EVALUATION OF SINGULAR AND NEARLY SINGULAR INTEGRALS IN THE BEM WITH EXACT GEOMETRICAL REPRESENTATION＊  

作　　者：Yaoming Zhang Wenzhen Qu Yan Gu 

机构地区：[1]Institute of Applied Mathematics, Shandong University of Technology, Zibo 255039, China [2]State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China [3]Center for Numerical Simulation software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Nanjing 210098, China

出　　处：《Journal of Computational Mathematics》2013年第4期355-369,共15页计算数学（英文）

基　　金：Acknowledgement. The support of the National Natural Science Foundation of China （10571110）, the Opening Fund of the State Key Laboratory of Structural Analysis for Industrial Equipment （GZ1017）, and the National Natural Science Foundation of Shandong Province of China （ZR2010AZ003） are gratefully acknowledged.

摘　　要：The geometries of many problems of practical interest are created from circular or ellip- tic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations （BIEs） and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular proper- ties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occur- ring in the boundary element method （BEM） for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.The geometries of many problems of practical interest are created from circular or ellip- tic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations （BIEs） and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular proper- ties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occur- ring in the boundary element method （BEM） for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

关 键 词：BEM Singular integrals Nearly singular integrals Boundary layer effect Thinwalled structures Exact geometrical representation. 

分 类 号：O343[理学—固体力学] TB115[理学—力学]