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

Hornung, Peter; Velčić, Igor

doi:10.1016/j.anihpc.2014.05.003

Hornung, Peter ; Velčić, Igor

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 1039-1070.

Résumé

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 $h ≪ ϵ$ .

MR Zbl

DOI : 10.1016/j.anihpc.2014.05.003

Mots-clés : 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},
     publisher = {Elsevier},
     volume = {32},
     number = {5},
     year = {2015},
     doi = {10.1016/j.anihpc.2014.05.003},
     mrnumber = {3400441},
     zbl = {1329.74178},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.05.003/}
}

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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. http://www.numdam.org/articles/10.1016/j.anihpc.2014.05.003/

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