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Crack tip enrichment in the XFEM using a cutoff function
Author(s) -
Chahine Elie,
Laborde Patrick,
Renard Yves
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2265
Subject(s) - extended finite element method , computation , convergence (economics) , rate of convergence , mathematics , function (biology) , finite element method , cutoff , coupling (piping) , mathematical optimization , mathematical analysis , algorithm , computer science , key (lock) , structural engineering , physics , engineering , mechanical engineering , computer security , quantum mechanics , evolutionary biology , economics , biology , economic growth
We consider a variant of the eXtended Finite Element Method (XFEM) in which a cutoff function is used to localize the singular enrichment surface. The goal of this variant is to obtain numerically an optimal convergence rate while reducing the computational cost of the classical XFEM with a fixed enrichment area. We give a mathematical result of quasi‐optimal error estimate. One of the key points of this paper is to prove the optimality of the coupling between the singular and the discontinuous enrichments. Finally, we present some numerical computations validating the theoretical result. These computations are compared with those of the classical XFEM and a non‐enriched method. Copyright © 2008 John Wiley & Sons, Ltd.