Asymptotic Behavior for Textiles in von-K{\'a}rm{\'a}n regime
Analysis of PDEs
2019-12-24 v1 Numerical Analysis
Numerical Analysis
Abstract
The paper is dedicated to the investigation of simultaneous homogenization and dimension reduction of textile structures as elasticity problem with an energy in the von-K{\'a}rm{\'a}n-regime. An extension for deformations is presented allowing to use the decomposition of plate-displacements. The limit problem in terms of displacements is derived with the help of the unfolding operator and yields in the limit the von-K{\'a}rm{\'a}n plate with linear elastic cell-problems. It is shown, that for homogeneous isotropic beams in the structure, the resulting plate is orthotropic. As application of the obtained limit plate we study the buckling behavior of orthotropic textiles.
Keywords
Cite
@article{arxiv.1912.10928,
title = {Asymptotic Behavior for Textiles in von-K{\'a}rm{\'a}n regime},
author = {Georges Griso and Julia Orlik and Stephan Wackerle},
journal= {arXiv preprint arXiv:1912.10928},
year = {2019}
}