双材料平面斜裂纹问题超奇异积分方程方法  

HYPER-SINGULAR INTEGRAL EQUATION METHOD FOR OBLIQUE CRACK IN PLANE BI-MATERIAL

作　　者：杜云海[1] 乐金朝[2] 

机构地区：[1]郑州大学工程力学系,郑州450002 [2]郑州大学环境与水利学院,郑州450002

出　　处：《机械强度》2004年第3期326-331,共6页Journal of Mechanical Strength

基　　金：河南省杰出青年科学基金资助项目 (0 2 1 2 0 0 1 80 0 )~~

摘　　要：由双材料平面问题的弹性力学基本解 ,应用互等功定律和坐标变换 ,得到双材料平面任意斜裂纹问题位移场及应力分量表达式 ,经代入裂纹岸应力边界条件 ,获得以裂纹岸位移间断作为基本未知量的超奇异积分方程组 ;通过适当的积分变换 ,用有限部积分原理处理超奇异积分 ,建立该问题的相应数值算法。文中对任意位置的裂纹问题进行计算 ,并较为系统地分析界面对裂纹应力强度因子的影响 ,当裂纹垂直或平行于双材料界面时 。The problem of an oblique crack in a plane bi-material is considered. Based on the fundamental solution of elasticity for two-half plane, the stresses and the displacements of the problem are derived by use of Betti's reciprocal theorem and the coordinate change. In consideration of the stress boundary conditions of the crack, the hyper-singular integral equations to describe the crack problem are gained. Further more, by use of a suitable integral transformation and the finite-part integral theory, a numerical method used to solve the hyper-singular integral equations is established. Finally, some examples are calculated, in which the location and direction of the crack and the different shear elastic modulus ratios are considered. When the crack is parallel, or perpendicular to the interface of the bi-material, the calculated result is consistent with the results in literatures.

关 键 词：双材料 斜裂纹 超奇异积分方程 应力强度因子 

分 类 号：O241.83[理学—计算数学] O175.5[理学—数学]