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

The half-plane antiplane multiple-edge crack problems aresolved by using complex variable function and singular integral equationapproach. The fundamental solution of a single-edge crack inhalf-plane is proposed, which is obtained by distributing the dislocationdensity along the crack configuration, and considering the traction-freecondition along the boundary of the half-plane. The fundamental solution is afunction of the distributed dislocation density and is composed of theprincipal part and the complementary part. The half-plane multiple-edge crack problem can be considered as a superposition of many single-edge crackproblems. Thus, a system of Cauchy singular integral equations can beformulated. By using a semi-open quadrature rule, the singular integralequations are solved. And the stress intensity factors at the crack tips canbe calculated. Finally, some numerical examples are given.