Preprint 58/2001

Rigorous derivation of nonlinear plate theory and geometric rigidity

Gero Friesecke, Richard D. James, and Stefan Müller

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Submission date: 30. Aug. 2001
Pages: 13
published in: Comptes rendus mathematique, 334 (2002) 2, p. 173-178 
DOI number (of the published article): 10.1016/S1631-073X(02)02133-7
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We show that nonlinear plate theory arises as a tex2html_wrap_inline8-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps tex2html_wrap_inline10. We show that the tex2html_wrap_inline12 distance of tex2html_wrap_inline14 from a single rotation is bounded by a multiple of the tex2html_wrap_inline12 distance from the set SO(3) of all rotations.

24.11.2021, 02:11