A quasi-optimal convergence result for fracture mechanics with XFEM
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Chahine et al. as discussed by the authors gave a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area.About:
This article is published in Comptes Rendus Mathematique.The article was published on 2006-04-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Extended finite element method & Rate of convergence.read more
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Dissertation
Vérification des facteurs d'intensité de contrainte calculés par XFEM
TL;DR: In this article, the authors propose a technique a meme de fournir un encadrement conservatif des FIC evalues par une methode elements finis classique and par la XFEM.
Journal ArticleDOI
On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity
TL;DR: In this article, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU with high-regularity.
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Analysis of crack propagation in longitudinal beam of high- pile wharf during winter temperature decrease period
Z L Huang,Z Y Huo,Z Y Huang +2 more
TL;DR: Wang et al. as mentioned in this paper carried out numerical analysis on crack propagation of reinforced concrete longitudinal beams of a high-piled wharf in China with ABAQUS software and extended finite element method (XFEM).
Dissertation
Modeling Strong Discontinuities Using Generalized Finite Element Method (GFEM)
TL;DR: Stress analysis and shape sensitivity can be done with any simulation method such as finite element method, finite difference method, Rayleigh-Ritz method, weighted residual method or least square method.
Estimateurs d'erreur pour la méthode XFEM
TL;DR: In this article, an estimateur d'erreur for le problem d'elasticite lineaire in deux dimensions discretise par la methode XFEM is proposed.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
Journal ArticleDOI
A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Related Papers (5)
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more