计算力学学报Issue(1)：1-6,13,7.DOI:10.7511/jslx201501001
高阶边界元奇异积分的一种通用高效计算方法
An efficient method for numerically evaluating singular integrals in high order boundary element method
摘要
Abstract
A general and efficient method for numerically evaluating singular integrals of various orders in boundary element method (BEM)is presented in this paper.The method is based on Taylor expansions of the integrands in polar coordinate system.Since the singular terms are extracted numerically rather than analytically as in existing methods,the present method is capable of treating various orders of sin-gularities in a general form,independent on the explicit expressions of integrands.Nearly singularities caused by the large aspect ratio of the physical elements and the closeness of the singular points to the element boundary are circumvented by a conformal transformation and a sigmoidal transformation, respectively.Numerical results show that our method could maintain high accuracy with few quadrature points regardless the shape of the element being distorted or not.Performance of this method is further verified by incorporating into a Nyström BEM to solve elastodynamic problems.Our method is imple-mented in C language and is freely available.关键词
边界元/高阶奇异积分/高阶 Nyström 方法/弹性力学/声学Key words
boundary element methods/high order singular integration/high order Nyström method/elastodynamics/acoustics分类
数理科学引用本文复制引用
姚厚朴,校金友,立华..高阶边界元奇异积分的一种通用高效计算方法[J].计算力学学报,2015,(1):1-6,13,7.基金项目
国家自然科学基金(11102154,11074201) （11102154,11074201）
教育部博士点基金(20106102120009,2011 6102110006)资助项目 （20106102120009,2011 6102110006）
