# Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element

Nguyen-Van, H. and Mai-Duy, N. and Tran-Cong, T. (2008) Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element. Journal of Sound and Vibration, 313 (1-2). pp. 205-223. ISSN 0022-460X

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Identification Number or DOI: doi: 10.1016/j.jsv.2007.11.043

## Abstract

This paper reports numerical analyses of free vibration of laminated composite plate/ shell structures of various shapes, span-to-thickness ratios, boundary conditions and lay-up sequences. The method is based on a novel four-node quadrilateral element, namely MISQ20, within the framework of the first-order shear deformation theory (FSDT). The element is built by incorporating a strain smoothing method into the bilinear four-node quadrilateral finite element where the strain smoothing operation is based on mesh-free conforming nodal integration. The bending and membrane stiffness matrices are based on the boundaries of smoothing cells while the shear term is evaluated by $2\times2$ Gauss quadrature. Through several numerical examples, the capability, efficiency and simplicity of the element are demonstrated. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and free of locking.

Item Type: Article (Commonwealth Reporting Category C) Accepted Manuscript deposited in accordance with the copyright policy of the publisher. free vibration; laminated plate/shells; strain smoothing method; shear-locking free; first-order shear deformation theory 09 Engineering > 0912 Materials Engineering > 091202 Composite and Hybrid Materials09 Engineering > 0913 Mechanical Engineering > 091304 Dynamics, Vibration and Vibration Control09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation 290000 Engineering and Technology E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering 4582 25 May 2009 16:11 02 Mar 2012 09:46

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