# 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.

## 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.

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