A DUAL BOUNDARY INTEGRAL EQUATION METHOD BASED ON DIRECT EVALUATION OF HIGHER ORDER SINGULAR INTEGRAL FOR CRACK PROBLEMS

Compared with finite element method, boundary element method has special advantages in solving the problems of fracture mechanics.The existing methods mainly include the subdomain method and dual boundary integral equation method.This paper presents an improved dual boundary integral equation method to evaluate stress intensity factors for two and three-dimensional crack problems.The method uses a pair of boundary integral equations, in which the traditional displacement boundary integral equation is collocated on the external boundary and the traction boundary integral equation is collocated on one of the crack surfaces.The relative crack opening displacements(CODs) are introduced as unknowns on the crack surface, and the evaluating results of CODs are used to evaluate the stress intensity factors(SIFs) of crack directly.The method uses a direct method to evaluate the hypersingular integral appeared in traction boundary integral equation.For crack tip elements, three kinds of interpolation functions for CODs are provided, and two of these are constructed in the present study.Two-point formula is used to evaluate the SIFs.Some examples are given to verify the correctness of the presented method, compared with the existing exact solution or reference solution, to show that this method can get high precision of the calculation results.