR2010AZ003);工业装备结构分析国家重点实验室开放基金(GZ1017)资助项目~~

摘　　要：基于转化域方程为边界积分方程的极限定理及一个新颖的基本解分解技术,建立间接变量规则化边界积分方程,它有效地避免了奇异积分的直接计算.与已有方法比,该方法不将问题变换为各向同性的问题去处理,因而无需反演运算,也有别于Galerkin方法,无需计算重积分.可计算任意边界位势梯度,而不仅限于法向通量.针对椭圆边界的边值问题,提交一种精确单元来描述边界几何.数值算例表明,所提算法稳定且效率高,所得数值结果与精确解吻合较好.The presentation is mainly devoted to the research on the regularized BEM formulations for homogeneous anisotropic potential problems.Based on a limit theorem for the transformation from domain integral equations into boundary integral equations（BIEs）and a novel decomposition technique to the fundamental solutions,the regularized BIEs with indirect unknowns,which don＇t involve singular integrals,are established. Compared with the existing methods,the presented method can solve the considered problems directly instead of transforming them into isotropic ones,and for this reason,no inverse transform is required.In addition,this method doesn＇t require to calculate multiple integral as the Galerkin method,but rather evaluate CPV integrals indirectly,and so it is simple and easy to program.Furthermore,the proposed gradient BIEs are suited for the computation of■u/■x_i（i=1,2）on the boundary,not only limited to normal flux■u/■n.Especially,for the boundary value problems with elliptic boundary,an exact element is developed to model its boundary with almost no error.The convergence and accuracy of the proposed algorithm are investigated and compared for several numerical examples,demonstrating that a better precision and high computational efficiency can be achieved.

关 键 词：BEM 各向异性 位势问题 规则化边界积分方程 

分 类 号：O342[理学—固体力学]