Abstract
AbstractThe best approach for the numerical determination of stress intensity factors at crack tips in plane and antiplane elasticity problems is frequently the numerical solution of the corresponding Cauchy‐type singular integral equation by the Gauss–Chebyshev method, followed by the application of the natural extrapolation formula for the numerical determination of the stress intensity factors. It is shown here that this approach converges for Hölder‐continuous and discontinuous (with jump discontinuities) loading distributions along the crack (or cracks) and that in all cases the rate of convergence is greater than that believed up to now. This superconvergence result is based on a theorem on the numerical equivalence of the Gauss–Chebyshev direct method to a relevant indirect method for the numerical solution of Cauchy‐type singular integral equations, also proved here. Numerical results in various crack problems corroborate the theoretical ones.
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