Weakly singular BIE-based procedure for T-stress analysis of cracks in 3D anisotropic linear elastic finite media

摘要

A weakly singular boundary integral equation (BIE) method is developed for the analysis of T-stresses for cracks in three-dimensional, anisotropic, linearly elastic, finite bodies. A system of BIEs governing unknown data on the boundary and crack-face displacement is developed in a broad framework, allowing for the treatment of material anisotropy, finite boundaries, cracks of arbitrary shape, and general loading conditions. To alleviate the requirement on handling all involved singular integrals, a regularization approach is also used to finally obtain BIEs containing only weakly singular kernels. An efficient solution procedure based on a symmetric Galerkin boundary element method and a Galerkin-based approach is implemented to solve the resulting governing BIEs. The near-front field's structure is used to enhance the approximation of crack-face displacement and to provide accurate and direct means for calculating the T-stresses from solved sum of the crack-face displacement. The results of a comprehensive numerical study show that the proposed technique is not only accurate but also capable of handling finite cracked bodies under various scenarios.