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The Föppl-von Kármán plate theory as a low energy $$\Gamma$$-limit of nonlinear elasticity. (English. Abridged French version) Zbl 1041.74043
Summary: We show that the Föppl-von Kármán theory arises as a low energy $$\Gamma$$-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [the authors, ibid. 334, No. 2, 173–178 (2002; Zbl 1012.74043)] that for maps $$v:(0, 1)^3\to\mathbb{R}^3$$, the $$L^2$$ distance of $$\nabla v$$ from a single rotation is bounded by a multiple of the $$L^2$$ distance from the set SO(3) of all rotations.

##### MSC:
 74K20 Plates 74B20 Nonlinear elasticity
##### Keywords:
$$L(2)$$-distance; rotation
Full Text:
##### References:
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