• DOI:10.1016/J.ANIHPC.2014.05.003
• Corpus ID: 53325129

Derivation of a homogenized von Kármán shell theory

@inproceedings{Hornung2012DerivationOA,
  title={Derivation of a homogenized von K{\'a}rm{\'a}n shell theory},
  author={Peter Hornung and Igor Vel{\vc}i{\'c}},
  year={2012}
}

• Peter Hornung, I. Velčić
• Published 31 October 2012
• Mathematics, Physics

We derive the model of homogenized von K\'arm\'an 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 $h\ll\e$.