Stress intensity factors computations using the singularity subtraction technique incorporated with the Tau Method

Abstract

In this paper we discuss the use of the singularity subtraction technique incorporated with the Tau Method for the numerical solution of singular partial differential equations which are relevant to the linear elastic fracture mechanics. To treat the singularity, we apply the singularity subtraction technique to the singular boundary value problems. The problems arising in this application are not in the standard form required by the Tau software. By introducing the pseudo-differential equations, A_k~ = 0, k = l(l)m, to determine the stress intensity and higher order factors A_k results in the standard boundary value problems. We consider two model crack problems including Motz' anti-plane crack problem and a plane strain problem defined by the biharmonic equation. We obtain results of considerable accuracy which compare favorably with those published in the recent literature.