The extended/generalized finite element method: An overview of the method and its applications
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An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented in this article, which enables accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements.Abstract:
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.read more
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Basic principles of Virtual Element Methods
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Level-set methods for structural topology optimization: a review
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Isogeometric analysis: an overview and computer implementation aspects
TL;DR: An introduction to IGA applied to simple analysis problems and the related computer implementation aspects is presented, and implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is presented.
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Equivalent projectors for virtual element methods
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Mimetic finite difference method
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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.
Journal ArticleDOI
Yielding of steel sheets containing slits
TL;DR: In this article, a relation between extent of plastic yielding and external load applied was investigated, and panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
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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.
Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.
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Level Set Methods and Dynamic Implicit Surfaces
Stanley Osher,Ronald Fedkiw +1 more
TL;DR: A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.
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