An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics

By K. Y. Dai, Guirong Liu, T. Nguyen. 2007

314 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b71dd553578b66b709ed6e64ae68309964622f1e

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, methodology): “The SFEM has been developed for general n-sided polygonal elements [17], and further extended for plate and shell analyses [18, 19].”
On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM) (2009, methodology): “The SFEM has also been developed for general n-sided polygonal elements (nSFEM) [5], dynamic analyses [6] and further extended for plate and shell analyses [7–11], and piezoelectric structures [12].”
A smoothed finite element method for plate analysis (2008, unknown): “It was shown that the SFEM is stable, accurate and effective [20,21,47].”
A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates (2010, methodology): “By using a proper number of smoothing cells in each element (for example four smoothing cells), CS-FEM can increase significantly the accuracy of the solutions [41–52].”
A novel singular node‐based smoothed finite element method (NS‐FEM) for upper bound solutions of fracture problems (2010, methodology): “The CS-FEM has been developed for general n-sided polygonal elements (nCS-FEM) [29] dynamic analyses [30], incompressible materials using selective integration [31, 32], plate and shell analyses [33–36], and further extended for the XFEM to solve fracture mechanics problems in 2D continuum and plate”
ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS (2009, methodology): “The CS-FEM has been extended for general n-sided polygonal elements (nSFEM or nCS-FEM) [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.…”
An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids (2009, background): “This gives tremendous freedom in shape function construction, and the shape functions do not need to form explicitly and their values at interest points can be obtained by simple interpolation [7].”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “Note also that, the NS-FEM is evolved from the SFEM [8,18] in which the strain smoothing technique was applied based on elements, and they all have the same features of strain smoothing operation.”
Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013, methodology): “The corrected strain operator is also used in the smoothed finite element method on polygonal meshes [58, 59].”