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Chien Thai-Hoang, Nhon Nguyen-Thanh, Hung Nguyen-Xuan, Timon Rabczuk and Stephane Bordas (2010). A cell - based smoothed finite element method for free vibration and buckling analysis of shells. Received January 4, 2010/Accepted May 6, 2010.
Abstract: This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient smoothing operator is adopted. The membrane-bending and geometrical stiffness matrices are computed along the boundaries of the smoothing cells while the shear stiffness matrix is calculated by an independent interpolation in the natural coordinates as in the MITC4 (the Mixed Interpolation of Tensorial Components) element. Various numerical results are compared with existing exact and numerical solutions and they are in good agreement. The advantage of the present formulation is that it retains higher accurate than the MITC4 element even for heavily distorted meshes without increasing the computational cost.
Keywords: free vibration, buckling, transverse shear locking, finite element method, smoothed finite element method, flat shell element.