An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner–Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.

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A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates

SUMMARY

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.

S. Aomura

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