Shell theories arising as low energy \Gamma-limit of 3d nonlinear elasticity
Functional Analysis
2008-03-05 v1 Mathematical Physics
math.MP
Abstract
We discuss the limiting behavior (using the notion of \Gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h^4 (where h is the thickness of a shell), we derive a limiting theory which is a generalization of the von K\'arm\'an theory for plates.
Keywords
Cite
@article{arxiv.0803.0358,
title = {Shell theories arising as low energy \Gamma-limit of 3d nonlinear elasticity},
author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad},
journal= {arXiv preprint arXiv:0803.0358},
year = {2008}
}
Comments
36 pages, 1 figure