Boundary integral equation method to solve embedded planar crack problems under shear loading

The solution of three-dimensional planar cracks under shear loading are investigated by the boundary integral equation method. A system of two hypersingular integral equations of a three-dimensional elastic solid with an embedded planar crack are given. The solution of the boundary integral equations is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack without a polygonal contour shape and permit the fast convergence for the results. The stress intensity factors at the crack front are calculated in the case of a circular and an elliptic crack and are compared with the analytical solution.