多裂纹问题积分方程方法及相关问题  

INTEGRAL EQUATION METHODS FOR MULTIPLE CRACK PROBLEMS AND RELATED TOPICS

作　　者：陈宜周[1] 

机构地区：[1]江苏大学工程力学研究所,镇江212013

出　　处：《力学进展》2008年第3期358-387,共30页Advances in Mechanics

基　　金：国家自然科学基金(10272053)资助项目~~

摘　　要：综述了平面弹性力学多裂纹问题的一些近代先进解法.一些基本解被着重提出,它们是构成积分方程的基础.这些基本解包括由点源引起和沿裂纹线分布载荷引起.关于平面弹性力学多裂纹问题,介绍了二类奇异积分方程,三类Fredholm积分方程和一类超奇异积分方程.文中还研究了奇异积分方程的正则化问题,即转化为Predholm积分方程的方法,为了求解上述积分方程,介绍了相应求积公式,并详细介绍求解其它众多多裂纹问题的各种方法,阐明了多裂纹解的应用.本文强调了修正复位函数这一概念的重要性,因为它扩大了求解范围.还研究了下列多裂纹问题:(1)多半无限长裂纹问题;(2)一般载荷情况下的多裂纹问题;(3)粘合半平面情况下的多裂纹问题;(4)有限区域的多裂纹问题;(5)网形域多裂纹问题;(6)反平面弹性情况下的多裂纹问题;(7)多裂纹问题中的T应力;(8)周期裂纹问题及其它等等.本综述共引用了187篇学术论文.The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential （MCP） is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include： （i） multiple semi-infinite crack problem, （ii） multiple crack problem with a general loading, （iii） multiple crack problem for the bonded half-planes, （iv） multiple crack problem for a finite region, （v） multiple crack problem for a circular region, （vi） multiple crack problem in antiplane elasticity, （vii） T-stress in the multiple crack problem, and （viii） periodic crack problem and many others. This review article cites 187 references.

关 键 词：平面弹性力学 多裂纹问题 基本解 修正复位复数 积分方程方法 

分 类 号：O241.83[理学—计算数学] TB115[理学—数学]