# On the justification of plate models

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

## 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.

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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English March 2011 21 Sep 2011 09:43 05 Apr 2016 15:01 Springer 0374-3535 The original publication is available at www.springerlink.com 10.1007/s10659-010-9271-8
Permanent URL: http://doi.org/10.5167/uzh-49740