Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 1 (2019), 245-258.

On a boundary value problem for conically deformed thin elastic sheets

Heiner Olbermann

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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.

Article information

Source
Anal. PDE, Volume 12, Number 1 (2019), 245-258.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1534384918

Digital Object Identifier
doi:10.2140/apde.2019.12.245

Mathematical Reviews number (MathSciNet)
MR3842912

Zentralblatt MATH identifier
06930187

Subjects
Primary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90] 74K20: Plates

Keywords
thin elastic sheets d-cone

Citation

Olbermann, Heiner. On a boundary value problem for conically deformed thin elastic sheets. Anal. PDE 12 (2019), no. 1, 245--258. doi:10.2140/apde.2019.12.245. https://projecteuclid.org/euclid.apde/1534384918


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