The extended/generalized finite element method: An overview of the method and its applications

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements. This is achieved...

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Vydané v:International journal for numerical methods in engineering Ročník 84; číslo 3; s. 253 - 304
Hlavní autori: Fries, Thomas-Peter, Belytschko, Ted
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Chichester, UK John Wiley & Sons, Ltd 15.10.2010
Wiley
Predmet:
Approximation
Computer simulation
Condensed matter: structure, mechanical and thermal properties
Copyrights
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
extended finite element method
Finite element method
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
generalized finite element method
GFEM
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
partition of unity method
Physics
PUM
review
Sciences and techniques of general use
Simulation
Solid mechanics
Solid-liquid transitions
Solidification
Specific phase transitions
Structural and continuum mechanics
XFEM
Singularity
Partition method
Polynomial approximation
GFEM
Kinking
PUM
Modeling
Dislocation
Solidification
Finite element method
Shear fracture
partition of unity method
review
generalized finite element method
Unity partition
eXtended Finite Element Method
XFEM
ISSN:0029-5981, 1097-0207, 1097-0207
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Shrnutí:An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non‐smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi‐field problems. Copyright © 2010 John Wiley & Sons, Ltd.
Bibliografia:German Research Foundation (DFG)
Office of Naval Research - No. N00014-08-1-1191
Army Research Office - No. W911NF-08-1-0212
ArticleID:NME2914
ark:/67375/WNG-SVNZ4K6V-V
istex:A4E0CE0867DB536AF78C1A0C973D706A84C4D449
Chair.
ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.2914