A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics

Simpson, Robert; Trevelyan, Jon

Abstract

This paper introduces an enriched Boundary Element Method in which functions are introduced that are known to model singularities or discontinuities from a priori knowledge of the solution space. Additional fundamental solutions are introduced to solve for the additional unknowns created by enrichment and a numerical integration routine is outlined for the evaluation of strongly singular and hypersingular enriched boundary integrals. The solution of a curved crack in an infinite domain by Muskhelishvili is used to assess the accuracy of the method. Using an appropriate technique to evaluate J1 and J2 integrals, it is found that very good agreement with the exact solution is seen with improvements in accuracy over similar FEM implementations.

Citation

Simpson, R., & Trevelyan, J. (2011). A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics. Computer Methods in Applied Mechanics and Engineering, 200(1-4), 1-10. https://doi.org/10.1016/j.cma.2010.06.015

• Journal Article Type: Article
• Publication Date: Jan 1, 2011
• Deposit Date: Nov 29, 2010
• Publicly Available Date: Dec 2, 2010
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Electronic ISSN: 1879-2138
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 200
• Issue: 1-4
• Pages: 1-10
• DOI: https://doi.org/10.1016/j.cma.2010.06.015
• Keywords: BEM, Fracture, Partition of Unity, Enrichment.
• Public URL: https://durham-repository.worktribe.com/output/1512766