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Assumed stress quasi‐conforming technique for static and free vibration analysis of Reissner–Mindlin plates
Author(s) -
Wang Changsheng,
Wang Xuan,
Zhang Xiangkui,
Hu Ping
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5510
Subject(s) - quadrilateral , mathematics , vibration , node (physics) , displacement (psychology) , finite element method , variational principle , mathematical analysis , element (criminal law) , bending of plates , bending , geometry , structural engineering , engineering , physics , law , psychology , quantum mechanics , political science , psychotherapist
Summary This paper presents a novel formulation based on Hellinger–Reissner variational principle in the framework of quasi‐conforming method for static and free vibration analysis of Reissner–Mindlin plates. The formulation starts from polynomial approximation of stresses, which satisfy the equilibrium equations of Reissner–Mindlin plate theory. Then the stress matrix is treated as the weighted function to weaken the strain‐displacement equations after the strains are derived by using the constitutive equations. Finally, the string‐net functions are introduced to calculate strain integration. As examples, two new plate bending elements, a 4‐node quadrilateral element QC‐P4‐11 β and a 3‐node triangular element QC‐P3‐7 β , are proposed. Several benchmark examples are demonstrated to show the performance of the elements, and the results obtained are compared with other available ones. Numerical results have proved that both elements possess excellent precision. In particular, the quadrilateral element performs well even when the element shape degenerates into a triangle or concave quadrangle. Copyright © 2017 John Wiley & Sons, Ltd.