An Asymptotic Variational Problem Modeling a Thin Elastic Sheet on a Liquid, Lifted at One End
Analysis of PDEs
2020-05-20 v1
Abstract
We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include the membrane and bending energy of the sheet as well as terms due to gravity and surface tension. By studying a suitable Gamma-limit, we identify a parameter regime in which the sheet is inextensible, and the bending energy and weight of the sheet are negligible. In this regime, the problem simplifies to one with a simple and explicit solution.
Keywords
Cite
@article{arxiv.1904.11391,
title = {An Asymptotic Variational Problem Modeling a Thin Elastic Sheet on a Liquid, Lifted at One End},
author = {David Padilla-Garza},
journal= {arXiv preprint arXiv:1904.11391},
year = {2020}
}