Geodesic
Derivation of a homogenized von-Kármán shell theory from 3D elasticity
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 1039-1070
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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≪ϵ we identify two different asymptotic theories, depending on the ratio of h and ϵ 2 . In the case of convex shells we obtain a complete picture in the whole regime h≪ϵ.

DOI : 10.1016/j.anihpc.2014.05.003
Keywords: Elasticity, Dimension reduction, Homogenization, Shell theory, Two-scale convergence 
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     author = {Hornung, Peter and Vel\v{c}i\'c, Igor},
     title = {Derivation of a homogenized {von-K\'arm\'an} shell theory from {3D} elasticity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1039--1070},
     year = {2015},
     publisher = {Elsevier},
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     number = {5},
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Hornung, Peter; Velčić, Igor. Derivation of a homogenized von-Kármán shell theory from 3D elasticity. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 1039-1070. doi: 10.1016/j.anihpc.2014.05.003

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