Three iterative methods for the numerical determination of stress intensity factors

Abstract

Three iterative methods for the numerical determination of stress intensity factors at crack tips (by using the method of singular integral equations with Cauchy-type kernels) are proposed. These methods are based on the Neumann iterative method for the solution of Fredholm integral equations of the second kind. Two of these methods are essentially used for the solution of the system of linear algebraic equations to which the singular integral equation is reduced when the direct Lobatto-Chebyshev method is used for its approximate solution, whereas the third method is a generalization of the first two and is related directly to the singular integral equation to be solved. The proposed methods are useful for the determination of stress intensity factors at crack tips. Some numerical results obtained in a crack problem show the effectiveness of all three methods.