Periodically wrinkled plate of the Föppl-von Kármán type

2011/04/04 by Velčić, Igor
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1104.0661

Abstract

In this paper we derive, by means of Γ-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is h² and that the mid-surface of the plate is given by (x₁,x₂) → (x₁,x₂,h²θ(\per)), where θ is [0,1]² periodic function. We also assume that the strain energy of the plate has the order h⁸=(h²)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.

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