New Numerical Quadrature of Integrand with Singularity of 1/r and its Application

Abstract:

A new quadrature method is proposed for numerical integration of integrands with the singularity of 1/r occurring at the computation of stiffness matrix when a singular physical cover is introduced to the numerical manifold method (NMM) for linear fracture problems. The detailed proof is presented, which shows the Jacobian has a factor of r that can be used to eliminate the singularity. Compared with the Duffy transformation, it proves more simple and easier to implement while owning the same precision. A numerical example in elastic fracture by the NMM is presented to illustrate the performance of the proposed method. The result has a good agreement with the reference solution.

• Periodical: Applied Mechanics and Materials (Volumes 444-445)
• Pages: 641-649
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.444-445.641
• Online since: October 2013
• Authors: Dong Dong Xu, Hong Zheng, Kai Wen Xia
• Keywords: 1/r Singularities, Duffy Transformation, NMM, Stress Intensity Factor (SIF)

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