双材料中平片裂纹问题的超奇异积分方程解法

利用三维断裂力学的超奇异积分方程方法，对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。首先根据双材料空间的弹性力学基本解，使用边界积分方程方法，在有限部积分的意义下导出了以裂纹面位罗间断为未知函数的超奇异积分方程，并为其建立了数值法。在此基础上，讨论了用裂纹面位移问题计算应力强度因子的方法。最后用此计算了几个典型的Ⅰ型下片裂纹问题的应力强度因子，其数值结果令人满意。

Method of Hypersingular Integral Equation for a Planar Crack Subjected to Tension in Bimaterial

In this paper, the problem of an arbitrarily shaped planar crack which is perpendicular to the interface of bimaterial and loaded by interior normal pressure is studied by means of the method of hypersingular integral equation in three dimensional fracture mechanics. Based on the fundamental solution of two perfectly bonded elastic halfspaces, the boundary integral equation method is used to reduce the problem to a hypersingular integral equation in which the unknown function is the crack opening displacement discontinuity. Then its numerical method is presented, and the method for calculating the stress intensity factor by making use of the displacement discontinuity of crack surface is discussed. Finally, several typical examples are calculated and the numerical results are satisfactory.