Calculus of Variations and Geometric Measure Theory
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H. Olbermann

On a boundary value problem for conically deformed thin elastic sheets

created by olbermann on 23 Jul 2019

[BibTeX]

preprint

Inserted: 23 jul 2019

Year: 2017

ArXiv: 1710.01707 PDF

Abstract:

We consider a thin elastic sheet in the shape of a disk that is clamped at its boundary such that the displacement and the deformation gradient coincide with a conical deformation with no stretching there. We define the free elastic energy as a variation of the von K\'arm\'an energy, that penalizes bending energy in $L^p$ with $p\in (2,\frac83)$ (instead of, as usual, $p=2$). We prove ansatz free upper and lower bounds for the elastic energy that scale like $h^{p/(p-1)}$, where $h$ is the thickness of the sheet.

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