Alternative Integration Approaches in the Weight Function ‎Method for Crack Problems

Document Type : Research Paper

Authors
Martin A. Eder
Xiao Chen
Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark‎
10.22055/jacm.2021.37137.2968
Abstract
This study proposes two alternative approaches to complement existing integration strategies used in the weight function method for linear elastic crack problems. The first approach is based on an interpolation type integration scheme and the second approach is based on Gauss quadrature. The proposed approaches enable a computationally efficient numerical integration for computing stress intensity factors in 2D fracture problems. The efficiency is gained through a comparatively low number of integration points facilitated by higher-order approximation. The integration weights only need to be computed once for a given crack length-to-width ratio and can be applied to arbitrary continuous and smooth stress distributions. The proposed approaches show excellent accuracy. In particular, the Gauss quadrature approach exhibits several orders of magnitude more accuracy compared to the most commonly used trapezoidal integration.
Keywords
Stress intensity factor
fracture mechanics
crack length
singularity
weight function integration
Subjects
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Journal of Applied and Computational Mechanics
Volume 7, Issue 3
Summer 2021
Pages 1719-1725