Singular integral equation method for the solution of multiple curved crack problems

摘要

A method based on complex potentials for distributions of dislocations along curved cracks is used to solve multiple curved crack problems in plane elasticity. The method allows evaluation of the interaction between curved cracks. A crack problem is reduced to a system of singular integral equations and the crack curve length is taken as the coordinate in the associated integral equations. A crack is then mapped on the real axis in an interval (-a, a), where 2a is the length of crack and the original singular integral equations are transformed accordingly. The method allows cracks with a general curvature and is not restricted to slightly curved crack configurations. The resulting singular integral equation system is solved through Gauss quadrature. A few numerical examples of problems with two cracks are given and crack interaction, i.e., the shielding effect of a curved crack surrounding by another, is also studied. (C) 2004 Published by Elsevier Ltd.