TAILIEUCHUNG - Smoothed finite element method for two-dimensional elasto-plasticity
This communication shows how the smoothed finite element method (SFEM) very recently proposed by . Liu [14] can be extended to elasto-plasticity. The SFEM results are in excellent agreement with the finite element (FEM) and analytical results. For the examples treated, the method is quite insensitive to mesh distortion and volumetric locking. | Vietnam Journal of Mechanics, VAST, Vol. 31, No. 3 &4 (2009), pp. 293 – 312 SMOOTHED FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL ELASTO-PLASTICITY Stéphane Pierre Alain Bordascorres1 , Hung Nguyen-Dang2 , Quyen Phan-Phuong3 , Hung Nguyen-Xuan4 , Sundararajan Natarajan1 , Marc Duflot 5 1 University of Glasgow, G12 8LT, Scotland, UK. 2 Institut de Mecanique et Genie Civil, Liege, Belgique 3 University of Technology HCM, Vietnam 4 University of Natural Sciences -VNU-HCM, Vietnam 5 Centre of excellence in aeronautical research (CENAERO) Rue des Frères Wright 29 B-6041 Gosselies (Belgium) Abstract. This communication shows how the smoothed finite element method (SFEM) very recently proposed by . Liu [14] can be extended to elasto-plasticity. The SFEM results are in excellent agreement with the finite element (FEM) and analytical results. For the examples treated, the method is quite insensitive to mesh distortion and volumetric locking. Moreover, the SFEM yields more compliant load-displacement curves compared to the standard, displacement based FE method, as expected from the theoretical developments recently published in [4], [3] and [6]. 1. INTRODUCTION Recently, G. R. Liu et al. proposed a new finite element method based on strain smoothing, which they coined the Smoothed Finite Element Method – SFEM [14]. Theoretical developments, accuracy, convergence and stability investigations are discussed in [4, 6]. Basically, the strain field is calculated as the spatial average of the compatible strain field. Different numbers of smoothing cells (nc) per element provide the method with different properties. The SFEM was very recently coupled to the MITC [11, 12] formulation to yield plate [1] and shell [2] elements with particular insensitivity to mesh distortion. The introduction of partition of unity enrichment in the SFEM to create the smoothed extended finite element method (SmXFEM) or Flexible extended finite element method(FleXFEM) was proposed in [6] simplifying
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