双相材料平行于界面裂纹问题的超奇异积分方程法  

HYPER-SINGULAR INTEGRAL EQUATION METHOD FOR PROBLEM OF CRACK PARALLELED WITH INTERFACE IN PLANE BI-MATERIAL

作　　者：杜云海[1] 徐建国[2] 温玲君[1] 韩连元[1] 

机构地区：[1]郑州大学工程力学系,郑州450002 [2]佛山大学数学系,佛山528000

出　　处：《机械强度》2003年第2期174-177,共4页Journal of Mechanical Strength

基　　金：河南省自然科学基金资助项目 (9740 51 70 0 )~~

摘　　要：由双相材料平面问题的弹性力学基本解和相应裂纹问题的应力场一般表达式 ,通过微分运算及极限分析得到平行于界面裂纹问题的超奇异积分方程组 ,并在有限部积分的意义下建立相应的数值算法 ,把该问题的计算转化为对一个线性方程组的求解。就典型问题无量纲应力强度因子的计算结果表明 ,该方法与体力法及边界元分析基本一致。The crack in a plane bi-material was considered. It is parallel to the interface, and subject to the distributed loads at its surface only. Based on the fundamental solution of the elastic mechanics on the unit concentrated forces and the general formula of the stress field on the crack for a plane bi-material, the hyper-singular integral equations for this problem was derived, through the differentiating process and the limit analysis. Using the dimensionless variables, the suitable function transforms and the finite-part integral of the hyper-singular integral containing Chebyshev polynomial of the second kind, and taking the zeros of the second kind Chebyshev polynomial of degree N +1 as the configuration points, the corresponding numerical method was established, and reduced the calculation of this question to solve a linear equations. Moreover, the non-dimensional stress intensity factors of the typical question of the crack under the uniform pressure were calculated by this method. The calculating result shows that it is consistent with both the body force method and the boundary element analysis.

关 键 词：双相材料 裂纹 超奇异积分方程 应力强度因子 

分 类 号：O346.1[理学—固体力学] O175.5[理学—力学]