SINGULAR INTEGRAL EQUATION APPROACH FOR HALF-PLANE ANTIPLANE MULTIPLE-EDGE CRACK PROBLEMS
半平面多边缘裂纹反平面问题的奇异积分方程

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.