Symmetric weak-form integral equation method for three-dimensional fracture analysis

A symmetric Galerkin boundary element method is developed for the analysis of linearly elastic, isotropic three-dimensional solids containing fractures. The formulation is based upon a weak-form displacement integral equation and a weak-form traction integral equation recently developed by Li and Mear (1997). These integral equations are only weakly singular, and their validity requires only that the boundary displacement data be continuous, hence, allowing standard Co elements to be employed. As part of the numerical implementation a special crack-tip element is developed which has a novel feature in that there exist degrees of freedom associated with the nodes at the crack front. As a result, a higher degree of approximation is achieved for the relevant displacement data on the crack and, further, the stress intensity factors are obtained directly in terms of the crack-front nodal data. Various examples are treated for cracks in unbounded domains and for cracks in finite domains (including both embedded and surface breaking cracks), and it is demonstrated that highly accurate results can be achieved using relatively coarse meshes.