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MiS Preprint

Derivation of a homogenized von Kármán shell theory

Peter Hornung and Igor Velčić


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 $\epsilon$ and the thickness of the shell $h$. Depending on the asymptotic ratio of these two parameters, we obtain different asymptotic theories. In the case $h\ll\epsilon$ we identify two different asymptotic theories, depending on the ratio of $h$ and $\epsilon^2$. In the case of convex shells we obtain a complete picture in the whole regime $h\ll\epsilon$.

elasticity, dimension reduction, homogenization, shell theory, two scale convergence

Related publications

2015 Repository Open Access
Peter Hornung and Igor Velčić

Derivation of a homogenized von-Karman shell theory from 3D elasticity

In: Annales de l'Institut Henri Poincaré / C, 32 (2015) 5, pp. 1039-1070