Analysis & PDE
- Anal. PDE
- Volume 12, Number 1 (2019), 245-258.
On a boundary value problem for conically deformed thin elastic sheets
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 with (instead of, as usual, ). We prove ansatz-free upper and lower bounds for the elastic energy that scale like , where is the thickness of the sheet.
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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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