Interior formulation of axisymmetric Levinson plate theory

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2016-06-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
5
34-38
Series
MECHANICS RESEARCH COMMUNICATIONS, Volume 74
Abstract
In this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.
Description
Keywords
Clapeyron's theorem, Finite element, Interior plate, Levinson theory, Saint Venant's principle
Other note
Citation
Karttunen , A T & Von Hertzen , R 2016 , ' Interior formulation of axisymmetric Levinson plate theory ' , MECHANICS RESEARCH COMMUNICATIONS , vol. 74 , pp. 34-38 . https://doi.org/10.1016/j.mechrescom.2016.03.008