Selective smoothed finite element method

Nguyen, Thanh Thuy; Liu, G. R.; Dai, K. Y.; Lam, K.Y.

doi:10.1016/s1007-0214(07)70125-6

Cited by 83 publications

(60 citation statements)

References 8 publications

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“…Based on the idea of SFEM for 2D solid elements [17,[22][23][24], Nguyen et al [21] have proposed a MISC element with the mixed interpolation and smoothed curvatures for plates. In the MISC elements, we 1. apply the curvature smoothing operation that was used in mesh-free methods based on the nodal integration [18][19][20] and recently in the SFEM [17,[22][23][24] to the bending strains and 2. approximate the shear strains with independent interpolation functions in the MITC4 element [9].…”

Section: The Mitc4 Elementmentioning

confidence: 99%

“…In the MISC elements, we 1. apply the curvature smoothing operation that was used in mesh-free methods based on the nodal integration [18][19][20] and recently in the SFEM [17,[22][23][24] to the bending strains and 2. approximate the shear strains with independent interpolation functions in the MITC4 element [9]. In the smoothed operation, a smoothing function can be chosen in different ways.…”

Section: The Mitc4 Elementmentioning

confidence: 99%

“…Based on the idea of SFEM, Nguyen et al [21] formulated a plate element the so-called mixed interpolation and smoothed curvature (MISCk) elements by incorporating the curvature smoothing operation (the strain smoothing method) with the original MITC4 element [9]. The properties of the SFEM are studied in detail by Liu et al [22,23]. The SFEM has also been applied to dynamic problems for 2D solids [24].…”

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confidence: 99%

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A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates

Nguyen‐Xuan

Nguyen-Thoi

2008

Commun. Numer. Meth. Engng.

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SUMMARYA free vibration analysis of Mindlin-Reissner plates using the stabilized smoothed finite element method is studied. The bending strains of the MITC4 and STAB elements are incorporated with a cell-wise smoothing operation to give new proposed elements, the mixed interpolation and smoothed curvatures (MISCk) and SMISCk elements. The corresponding bending stiffness matrix is computed along the boundaries of the smoothing elements (smoothing cells). Note that shearing strains and the shearing stiffness matrix of the proposed elements are unchanged from the original elements, the MITC4 and STAB elements. It is confirmed by numerical tests that the present method is free of shear locking and has the marginal improvements compared with the original elements.

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Section: The Mitc4 Elementmentioning

confidence: 99%

Section: The Mitc4 Elementmentioning

confidence: 99%

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confidence: 99%

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A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates

Nguyen‐Xuan

Nguyen-Thoi

2008

Commun. Numer. Meth. Engng.

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“…Recently, Liu et al [18] have applied a strain smoothing technique to a cell/element-based smoothed finite element method (SFEM or CS-FEM) for 2D solids. Subsequently, the theoretical aspects of SFEM were studied in [19,20], and numerous numerical investigations and applications of SFEM have also been reported [21][22][23][24][25][26]. It is shown that the method retains most properties of the strain smoothing technique and advantages of FEM, and therefore yields solutions that are accurate, locking free and computational inexpensive.…”

Section: Introductionmentioning

confidence: 99%

A cell‐based smoothed finite element method for kinematic limit analysis

Nguyen‐Xuan

Askes

et al. 2010

Numerical Meth Engineering

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Published paperLe, Canh V., Nguyen-Xuan, H., Askes, H., Bordas , Stéphane P. A., Rabczuk, T. and Nguyen-Vinh, H. (2010) SUMMARYThis paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method (CS-FEM) with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.

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“…To overcome the volumetric locking in nearly incompressible problems, the first common technique is to use selective reduced integration [17,30]. The idea of this technique is to decompose the material property matrix into two parts, volume part and remaining part, and the stiffness matrix is also decomposed into two parts correspondingly.…”

Section: Introductionmentioning

confidence: 99%

A novel FEM by scaling the gradient of strains with factor α (αFEM)

2008

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This paper presents a novel finite element method of quadrilateral elements by scaling the gradient of strains and Jacobian matrices with a scaling factor α (αFEM). We first prove that the solution of the αFEM is continuous for α ∈ [0, 1] and bounded from both below and above, and hence is convergent. A general procedure of the αFEM has been proposed to obtain the exact or best possible solution for a given problem, in which an exact-α approach is devised for overestimation problems and a zero-α approach is suggested for underestimation problems. Using the proposed αFEM approaches, much more stable and accurate solutions can be obtained compared to that of standard FEM. The theoretical analyses and intensive numerical studies also demonstrate that the αFEM effectively overcomes the following wellknown drawbacks of the standard FEM: (1) Overestimation of stiffness matrix when the full Gauss integration is used; (2) Instability problem known as hour-glass locking (presence of hour-glass modes or spurious zero-energy modes) when the reduced integration is used; (3) Volumetric locking in nearly incompressible problems when the bulk modulus becomes infinite.

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Selective smoothed finite element method

Cited by 83 publications

References 8 publications

A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates

A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates

A cell‐based smoothed finite element method for kinematic limit analysis

A novel FEM by scaling the gradient of strains with factor α (αFEM)

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