Smooth finite element methods: Convergence, accuracy and properties

By Hung Nguyen-Xuan, Stéphane P.A. Bordas, H. Nguyen‐Dang. 2008

155 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6594462d4dd42f7bf644c0ec8fe867408f9ff7ca

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In Biomedical Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates (2010, background): “The theoretical aspects of CS-FEMwere fully studied in [29,31,32].”
Second‐order accurate derivatives and integration schemes for meshfree methods (2012, background): “This is also the essential ingredient of the smoothed FEM recently under intensive studies [19–21].”
A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media (2011, unknown): “More recently, Liu [35,36] has generalized the gradient (strain) smoothing technique [37] and applied it in the FEM context to formulate a cell-based smoothed finite element method (SFEM or CS-FEM) [38–41].”
Computation of limit and shakedown loads using a node‐based smoothed finite element method (2012, methodology): “The CS-FEM has been studied theoretically in [3–5], and further extended to the general n-sided polygonal elements (nSFEM or nCS-FEM) [6], dynamic analyses [7], incompressible materials using selective integration [8, 9], plate and shell analyses [10–12], fracture mechanics problems [13, 14], and li”
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, methodology): “The convergence, stability, accuracy and important computational aspects of this method were studied in detail in [8].”
Analysis of functionally graded plates using an edge-based smoothed finite element method (2011, methodology): “Several theoretical aspects of the S-FEM models have then been provided [38,41,59].”
A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis (2011, unknown): “…(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, Nguyen-Xuan, Askes, Rabczuk, and Nguyen-Vinh (2010)], node-based SFEM…”
A theoretical study on the smoothed FEM (S‐FEM) models: Properties, accuracy and convergence rates (2010, methodology): “The S-FEM models in 2D domains (CS-FEM, NS-FEM and ES-FEM) can use general n-sided polygonal elements [17, 24, 28] including 3-node triangular and 4-node quadrilateral elements [14, 15, 18, 24, 27, 28].”
ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS (2009, methodology): “…[Dai et al. (2007)], dynamic analyses [Dai and Liu (2007)], incompressible materials using selective integration [Nguyen-Thoi et al. (2007); Nguyen-Xuan et al. (2008b)], plate and shell analyses [Cui et al. (2008); Nguyen-Thanh et al. (2008); Nguyen-Van et al. (2008); Nguyen-Xuan and…”