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See detailA cell-based smoothed finite element method for three dimensional solid structures
Nguyen-Xuan, Hung; Nguyen, Ha Manh UL; Bordas, Stéphane UL et al

in KSCE Journal of Civil Engineering (2012), 16(7), 1230-1242

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 ... [more ▼]

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. [less ▲]

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See detailA cell - based smoothed finite element method for free vibration and buckling analysis of shells
Thai-Hoang, Chien; Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung et al

in KSCE Journal of Civil Engineering (2011), 15(2), 347-361

This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient ... [more ▼]

This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient smoothing operator is adopted. The membrane-bending and geometrical stiffness matrices are computed along the boundaries of the smoothing cells while the shear stiffness matrix is calculated by an independent interpolation in the natural coordinates as in the MITC4 (the Mixed Interpolation of Tensorial Components) element. Various numerical results are compared with existing exact and numerical solutions and they are in good agreement. The advantage of the present formulation is that it retains higher accurate than the MITC4 element even for heavily distorted meshes without increasing the computational cost. © 2011 Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg. [less ▲]

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