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  • Open Access


    Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

    Changkye Lee1, Sundararajan Natarajan2, Jack S. Hale3, Zeike A. Taylor4, Jurng-Jae Yee1,*, Stéphane P. A. Bordas3,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 411-436, 2021, DOI:10.32604/cmes.2021.014947

    Abstract This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several More >

  • Open Access


    A Cell-Based Smoothed Finite Element Method for Modal Analysis of Non-Woven Fabrics

    Nguyễn T. Quyền1,*, N. Dourado2, A. J. P. Gomes3,4, F. B. N. Ferreira1

    CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2765-2795, 2021, DOI:10.32604/cmc.2021.013164

    Abstract The combination of a 4-node quadrilateral mixed interpolation of tensorial components element (MITC4) and the cell-based smoothed finite element method (CSFEM) was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures. This formulation was applied to numerous numerical examples of non-woven fabrics. As CSFEM schemes do not require coordinate transformation, spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two, three and four smoothing cells. An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,… More >

  • Open Access


    An Improved Quadrilateral Flat Element with Drilling Degrees of Freedom for Shell Structural Analysis

    H.Nguyen-Van1, N.Mai-Duy1 and T.Tran-Cong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.2, pp. 81-112, 2009, DOI:10.3970/cmes.2009.049.081

    Abstract This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane More >

  • Open Access


    A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates

    H. Nguyen-Van1, N. Mai Duy2, T. Tran-Cong 3

    CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 159-176, 2007, DOI:10.3970/cmc.2007.006.159

    Abstract This paper reports the development of a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behaviour within the framework of the first-order shear deformation theory. The approach incorporates the strain smoothing method for mesh-free conforming nodal integration into the conventional finite element techniques. The membrane-bending part of the element stiffness matrix is calculated by the line integral on the boundaries of the smoothing elements while the shear part is performed using an independent interpolation field in the natural co-ordinate system. Numerical results show that the element offered here is More >

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