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

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Abstract
We derive homogenized von Kármán shell theories starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the period of oscillation ε of the material properties and the thickness h of the shell. Depending on the asymptotic ratio of these two parameters, we obtain different asymptotic theories. In the case h \ll \varepsilon we identify two different asymptotic theories, depending on the ratio of h and \varepsilon ^{2} . In the case of convex shells we obtain a complete picture in the whole regime h \ll \varepsilon .
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  • Deutsche Forschungsgemeinschaft

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