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. encountered of these elements is the phenomenon of shear locking, which induces over-stiffness as the plate becomes progressively thinner.To avoid shear locking, many new numerical techniques and effective modifications have been proposed and tested, such as the reduced integration and selective reduced integration schemes proposed by Zienkiewicz et al. [21] and Hughes et al. [22,23], the stabilization procedure proposed by Belytschko et al. [24,25], free formulation method proposed by Bergan and Wang [26], the substitute shear strain method proposed by Hinton and Huang [27], mixed formulation/hybrid elements [28-31], etc. However, these elements are still subjected to some drawbacks such as instability because of rank deficiency or low accuracy or complex performance. To overcome these drawbacks, Macneal [32] introduced an assumed strain method on the physical elements, and then Park and Stanley at Stanford [33] first enlarged to the natural elements to give the so-called assumed natural strain method (ANS), which allows defining the shear strains independently from the approximation of kinematic variables. In this method, the shear strain field of a 3-node triangular or a 4-node quadrilateral element is interpolated independently by rational constant shear strains along each element side, and the shear locking problem will be overcome. It has been proved to be mathematically valid by Bathe and Brezzi [34,35] and Brezzi et al. [36]. On the basis of this method and different modifications, many successful models were then presented, including the mixed interpolated tensorial components (MITC) family proposed by Bathe and colleagues [34][35][36][37][38][39][40], the discrete Reissner-Mindlin (DRM) family [41,42] and the linked interpolation elements (Q4BL [43] and T3BL [44]) proposed by various authors, discrete Kirchhoff elements DKT [45] and DKQ [4...

Keywords:Reissner-Mindlin shell Shear locking Cell-based smoothed discrete shear gap technique (CS-DSG3) Smoothed finite element method Strain smoothing technique a b s t r a c t A cell-based smoothed discrete shear gap method (CS-DSG3) for static and free vibration analyses of Reissner-Mindlin shells is formulated by combining the cell-based strain smoothing technique with the discrete shear gap method (DSG3) using three-node triangular elements. In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole of the triangular element is used to smooth the strains on these three sub-triangles. The CS-DSG3 hence not only overcomes the drawback of the DSG3 but also improves the accuracy as well as the stability of the DSG3. The numerical examples demonstrated that the CS-DSG3 is free of shear locking and achieves the high accuracy compared to other existing shell elements.

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The cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular elements was recently proposed to improve the performance of the discrete shear gap method (DSG3) for static and free vibration analyses of isotropic Mindlin plates. In this paper, the CS-FEM-DSG3 is further extended for static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators. In the piezoelectric composite plates, the electric potential is assumed to be a linear function through the thickness of each piezoelectric sublayer. A displacement and velocity feedback control algorithm is used for active control of the static deflection and the dynamic response of the plates through closed loop control with bonded or embedded distributed piezoelectric sensors and actuators. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of other available numerical results.