Year: 2022
Type: preprint
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 $h.$ 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 $h$ and the indentation depth $d.$
Source: arXiv (Cornell University)
Author: Dengler, Marcel
Institution: University of Bonn
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4306818263