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

Peter Hornung; Igor Velcic

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arXiv · 1211.0045

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

Peter Hornung·Igor Velcic

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

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Peter Hornung, Igor Velcic. 2013-03-14. Derivation of a homogenized von-Karman shell theory from 3D elasticity. https://arxiv.org/abs/1211.0045

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