Periodically wrinkled plate model of the Föppl-von Kármán type

Velčić, Igor

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 2, pp. 275-307

Résumé

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 $(x_1,x_2)\to (x_1,x_2,h^2\theta (\frac{x_1}{h},\frac{x_2}{h}))$, where $\theta$ is ${[0,1]}^2$ 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.

Détail

Publié le : 2019-02-21

Classification : 74K20, 74B20