Numerical treatment of finite part integrals in 2-D boundary element analysis with application in fracture mechanics (Q1312586)

The authors consider the displacement boundary integral equation on one crack surface and the traction boundary integral equation (BIE) on the opposite one for the boundary element method formulation of crack problems instead of the subregion technique. They consider two- dimensional problems, and the hypersingular integrals contained in the traction BIE are treated in two ways. The first one, which is applicable to simple boundary geometry (linear or circular contour), consists in direct parametrization of the hypersingular contour integral in global space. Then, the finite part integral can be evaluated after scaling by using Kutt's formula. In the case of general geometry, they express the global parameter (length of the boundary contour from a fixed point to the integration point) via an intrinsic coordinate introduced on the boundary elements of the discretized boundary contour. The proposed formulation is applied to crack problems with using Overhauser spline crack tip elements for better approximation of asymptotic crack tip fields. Two simple numerical examples are considered in which the stress intensity factors are evaluated.