标题：Computation of nearly singular integrals in 3D BEM
作者：Zhang, Yaoming; Li, Xiaochao; Sladek, Vladimir; Sladek, Jan; Gao, Xiaowei
作者机构：[Zhang, Yaoming; Li, Xiaochao] Shandong Univ Technol, Inst Appl Math, Zibo 255049, Peoples R China.; [Zhang, Yaoming; Gao, Xiaowei] Dalian Univ Tech 更多
通讯作者地址：[Zhang, YM]Shandong Univ Technol, Inst Appl Math, Zibo 255049, Peoples R China.
来源：ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
关键词：3D BEM; 2D nearly singular integrals; High-order geometry elements;; Transformation; Elastostatics
摘要：This paper presents a general methodology for numerical evaluation of the nearly singular 2D integrals over the eight-node second-order quadrilateral geometry elements arising in 3D BEM. An accurate formula of distance between the source and the field point is proposed firstly. And then an extended form of the exponential transformation, which was firstly proposed by present author to regularize nearly singular integrals arising in 2D BEM, is developed to smooth out the rapid variation of the aforementioned formula of distance. Finally, several numerical examples involving boundary layer effect and thin body problems in 3D elastostatics are investigated to verify the proposed scheme, yielding very promising results. Moreover, it should be stressed that the proposed scheme is suitable for any high-order surface elements. (C) 2014 Elsevier Ltd. All rights reserved.