On a boundary value problem for conically deformed thin elastic sheets

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 Kármán energy, that penalizes bending energy in $L^p$ with $p\in (2,\frac{8}{3})$ (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.

14 pages; version 2: minor changes, acknowledgments added

References in corpus (4)

• Convex integration for the Monge-Ampère equation in two dimensions
• Energy Bounds for a Compressed Elastic Film on a Substrate
• Energy scaling law for the regular cone
• The shape of low energy configurations of a thin elastic sheet with a single disclination

Cited by in corpus (1)

• Wrinkling of an elastic sheet floating on a liquid sphere