Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners

摘要

The theoretical basis and performance characteristics of two new methods for the computation of the coefficients of the terms of asymptotic expansions at reentrant corners from finite element solutions are presented. The methods, called the contour integral method and the cutoff function method, are very efficient: The coefficients converge to their true values as fast as the strain energy, or faster. In order to make the presentation as simple as possible, we assume that the elastic body is homogeneous and isotropic, is loaded by boundary tractions only and, in the neighborhood of the reentrant corner, its boundaries are stress free. The methods described herein can be adapted to cases without such restrictions. Keywords: Finite element methods, P-extension, Fracture mechanics, Elasticity, Stress intensity factors, Mixed mode, Extraction methods, Convergence, Error estimate.