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On the smoothed finite element method. (English) Zbl 1195.74210
Int. J. Numer. Methods Eng. 76, No. 8, 1285-1295 (2008); corrigendum ibid. 77, No. 13, 1870 (2009).
Summary: Recently, G. R. Liu, K. Y. Dai and T. T. Nguyen [Comput. Mech. 39, No. 6, 859–877 (2007; Zbl 1169.74047)] proposed the smoothed finite element method by using the non-mapped shape functions and then introducing the strain smoothing operator when evaluating the element stiffness in the framework of the finite element method. However, the theories and examples by Liu et al. are not sufficient for general quadrilateral elements. This paper shows that the non-mapped shape functions used in the smoothed finite element have disadvantages in existence, linearity, non-negativity and patch test.
Editorial remark: Due to the corrigendum [Int. J. Numer. Methods Eng. 77, No. 13, 1870 (2009; Zbl 1195.74209)], the authors “misunderstood the crucial trick in the SFEM and therefore the comments on the SFEM presented here are incorrect”.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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