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2019 On a boundary value problem for conically deformed thin elastic sheets
Heiner Olbermann
Anal. PDE 12(1): 245-258 (2019). DOI: 10.2140/apde.2019.12.245

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. These are the boundary conditions of a so-called “d-cone”. We define the free elastic energy as a variation of the von Kármán energy, which penalizes bending energy in Lp with p(2,83) (instead of, as usual, p=2). We prove ansatz-free upper and lower bounds for the elastic energy that scale like hp(p1), where h is the thickness of the sheet.

Citation

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Heiner Olbermann. "On a boundary value problem for conically deformed thin elastic sheets." Anal. PDE 12 (1) 245 - 258, 2019. https://doi.org/10.2140/apde.2019.12.245

Information

Received: 4 January 2018; Revised: 5 March 2018; Accepted: 10 April 2018; Published: 2019
First available in Project Euclid: 16 August 2018

zbMATH: 06930187
MathSciNet: MR3842912
Digital Object Identifier: 10.2140/apde.2019.12.245

Subjects:
Primary: 49Q10 , 74K20

Keywords: d-cone , thin elastic sheets

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2019
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