Boundary elements for cracks and notches in three dimensions

Plane and curved cracks are modelled by boundary elements, of geometry defined by conforming quadratic and hybrid quadratic-Hermitian cubic shape functions. Displacement and traction are interpolated by the quadratic functions, supplemented by singular functions by which are multiplied stress intensity factors corresponding to each of the three modes of crack opening displacement, for the first three eigenvalues of the Williams eigenfunction expansion and its equivalent for antiplane strain. Singular and hypersingular boundary integral equations are taken at nodes of elements and auxiliary collocation points. Singular and hypersingular components of integrals are evaluated by consideration of trial displacement fields (simple solutions) for subdomains lying to either side of the crack. Examples are shown of buried and surface cracks, and computed results compared with those obtained by other methods. For surface cracks, the computed results reveal the cause of significant discrepancies between values given by well established empirical and other formulae. The modelling of notches is demonstrated by an analysis of stress in rock near a tunnel intersection. Computational efficiency is discussed, and improvements and extensions of the analysis are proposed