A Smoothed Finite Element Method for Mechanics Problems

By Gui-Rong Liu, K. Y. Dai, T. Nguyen. 2007

891 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a4a8f3f27792a301db51f3370d0d083d9e39a9b6

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks (2009, methodology): “In the SFEM, cell-based strain smoothing technique is incorporated to the standard FEM formulation, so as to reduce the over stiffness of the FEM model.”
Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) (2011, methodology): “The super-convergence of the recovery energy error norm ‖e−e‖L2 of NS-FEM almost equal to that of CS-FEM (or SFEM) using 1 SC for each quadrilateral element [22, 23, 52]; (4) the effectivity indexes of the error indicators of both NS-FEM and FEM approach to unity when the mesh is refined, but the re”
A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems (2010, methodology): “Smoothed finite element method (SFEM) One typical W2 model is the so-called smoothed finite element method (SFEM) [8, 16, 17].”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “The model that gives an upper bound can be one of the following models: the stress equilibrium FEM model [1], the recovery of a statically admissible stress field from displacement FEM model [2–4], the hybrid equilibrium FEM model [5,6], the element-based smoothed finite element method (SFEM) model ”
Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) (2008, methodology): “A typical example is the SFEM, with SC=1 we can have hourglass instability for some problems [21, 22].”
An arbitrary order variationally consistent integration for Galerkin meshfree methods (2013, methodology): “The SCNI approach has also been introduced as a nodal integration technique in finite elements [19].”
A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method (2009, methodology): “Using the GS-Galerkin weak formulation, the PIM shape and the node-based smoothing domains, a meshfree node-based smoothed point interpolation method (NS-PIMa) has been proposed for both 2D and 3D problems [Liu and Zhang et al. (2005); Zhang and Liu et al. (2007b)].”
A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis (2011, methodology): “…smoothed FEM models named SFEM [Liu, Nguyen, Dai, and Lam (2007); Nguyen-Thanh, Rabczuk, NguyenXuan, and Bordas (2008)], cell-based SFEM (CS-FEM) [Liu, Dai, and Nguyen (2007); Dai, Liu, and Nguyen (2007a); Nguyen-Xuan, Bordas, and Nguyen-Dang (2008); Bordas and Natarajan (2010); Canh,…”