A single-domain boundary element method for 3-d elastostatic crack analysis using continuous elements

A boundary element method is presented for single-domain analysis of cracked three-dimensional isotropic elastostatic solids. A numerical treatment For the hypersingular Boundary Integro-Differential Equation (BIDE) for displacement derivatives is described, in which continuous boundary elements may be used. Hadamard principal values of the hypersingular integrals arising in the formulation are evaluated using polar co-ordinates defined on the tangent planes at the source point, and the free term coefficients are calculated directly using a numerical technique. The forms of the Boundary Integral Equation (BIE) and the BIDE are considered for a source point on the coincident surfaces of a crack, and a scheme is given for defining the Traction Boundary Integral Equation TBIE so that it optimally incorporates the traction information deficient in its complementary partner, the BIE. Numerical results for some example mixed-mode crack problems are presented.