Derivation of a homogenized von-Kármán shell theory from 3D elasticity
Péter Hornung, Igor Velčić · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2014
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 .