Journal ArticleDOI
The design and analysis of the Generalized Finite Element Method
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TLDR
The GFEM is introduced as a combination of the classical Finite Element Method (FEM) and the Partition of Unity Method (PUM) to solve problems in domains with complex geometry with less error and less computer resources.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2000-01-07. It has received 898 citations till now. The article focuses on the topics: Extended finite element method & Mixed finite element method.read more
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The extended/generalized finite element method: An overview of the method and its applications
TL;DR: 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.
Journal ArticleDOI
Extended finite element method for three-dimensional crack modelling
TL;DR: In this article, an extended finite element method (X-FEM) for three-dimensional crack modeling is described, where a discontinuous function and two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity.
Journal ArticleDOI
Modeling holes and inclusions by level sets in the extended finite-element method
TL;DR: In this paper, a methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed, which couples the level set method with the extended finite element method (X-FEM).
Journal ArticleDOI
A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering
TL;DR: In this paper, the authors present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics and discuss the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations.
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Arbitrary branched and intersecting cracks with the eXtended Finite Element Method
TL;DR: In this paper, a new technique for the finite element modeling of cracks with multiple branches, multiple holes and cracks emanating from holes is presented, which allows the representation of crack discontinuities and voids independently of the mesh.
References
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Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Journal ArticleDOI
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
Journal ArticleDOI
Meshless methods: An overview and recent developments
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.
Book
Finite Element Analysis
B. A. Szabó,Ivo Babuška +1 more
TL;DR: In this article, the authors present a general solution based on the principle of virtual work for two-dimensional linear elasticity problems and their convergence rates in one-dimensional dimensions. But they do not consider the case of three-dimensional LEL problems.
Journal ArticleDOI
The Partition of Unity Method
Ivo Babuška,Jens Markus Melenk +1 more
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
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The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more