Numerical Solution of Singular Integral Equations Using Polynomial Expansion Method

Abstract

In this paper, the continuously distributed dislocation model method is applied and the crack problems are formulated as the singular integral equations with Cauchy-type kernel. In the numerical calculation, the unknown dislocation densities are approximated by the products of the weight function and Chebyshev polynomials. The accuracy of stress intensity factors obtained by this method is verified by comparing these values with the exact solution and the reliable numerical solution obtained by other researchers. The present method is found to give rapidly converging numerical results not only for internal crack problems but also for edge crack problems.