Variational problems in thin elastic structures
arXiv:2210.08324
Abstract
For two different scenarios regarding thin elastic structures, described by 2d-Föppl-von Kármán plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain fairly optimal upper- and lower energy bounds and we highlight how those bounds scale wrt. the thickness-parameter Secondly, we consider the half sphere, while being indented by a thin object at the top and perpendicular to its surface. In this situation we provide an energy-scaling law, for radial symmetric admissible maps, this time, depending on and the indentation depth