Periodic group edge crack problem of half-plane in antiplane elasticity.

Using complex variable function, an elementary solution of a single-edge crack problem for half-plane is proposed. The elementary solution is obtained by distributing the dislocation density along the prospective place of crack, and it is composed of the principal part and the complementary part. Based on the elementary solution and the principle of superposition, a system of Cauchy singular integral equations for periodic group edge crack problems of half-plane in antiplane elasticity can be formulated. In the solution of the singular integral equation, the influences of many neighbouring groups on the central group are evaluated exactly. In addition, the influences on the central group by the many remote groups are considered approximately. By using a semi-open quadrature rule, the singular integral equations are solved and the stress intensity factors at the crack tips are evaluated. Several numerical examples are given. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]