Lower bounds for the energy in a crumpled elastic sheet – A minimal ridge
نویسنده
چکیده
We study the linearized Föpl – von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2α. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness σ and the bending angle. We show that the minimum energy scales as σα. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as σ. AMS classification scheme numbers: 49J40,74K15,47J20,46N10 Submitted to: Nonlinearity
منابع مشابه
The Energy of Crumpled Sheets in Föppl-von Kármán Plate Theory
Abstract. We study investigate a long, thin rectangular elastic membrane that is bent through an angle 2α, using the Föppl–von Kármán ansatz in a geometrically linear setting. We study the associated variational problem, and show the existence of a minimizer for the elastic energy. We also prove rigorous upper and lower bounds for the minimum energy of this configuration in terms of the plate t...
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