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A new triangular hybrid displacement function element for static and free vibration analyses of Mindlin-Reissner plate / Chenfeng Li

Latin American Journal of Solids and Structures, Volume: 14, Pages: 765 - 804

Swansea University Author: Li, Chenfeng

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DOI (Published version): 10.1590/1679-78253036

Abstract

A new 3-node triangular hybrid displacement function Mindlin- Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking...

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Published in: Latin American Journal of Solids and Structures
ISSN: 1679-7817
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URI: https://cronfa.swan.ac.uk/Record/cronfa34341
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Abstract: A new 3-node triangular hybrid displacement function Mindlin- Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses.
College: College of Engineering
Start Page: 765
End Page: 804