Stress intensity factors at crack tips near boundaries or other geometrical discontinuities

Abstract

A modification of the Lobatto-Chebyshev method for the numerical solution of Cauchy type singular integral equations appearing in plane or antiplane elasticity crack problems and the determination of stress intensity factors at crack tips is presented. This modification, based on a variable transformation, permits the selection of abscissas and collocation points used to be modified so as to obtain rapid convergence of the numerical results for the stress intensity factors to their correct values. The proposed technique is seen to be particularly effective for crack problems with crack tips near boundaries, interfaces or other geometrical discontinuities. Two applications of the method, to a periodic array of cracks in plane elasticity and to an antiplane shear crack near a boundary, show the effectiveness of the method.