Journal ArticleDOI
Modeling fracture in Mindlin–Reissner plates with the extended finite element method
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TLDR
In this paper, a technique for the modeling of cracks and crack growth in plates using the extended finite element method (X-FEM) is presented, which allows for modeling of crack geometries which are independent of the finite element mesh topology.About:
This article is published in International Journal of Solids and Structures.The article was published on 2000-11-12. It has received 256 citations till now. The article focuses on the topics: Extended finite element method & Mixed finite element method.read more
Citations
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Journal ArticleDOI
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
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 extended/generalized finite element methods for material modeling
TL;DR: In this article, the extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: fracture, dislocations, grain boundaries and phase interfaces.
Journal ArticleDOI
The generalized finite element method
TL;DR: In this article, the authors describe a pilot design and implementation of the generalized finite element method (GFEM), which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the FEM.
Journal ArticleDOI
Discontinuous enrichment in finite elements with a partition of unity method
TL;DR: An approximate analytical method is presented to evaluate efficiently and accurately the call blocking probabilities in wavelength routing networks with multiple classes of calls, and path decomposition algorithms for single-class wavelength routing Networks may be readilt extended to the multiclass case.
References
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Book
Finite Element Procedures
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
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.
Book
Elliptic Problems in Nonsmooth Domains
TL;DR: Second-order boundary value problems in polygons have been studied in this article for convex domains, where the second order boundary value problem can be solved in the Sobolev spaces of Holder functions.
Journal ArticleDOI
Elastic crack growth in finite elements with minimal remeshing
Ted Belytschko,T. Black +1 more
TL;DR: In this article, a minimal remeshing finite element method for crack growth is presented, where Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.
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.
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The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more