On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM)

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ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS (2009, methodology): “The numerical results of ES-FEM using examples of static, free and forced vibration analyses of solids [Liu et al. (2009a)] demonstrated the following excellent properties: (1) ES-FEM is often found super-convergent and much more accurate than FEM using triangular elements (FEM-T3) and even more…”
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”
An edge‐based smoothed finite element method for primal–dual shakedown analysis of structures (2010, methodology): “CS-FEM is formulated using smoothing domains located inside the elements and proven effectively in solving 2D solid mechanics problems by using a proper number of smoothing cells in each element (for example four smoothing cells) [18, 19, 21, 22].”
On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) (2011, methodology): “A discussion on shape function calculations in SFEM was started by a series of letters to the editor [5, 14, 15].”