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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-49740

Braess, D; Sauter, S; Schwab, C (2011). On the justification of plate models. Journal of Elasticity, 103(1):53-71.

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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
Elastizit¨atstheorie. 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
rˆole 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.

Citations

4 citations in Web of Science®
3 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:March 2011
Deposited On:21 Sep 2011 09:43
Last Modified:28 Nov 2013 00:44
Publisher:Springer
ISSN:0374-3535
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:10.1007/s10659-010-9271-8

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