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.
PDF (Accepted mauscript)
View at publisher
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.
25 downloads since deposited on 21 Sep 2011
5 downloads since 12 months
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Deposited On:||21 Sep 2011 09:43|
|Last Modified:||28 Nov 2013 00:44|
|Additional Information:||The original publication is available at www.springerlink.com|
Users (please log in): suggest update or correction for this item
Repository Staff Only: item control page