Derivation of a homogenized von Kármán shell theory

Peter Hornung and Igor Velčić

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Submission date: 11. Mar. 2013
Pages: 44
published in: Annales de l'Institut Henri Poincaré / C, 32 (2015) 5, p. 1039-1070 
DOI number (of the published article): 10.1016/j.anihpc.2014.05.003
Bibtex
with the following different title: Derivation of a homogenized von-Karman shell theory from 3D elasticity
Keywords and phrases: elasticity, dimension reduction, homogenization, shell theory, two scale convergence
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Abstract:
We derive the model of homogenized von Kármán shell theory, starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the oscillations of the material ϵ and the thickness of the shell h. Depending on the asymptotic ratio of these two parameters, we obtain different asymptotic theories. In the case h ≪ ϵ we identify two different asymptotic theories, depending on the ratio of h and ϵ². In the case of convex shells we obtain a complete picture in the whole regime h ≪ ϵ.