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A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates

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Abstract

The cell-based strain smoothing technique is combined with the well-known three-node Mindlin plate element (MIN3) to give a so-called the cell-based smoothed MIN3 (CS-MIN3) for static and free vibration analyses of plates. In the process of formulating the system stiffness matrix of the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized MIN3 is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole the triangular element is used to smooth the strains on these three sub-triangles. The numerical examples demonstrated that the CS-MIN3 is free of shear locking, passes the patch test and shows four superior properties such as: (1) be a strong competitor to many existing three-node triangular plate elements in the static analysis, (2) can give high accurate solutions for problems with skew geometries in the static analysis, (3) can give high accurate solutions in free vibration analysis, (4) can provide accurately the values of high frequencies of plates by using only coarse meshes.

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Authors and Affiliations

  1. Department of Mechanics, Faculty of Mathematics & Computer Science, University of Science, Vietnam National University HCM, 227 Nguyen Van Cu, Dist. 5, Hochiminh City, Vietnam

    T. Nguyen-Thoi & H. Nguyen-Xuan

  2. Division of Computational  Mechanics, Ton Duc Thang University, 98 Ngo Tat To St., Ward 19, Binh Thanh Dist., Hochiminh City, Vietnam

    T. Nguyen-Thoi, P. Phung-Van & H. Nguyen-Xuan

  3. Faculty of Civil Engineering, Hochiminh City University of Technology (HCMUT), Hochiminh City, Vietnam

    H. Luong-Van

  4. Faculty of Civil Engineering, Hochiminh City University of Architecture, Hochiminh City, Vietnam

    H. Nguyen-Van

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  1. T. Nguyen-Thoi
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  2. P. Phung-Van
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  3. H. Luong-Van
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  4. H. Nguyen-Van
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  5. H. Nguyen-Xuan
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Correspondence to T. Nguyen-Thoi.

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Nguyen-Thoi, T., Phung-Van, P., Luong-Van, H. et al. A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates. Comput Mech 51, 65–81 (2013). https://doi.org/10.1007/s00466-012-0705-y

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