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.
"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