A Hermite differential quadrature finite element method and its application to free vibration of thin plates

XING Yufeng; WU Yang

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A Hermite differential quadrature finite element method and its application to free vibration of thin plates

XING Yufeng *,WU Yang

The Solid Mechanics Research Centre, Beihang University (BUAA), Beijing 100191

*Correspondence author

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Funding: FCT-Fundação para a Ciência e a Tecnologia （No.PTDC/EMS-PRO/2044/, SFRH/BPD/99591/2014）, Specialized Research Fund for the Doctoral Program of Higher Education（No.20131102110039）, National Science Foundation of China （No.11402015, 11372021,11672019）

Opened online:16 May 2017

Accepted by: none

Citation: XING Yufeng,WU Yang.A Hermite differential quadrature finite element method and its application to free vibration of thin plates[OL]. [16 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4732449

A Hermitedifferential quadraturefinite element method (Hermite DQFEM) is proposed and elaborated in this paper.Hermite differential quadrature (HDQ) rules based on the Hermite interpolation on two end points and Lagrange interpolation at other nodes are formulated. The optimized sampling points for the HDQ rules that provide the best interpolation accuracy were shown to be roots Jacobi polynomials with weights(3, 3). The HDQ rules together with the Gauss-Lobatto-Legendre integration rules were used to discretize the potential functional of thin plates in curvilinear domainto obtained HermiteDQFEM or weak form HDQ matrices. In comparison with Lagrange DQFEM results or available exact andother numerical results, high accuracy and rapid convergence were achieved without numerical stability even with a large number of sampling points, which indicates that the Hermite DQFEM has attractive potential as a novel numerical technique.

Keywords:solid mechanics; differential quadrature method; finite element method; vibration of thin plates

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