UNSPECIFIED. (2006) A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 180 (2). pp. 183-236. ISSN 0003-9527

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Abstract

We derive a hierarchy of plate models from three-dimensional nonlinear elasticity by Gamma-convergence. What distinguishes the different limit models is the scaling of the elastic energy per unit volume similar to h(beta), where h is the thickness of the plate. This is in turn related to the strength of the applied force similar to h(alpha). Membrane theory, derived earlier by Le Dret and Raoult, corresponds to alpha = beta = 0, nonlinear bending theory to alpha = beta = 2, von Karman theory to alpha = 3, beta = 4 and linearized vK theory to alpha > 3. Intermediate values of alpha lead to certain theories with constraints. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [29] which states that for maps nu : (0,1)(3) -> R-3, the L-2 distance of del nu from a single rotation is bounded by a multiple of the L(2)supercript stop distance from the set SO(3) of all rotations.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery
Journal or Publication Title:	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Publisher:	SPRINGER
ISSN:	0003-9527
Date:	May 2006
Volume:	180
Number:	2
Number of Pages:	54
Page Range:	pp. 183-236
Identification Number:	10.1007/s00205-005-0400-7
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/33836

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