A smoothed finite element method for plate analysis

Division of Computational Mechanics, Department of Mathematics and Informatics, University of Natural Sciences, VNU-HCM, 227 Nguyen Van Cu, Viet Nam; Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand; University of Glasgow, Civil Engineering, Rankine building, G12 8LT, United Kingdom; Division of Manufacturing, University of Liège, Bâtiment B52/3 Chemin des Chevreuils 1, B-4000 Liège 1, Belgium
Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.62). 02/2008; 197(13-16):1184-1203. DOI: 10.1016/j.cma.2007.10.008

ABSTRACT A quadrilateral element with smoothed curvatures for Mindlin–Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements (smoothing cells). Numerical results show that the proposed element is robust, computational inexpensive and simultaneously very accurate and free of locking, even for very thin plates. The most promising feature of our elements is their insensitivity to mesh distortion.

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    ABSTRACT: This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation.
    KSCE Journal of Civil Engineering 06/2014; 16(7):1230-1242. · 0.38 Impact Factor
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    ABSTRACT: In this paper, a cell based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first order shear deformation theory and the shear locking is suppressed by a discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence the gradient index, the plate aspect ratio, skewness of the plate and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied.
    Mathematical Problems in Engineering 06/2014; 2014:13. · 1.38 Impact Factor
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    ABSTRACT: We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bES-FEM and bFS-FEM) for nearly-incompressible elasticity problems. The crucial idea is that the space of piecewise linear polynomials used for the displacements is enriched with bubble functions on each element, while the pressure is a piecewise constant function. The meshes of triangular or tetrahedral elements required by these methods can be generated automatically. The enrichment induces a softening in the bilinear form allowing the weakened weak (W 2) procedure to produce a high-quality solution, free from locking and that does not oscillate. We prove theoretically that both methods confirm the uniform inf-sup and convergence conditions. Four numerical examples are given to validate the reliability of the bES-FEM and bFS-FEM. Keywords: Edge-based smoothed finite element method (ES-FEM); Face-based smoothed finite element method (FS-FEM); Bubble function; Volumetric locking; Nearly-incompressible elasticity.

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May 20, 2014