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

  • Peter Hornung

    Institut für Angewandte Mathematik, Universität Bonn, 53111 Bonn, Germany
  • Igor Velčić

    University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia, BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Bizkaia, Basque-Country, Spain


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 we identify two different asymptotic theories, depending on the ratio of h and . In the case of convex shells we obtain a complete picture in the whole regime .

Cite this article

Peter Hornung, Igor Velčić, Derivation of a homogenized von-Kármán shell theory from 3D elasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 5, pp. 1039–1070

DOI 10.1016/J.ANIHPC.2014.05.003