A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM

By David J. Benson, Yuri Bazilevs, E. De Luycker, Ming-Chen Hsu, Michael A. Scott, Thomas J. R. Hughes, Ted Belytschko. 2010

253 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e5ad0403b0807a0c2779e0a4ca4780eabad64aee

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In Computational Mechanics

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

An isogeometric analysis approach to gradient damage models (2011, methodology): “This makes it possible to construct bases for complex geometries, which can be obtained directly from a computer-aided design (CAD) tool [17, 18].”
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS (2012, background): “Extensive investigations including fluid–solid interaction [3,2], the extended finite element method [5] and electromagnetics [8] have additionally demonstrated the ability of isogeometric analysis to provide not only more precise geometric representations than traditional finite elements but also e”
A large deformation, rotation-free, isogeometric shell (2011, methodology): “The element is implemented using the generalized element formulation [12], and therefore may use any of the CAD basis functions that are, at the minimum, C(1) continuous.”
XFEM fracture analysis of orthotropic functionally graded materials (2013, unknown): “Recently, the automatic enrichment technique has also been developed to numerically determine the required enrichment functions for each problem [47] [48] [49] [50] [51].”
Extended isogeometric analysis for simulation of stationary and propagating cracks (2012, methodology): “In this method, each node may not use all the available enrichment functions [9].”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “A small sampling includes fluids and turbulence [5, 6, 7, 8], fluid-structure interaction [9, 10, 11, 12], incompressibility [13, 14, 15], structural and vibration analysis [16, 3], plates and shells [17, 18, 19, 20, 21], phase-field analysis [22, 23, 24], large deformation structural analysis with ”
A virtual element method with arbitrary regularity (2014, background): “Other approaches that generalize finite element methods to elements of general shape are found, for instance, in Belytschko et al. (1994), Benson et al. (2010), Cueto et al. (2003), Fries & Belytschko (2010), Mousavi & Sukumar (2011), Sukumar & Malsch (2006), Sukumar & Tabarraei (2004) and…”
Mimetic finite difference method (2014, background): “We mention the seminal paper [268] and the most recent papers [34] [83] [112] [204] [250] [251] [253].”