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High‐order extended finite element method for cracked domains
Author(s) -
Laborde Patrick,
Pommier Julien,
Renard Yves,
Salaün Michel
Publication year - 2005
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.1370
Subject(s) - heaviside step function , extended finite element method , finite element method , singularity , rate of convergence , mixed finite element method , mathematics , displacement (psychology) , convergence (economics) , mathematical analysis , smoothed finite element method , computer science , boundary knot method , structural engineering , engineering , boundary element method , channel (broadcasting) , psychology , computer network , economics , psychotherapist , economic growth
The aim of the paper is to study the capabilities of the extended finite element method (XFEM) to achieve accurate computations in non‐smooth situations such as crack problems. Although the XFEM method ensures a weaker error than classical finite element methods, the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity. The difficulty can be overcome by modifying the enrichment of the finite element basis with the asymptotic crack tip displacement solutions as well as with the Heaviside function. Numerical simulations show that the modified XFEM method achieves an optimal rate of convergence (i.e. like in a standard finite element method for a smooth problem). Copyright © 2005 John Wiley & Sons, Ltd.