反平面弹性圆形域边缘裂纹奇异积分方程方法  

Singular integral equation approach for edge crack problems of circular region in antiplane elasticity

作　　者：王钟羡[1] 张蕾[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2006年第3期266-269,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：江苏省高校自然科学研究计划项目(04kjd130039)

摘　　要：在反平面弹性情况下,采用在裂纹位置处放置分布位错的方法模拟裂纹,导出了求解圆域或含圆孔无限大域中多边缘裂纹问题的奇异积分方程.首先给出反平面弹性情况下,无限大域中多裂纹问题的复势函数.通过引入补充项,消除无限大域中多裂纹问题的解在圆域边界或圆孔周界上的作用,得到了圆域边界或圆孔周界自由的多边缘裂纹问题的基本解.再由裂纹边界条件建立以分布位错密度为未知函数的Cauchy型奇异积分方程.数值计算时,利用半开型积分法则求解奇异积分方程,得出位错密度函数的离散值,进而计算裂纹尖端处的应力强度因子.最后给出了两个算例,其结果表明所采用方法是可行和正确的,所得结果可以应用于工程实际.In antiplane elasticity, by placing distributed dislocations along cracks, singular integral equation can be formulated for the multiple edge-cracks problem in circular region or infinite region containing a circular hole. Firstly, complex potential of multiple cracks problem of infinite region in antiplane elasticity was given. Then in order to obtain the elementary solution satisfying traction-free condition along the circular boundary, a complementary term was introduced to eliminate the traction on the circle from the solution of the multiple crack in infinite region. Next by singular matching the traction along the cracks, Cauchy integral equations were obtained, in which the distributed dislocation density served as the unknown function. Finally, by using a semi-open quadrature rule, the singular integral equations were solved. Thus, the SIF values at the crack tips were calculated. Two numerical examples were given to verify this method. The results can be applied to actual projects.

关 键 词：断裂力学 多边缘裂纹 反平面弹性 圆域 含圆孔无限大域 奇异积分方程 应力强度因子 

分 类 号：O346.1[理学—固体力学]