An Obstacle Problem for Conical Deformations of Thin Elastic Sheets

摘要

A developable cone ("d-cone") is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance . Starting from a nonlinear model depending on the thickness h 0 of the sheet, we prove a -convergence result as to a fourth-order obstacle problem for curves in . We then describe the exact shape of minimizers of the limit problem when is small. In particular, we rigorously justify previous results in the physics literature.