Generalized finite element methods for three-dimensional structural mechanics problems

By Carlos Armando Duarte, Ivo Babuska, J. Tinsley Oden. 2000

661 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/30f1afd9ee4c57e24636c241e9eac2627e725357

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM (2012, methodology): “Copyright © 2012 John Wiley & Sons, Ltd. Received 8 March 2011; Revised 11 September 2011; Accepted 14 September 2011 KEY WORDS: GFEM; direct SIFs; crack growth; crack tip asymptotic field”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, neutral): “We recall for instance [4], [5], [6], [7], [8], [20], [21], [31], [34], [38], [41], [42], [43], [44] [47], [48], [51], [52], [58], [57], [60], [61], [62], [63], [65], [66], [67], [70].”
MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD (2001, methodology): “The recognition and use of partition of unity enrichment strategy to solve boundary-value problems with internal boundaries is due to Oden and co-workers [4] [5] [9] [10] ± the numerical technique was coined as the generalized ®nite-element method (GFEM).”
Analysis of Interacting Cracks Using the Generalized Finite Element Method With Global-Local Enrichment Functions (2008, background): “Expansions of the elasticity solution in the neighborhood of a crack (Westergaard functions) can be taken as enrichment functions at nodes near a crack front [14, 18–22].”
A generalized finite element method for the simulation of three-dimensional dynamic crack propagation (2001, neutral): “[ 11 ,12]. There are many situations in which the solution of a boundary value problem is not a smooth function.”
Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method (2003, methodology): “This idea was exploited by Oden and co-workers [27,12] for problems with internal boundaries—the numerical technique was referred to as the Generalized Finite Element Method (GFEM).”
A review of extended/generalized finite element methods for material modeling (2009, background): “The first works in GFEM involved global enrichments of the approximation space; however, as early as 2000, local enrichment for singularities at sharp corners were also developed [34].”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “This was first done in a method called the ‘extended finite element method’ [13] and the ‘generalized finite element method’ [14,15] which are both relying on the idea of multiplying the standard shape functions by enrichment functions which ‘know’ about the nature of the solution.”
Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, methodology): “We refer to [8,14,15,27,39,44,45,56,57] and the references therein, for details on the selection of these functions for the case 3-D linear elastic fracture mechanics problems like those considered in this paper.”
On Approximation in Meshless Methods (2005, methodology): “In the context of the partition of unity method/generalized FEM special approximation systems have been used in [69] for Helmholtz problems and in [90,34] for elasticity and crack problems.”
Bridging multiple structural scales with a generalized finite element method (2015, background): “! ̨/ ; ̨ 2 Ih, given by the orthotropic polynomial enrichment functions presented in [39, 40, 57].”
Meshless and Generalized Finite Element Methods: A Survey of Some Major Results (2003, methodology): “, the distribution of non-zero entries) obtained from GFEM is different from that obtained from classical FEM [20].”
The method of finite spheres (2000, neutral): “Hence some researchers (refer to Oden et al., 1998; Duarte et al., 1999) have reverted back to developing ®nite element techniques incorporating certain aspects of the meshless methods.”