One-dimensional von K\'arm\'an models for elastic ribbons
Analysis of PDEs
2017-01-11 v1
Abstract
By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von K\'arm\'an plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found starting from the "linearized" von K\'arm\'an energy corresponds to that of a linearly elastic beam that can twist but can deform in just one plane; while the model found from the von K\'arm\'an energy is a non-linear model that comprises stretching, bendings, and twisting. The "constrained" von K\'arm\'an energy, instead, leads to a new Sadowsky type of model.
Keywords
Cite
@article{arxiv.1701.02721,
title = {One-dimensional von K\'arm\'an models for elastic ribbons},
author = {Lorenzo Freddi and Peter Hornung and Maria Giovanna Mora and Roberto Paroni},
journal= {arXiv preprint arXiv:1701.02721},
year = {2017}
}