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T. Nguyen-Thoi, P. Phung-Van, H. Luong-Van, H. Nguyen-Van, H. Nguyen-Xuan, A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates. Computational Mechanics, DOI: 10.1007/s00466-012-0705-y, 2012.

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 three-node Mindlin plate element (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.

Keywords: Reissner-Mindlin plate, shear locking, finite element method (FEM), cell-based smoothed three-node Mindlin plate element (CS-MIN3), three-node Mindlin plate element (MIN3), strain smoothing technique.