A new boundary integral equation method for analysis of cracked linear elastic bodies

Abstract

A novel integral equation method is developed in this paper for the analysis of two-dimensional general anisotropic elastic bodies with cracks. In contrast to the conventional boundary integral methods based on reciprocal work theorem, the present method is derived from Stroh's formalism for anisotropic elasticity in conjunction with Cauchy's integral formula. The proposed boundary integral equations contain boundary displacement gradients and tractions on the non-crack boundary and the dislocations on the crack lines. In cases where only the crack faces are subjected to tractions, the integrals on the non-crack boundary are non-singular. The boundary integral equations can be solved using Gaussian-type integration formulas directly without dividing the boundary into discrete elements. Numerical examples of stress intensity factors are given to illustrate the effectiveness and accuracy of the present method.