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Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis
Author(s) -
Kim Jin Gon,
Kim Yoon Young
Publication year - 2001
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.176
Subject(s) - vibration , displacement (psychology) , shell (structure) , finite element method , spurious relationship , variational principle , interpolation (computer graphics) , quadratic equation , stress (linguistics) , cubic function , mathematical analysis , rotational symmetry , mathematics , structural engineering , physics , classical mechanics , geometry , materials science , engineering , composite material , acoustics , motion (physics) , psychology , linguistics , statistics , philosophy , psychotherapist
In this study, we present free vibration analysis of shells of revolution using the hybrid‐mixed finite element. The present hybrid‐mixed element, which is based on the modified Hellinger–Reissner variational principle, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out by the Guyan reduction. Several numerical examples show that the present element with cubic displacement interpolation functions and consistent quadratic stress functions is highly accurate for the free vibration analysis of shells of revolution, especially for higher vibration modes. Copyright © 2001 John Wiley & Sons, Ltd.