半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．

SINGULAR INTEGRAL EQUATION APPROACH FOR HALF-PLANE ANTIPLANE MULTIPLE-EDGE CRACK PROBLEMS

The half-plane antiplane multiple-edge crack problems are solved by using complex variable function and singular integral equation approach. The fundamental solution of a single-edge crack in half-plane is proposed, which is obtained by distributing the dislocation density along the crack configuration, and considering the traction-free condition along the boundary of the half-plane. The fundamental solution is a function of the distributed dislocation density and is composed of the principal part and the complementary part. The half-plane multiple-edge crack problem can be considered as a superposition of many single-edge crack problems. Thus, a system of Cauchy singular integral equations can be formulated. By using a semi-open quadrature rule, the singular integral equations are solved. And the stress intensity factors at the crack tips can be calculated. Finally, some numerical examples are given.