Preprint 33/2002

The Föppl-von Kármán plate theory as a low energy Gamma limit of nonlinear elasticity

Gero Friesecke, Richard D. James, and Stefan Müller

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Submission date: 10. Apr. 2002
Pages: 13
published in: Comptes rendus de l'Académie des Sciences / 1, 335 (2002) 2, p. 201-206 
DOI number (of the published article): 10.1016/S1631-073X(02)02388-9
MSC-Numbers: 74K20, 73C50, 49J45
PACS-Numbers: 46.70.-p, 46.25.-y, 46.15.-x
Keywords and phrases: plates, föppl von karman theory, gamma-convergence, nonlinear elasticity
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Abstract:
We show that the Föppl-von Kármán theory arises as a

low energy formula7-limit of

three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [G. Friesecke et al., C. R. Acad. Sci., Ser. I 334 (2002), 173-178] that for maps formula9, the formula11 distance of formula13 from a single

rotation is bounded by a multiple of the formula11 distance from the set

SO(3) of all rotations.

20.02.2013, 14:48