A cell-based smoothed discrete shear gap method (cs-dsg3) using triangular elements for free vibration analysis of reissner-mindlin plates

Nguyen Thoi Trung , Phung Van Phuc,
International Journal for Numerical Methods in Engineering
Volume 91, Issue 7, pages 705–741, 17 August 2012

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Abstract

The cell-based strain smoothing technique is combined with discrete shear gap method using three-node triangular elements to give a so-called cell-based smoothed discrete shear gap method (CS-DSG3) for static and free vibration analyses of Reissner–Mindlin plates. In the process of formulating the system stiffness matrix of the CS-DSG3, each triangular element will be divided into three subtriangles, and in each subtriangle, the stabilized discrete shear gap method 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 subtriangles. The numerical examples demonstrated that the CS-DSG3 is free of shear locking, passes the patch test, and shows four superior properties such as: (1) being 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; and (4) can provide accurately the values of high frequencies of plates by using only coarse meshes. Copyright © 2012 John Wiley & Sons, Ltd.

Keywords:  Reissner–Mindlin plate; shear locking; finite element method (FEM); cell-based smoothed discrete shear gap technique (CS-DSG3); discrete shear gap method (DSG); strain smoothing technique