Numerical computation of Muskhelishvili's integral equation in plane elasticity

Abstract

Based on Muskhelishvili's integral equation and the Schwarz-Christoffel integral, a numerical procedure is developed for solving the stress fields on plates with emphasis on the region around crack tips. The difficulties in the numerical determination of accessory parameters in the Schwarz-Christoffel transformation are overcome by separating the improper integral into two parts: a finite form of integral in a continuous region which can be integrated exactly; and, a definite integral free of singularity which can easily be computed numerically. Furthermore, the difficulties in the numerical computation of the kernel function in the boundary integral equation are resolved by finding the limit of the kernel function as the source point approaches the field point. Some numerical results of plane-stress problems are provided to demonstrate the accuracy of this approach.