Periodically wrinkled plate model of the Föppl-von Kármán type
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 2, p. 275-307

In this paper we derive, by means of $\Gamma$-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is ${h}^{2}$ and that the mid-surface of the plate is given by $\left({x}_{1},{x}_{2}\right)\to \left({x}_{1},{x}_{2},{h}^{2}\theta \left(\frac{{x}_{1}}{h},\frac{{x}_{2}}{h}\right)\right)$, where $\theta$ is ${\left[0,1\right]}^{2}$ periodic function. We also assume that the strain energy of the plate has the order ${h}^{8}={\left({h}^{2}\right)}^{4}$, which corresponds to the Föppl-von Kármán model in the case of the ordinary plate. The obtained model mixes the bending part of the energy with the stretching part.

Published online : 2019-02-21
Classification:  74K20,  74B20
@article{ASNSP_2013_5_12_2_275_0,
author = {Vel\v ci\'c, Igor},
title = {Periodically wrinkled plate model of the F\"oppl-von K\'arm\'an type},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 12},
number = {2},
year = {2013},
pages = {275-307},
zbl = {1271.74290},
mrnumber = {3114006},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2013_5_12_2_275_0}
}

Velčić, Igor. Periodically wrinkled plate model of the Föppl-von Kármán type. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 2, pp. 275-307. http://www.numdam.org/item/ASNSP_2013_5_12_2_275_0/

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