On a boundary value problem for conically deformed thin elastic sheets
Heiner Olbermann · Analysis & PDE · 2018
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 L p with p 2 2; 8 3 (instead of, as usual, p D 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.