Addressing volumetric locking and instabilities by selective integration in smoothed finite elements

By N. Hung, Stéphane P.A. Bordas, Nguyen Dang Hung. 2009

57 citations recorded by the source corpus.

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8e42ab8e113bdbfe02b73993566199824f57943b

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh (2009, methodology): “The CS-FEM has been developed for general n-sided polygonal elements (nSFEM or nCS-FEM) [7], dynamic analyses [6], incompressible materials using selective integration [20,25], plate and shell analyses [5,19,24,28,29], and further extended for the extended finite element method (XFEM) to solve fract”
An edge‐based smoothed finite element method for primal–dual shakedown analysis of structures (2010, methodology): “The CS-FEM has also been extended for general n-sided polygonal elements (nSFEM or nCS-FEM) [23], dynamic analyses [24], incompressible materials using selective integration [25, 26], plate and shell analyses [27–30], and further extended for the extended finite element method (XFEM) to solve fractu”
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 n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM) for solid mechanics (2010, methodology): “The CS-FEM has been developed for general n-sided polygonal elements (nCS-FEM) [15] dynamic analyses [16], incompressible materials using selective integration [17, 18], plate and shell analyses [19–23], and further extended for the extended finite element method (XFEM) to solve fracture mechanics p”
Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) (2011, methodology): “The CS-FEM has been developed for general n-sided polygonal elements [26], dynamic analyses [27], incompressible materials using selective integration [28, 29], and further extended for plate and shell analyses [30–34], respectively.”
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…”
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].”