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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

thin elastic sheets d-cone


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.

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