Journal ArticleDOI
Discontinuous enrichment in finite elements with a partition of unity method
TLDR
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.About:
This article is published in Finite Elements in Analysis and Design.The article was published on 2000-11-01. It has received 411 citations till now. The article focuses on the topics: Call blocking & Network model.read more
Citations
More filters
Journal ArticleDOI
Extended finite element method for cohesive crack growth
Nicolas Moës,Ted Belytschko +1 more
TL;DR: In this article, an extended finite element method is applied to modeling growth of arbitrary cohesive cracks, which is governed by requiring the stress intensity factors at the tip of the cohesive zone to vanish.
Journal ArticleDOI
Cracking particles: A simplified meshfree method for arbitrary evolving cracks
Timon Rabczuk,Ted Belytschko +1 more
TL;DR: A new approach for modelling discrete cracks in meshfree methods is described, in which the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed.
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
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.
Journal ArticleDOI
A three dimensional large deformation meshfree method for arbitrary evolving cracks
Timon Rabczuk,Ted Belytschko +1 more
TL;DR: In this paper, a new approach for modeling discrete cracks in mesh-free particle methods in 3D is described, where cracks can be arbitrarily oriented, but their growth is represented by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed.
References
More filters
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.
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.
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.
Related Papers (5)
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more