位势问题边界元法中几乎奇异积分的正则化

周焕林; 牛忠荣; 王秀喜

位势问题边界元法中几乎奇异积分的正则化

1.
中国科学技术大学, 力学系, 合肥, 230026;
2.
合肥工业大学, 工程力学系, 合肥, 230009

基金项目: 国家自然科学基金资助项目(10272039)

详细信息

作者简介:
周焕林(1973- ),男,安徽宿松人,博士生(E-mail:zhouhl@mail.ustc.edu.cn).

中图分类号: O343.1;O242.1
计量
- 文章访问数: 2497
- HTML全文浏览量: 102
- PDF下载量: 654
- 被引次数: 0
出版历程
- 收稿日期: 2001-11-27
- 修回日期: 2003-04-15
- 刊出日期: 2003-10-15

Regularization of Nearly Singular Integrals in the Boundary Element Method of Potential Problems

1.
Department of Mechanics, University of Science and Technology of China, Hefei 230026, P.R.China;
2.
Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009, P.R.China

摘要

摘要: 将一种通用算法应用于平面位势问题边界元法中近边界点几乎奇异积分的正则化。对线性单元,位势问题近边界点的几乎强和超奇异积分可归纳为两种形式。通过分部积分,将引起奇异的积分元素变换到积分号之外,从而对这两种积分分别给出了无奇异的正则化计算公式。除了线性元,二次元也应用于该算法。与近边界点临近的二次单元划分为两段线性单元,该算法仍然适用。算例证明了方法的有效性和精确性。对曲线边界问题,联合二次元和线性元可提高计算结果精确度。
- 边界元法 /
- 几乎奇异积分 /
- 正则化 /
- 位势问题
Abstract: A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems.For linear elements,the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts,so non-singular regularized formulas were presented for the two forms of integrals.Furthermore,quadratic elements are used in addition to linear ones.The quadratic element very close to the internal point can be divided into two linear ones,so that the algorithm is still valid.Numerical examples demonstrate the effectiveness and accuracy of this algorithm.Especially for problems with curved boundaries,the combination of quadratic elements and linear elements can give more accurate results.
- BEM /
- nearly singular integral /
- regularization /
- potential problem

HTML全文

参考文献(6)

[1]	Brebbia C A, Telles J C, Wrobel L C. Boundary Element Techniques[M].Berlin, Heidelberg:Springer-Verlag, 1984.
[2]	Ghosh N, Rajiyah H, Ghosh S, et al. A new boundary element method formulation for linear elasticity[J]. JAppl Mech, 1986,53(1) :69-76.
[3]	Huang Q, Cruse T A. Some notes on singular integral techniques in boundary element analysis[J].Internat J Numer Methods Engrg, 1993,36(3) :2643-2659.
[4]	Tanaka M, Sladek V, Sladek J. Regularization techniques applied to BEM[J].Appl Mech Rev,1994,47(10) :457-499.
[5]	牛忠荣,王秀喜,周焕林.边界元法计算近边界点参量的一个通用算法[J].力学学报,2001,33(2):276-283.
[6]	牛忠荣.边界元法中奇异积分问题的研究及其在固体力学中的应用[D].博士学位论文.合肥:中国科学技术大学,2001.