反平面弹性分叉裂纹问题的奇异积分方程解法

利用合理的位错模型模拟反平面弹性情况下的分叉裂纹问题，并采用经过改进的积分方案将集中位错放置在分叉点上，连续分布位错布置在分叉裂纹的各个分支上．这样，依据边界条件并以位错函数为未知量可以建立解决问题的奇异积分方程组．由位移单值条件可以得到另外一个约束方程．对各分支使用半开型数值积分法则，把原方程组简化为代数方程组．未知数的个数和方程的个数得到了自然的平衡．数值计算的结果与裂尖处的应力强度因子值直接相关．文中给出了两个数值算例验证所采用方法的正确性．

Singular integral method for branch crack problems in antiplane elasticity

Branch crack problem in antiplane elasticity is modeled by a reasonable distribution of the dislocation. An integration scheme is proposed in the following manner. A point dislocation is placed at the branch point and the distributed dislocations are assumed along all the branches. Thus, the singular integral equation and a constraint equation can be formulated for the branch crack problem. A semi-open quadrature rule is used, which can ensure that the number of unknowns is equal to the number of equations. The results of the numerical solution directly relate to the stress intensity factors at the branch tip. Finally, two numerical examples are given.