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Date
2009Type
- Report
ETH Bibliography
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Abstract
In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff--Love and Reissner--Mindlin. A fundamental investigation for
the Kirchhoff plate goes back to Morgenstern [Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie. Arch. Rational Mech. Anal. 4, 145--152 (1959)] and is based on the
two-energies principle of Prager and Synge. This was half a centenium ago. We will derive the Kirchhoff--Love model based on Morgenstern's ideas in a rigorous way (including the proper
treatment of boundary conditions). It provides insights a) for the relation of the (1,1,0)-model with the (1,1,2)-model that differ by a quadratic term in the ansatz for the third component
of the displacement field and b) for the role of the shear correction factor. A further advantage of the approach by the two-energy principle is that the extension to the Reissner--Mindlin
plate model becomes very transparent and easy. Our study includes plates with reentrant corners. Show more
Publication status
publishedJournal / series
Research reportsVolume
(No. 2009-30)Publisher
Eidgenössische Technische Hochschule Zürich, Seminar für Angewandte MathematikMore
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