Derivation of a homogenized von-Kármán shell theory from 3D elasticity
Hornung, Peter ; Velčić, Igor
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015), p. 1039-1070 / Harvested from Numdam
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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.

@article{AIHPC_2015__32_5_1039_0,
     author = {Hornung, Peter and Vel\v ci\'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},
     volume = {32},
     year = {2015},
     pages = {1039-1070},
     doi = {10.1016/j.anihpc.2014.05.003},
     mrnumber = {3400441},
     zbl = {1329.74178},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2015__32_5_1039_0}
}

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) pp. 1039-1070. doi : 10.1016/j.anihpc.2014.05.003. http://gdmltest.u-ga.fr/item/AIHPC_2015__32_5_1039_0/

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