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Mathematical Problems in Engineering
Volume 2017, Article ID 6492081, 33 pages
Research Article

A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

1School of Science, Yanshan University, Qinhuangdao 066004, China
2Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation, Shenyang Aerospace University, Shenyang 110136, China

Correspondence should be addressed to Xu Ma; nc.ude.usy@428uxam

Received 3 July 2017; Revised 20 September 2017; Accepted 6 November 2017; Published 27 November 2017

Academic Editor: Giovanni Garcea

Copyright © 2017 Tan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is devoted to develop a new 8-node higher-order hybrid stress element (QH8) for free vibration and buckling analysis based on the Mindlin/Reissner plate theory. In particular, a simple explicit expression of a refine method with an adjustable constant is introduced to improve the accuracy of the analysis. A combined mass matrix for natural frequency analysis and a combined geometric stiffness matrix for buckling analysis are obtained using the refined method. It is noted that numerical examples are presented to show the validity and efficiency of the present element for free vibration and buckling analysis of plates. Furthermore, satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis and can pass the nonzero shear stress patch test.