SYMMETRICAL WEAK-FORM INTEGRAL-EQUATION METHOD FOR 3-DIMENSIONAL FRACTURE-ANALYSIS

A symmetric Galerkin boundary element method is developed for the anal ysis of linearly elastic, isotropic three-dimensional solids containin g fractures. The formulation is based upon a weak-form displacement in tegral equation and a weak-form traction integral equation recently de veloped by Li and Mear (1997). These integral equations are only weakl y singular, and their validity requires only that the boundary displac ement data be continuous, hence, allowing standard C degrees elements to be employed. As part of the numerical implementation a special crac k-tip element is developed which has a novel feature in that there exi st degrees of freedom associated with the nodes at the crack front. As a result, a higher degree of approximation is achieved for the releva nt displacement data on the crack and, further, the stress intensity f actors are obtained directly in terms of the crack-front nodal data. V arious examples are treated for cracks in unbounded domains and for cr acks in finite domains (including both embedded and surface breaking c racks), and it is demonstrated that highly accurate results call be ac hieved using relatively coarse meshes.