A new boundary integral equation method for cracked 2-D anisotropic bodies

By using integration by parts to the traditional boundary integral formulation, a traction boundary integral equation for cracked 2-D anisotropic bodies is derived. The new traction integral equation involves only singularity of order 1/r   and no hypersingular term appears. The dislocation densities on the crack surface are introduced and the relations between stress intensity factors and dislocation densities near the crack tip are induced to calculate the stress intensity factors. The boundary element method based on the new equation is established and the singular interpolation functions are introduced to model the singularity of the dislocation density (in the order of 1/r) for crack tip elements. The proposed method can be directly used for the 2-D anisotropic body containing cracks of arbitrary geometric shapes. Several numerical examples demonstrate the validity and accuracy of BEM based on the new boundary integral equation.