Self-contact for rods on cylinders
Mathematical Physics
2009-09-29 v1 Classical Analysis and ODEs
math.MP
Abstract
We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a second-order functional of a single scalar variable, and the self-contact constraint is written as an integral inequality. Using techniques from ode theory (comparison principles) and variational calculus (cut-and-paste arguments) we fully characterize the structure of constrained minimizers. An important auxiliary result states that the set of self-contact points is continuous, a result that contrasts with known examples from contact problems in free rods.
Cite
@article{arxiv.math-ph/0411007,
title = {Self-contact for rods on cylinders},
author = {G. H. M. van der Heijden and M. A. Peletier and R. Planqué},
journal= {arXiv preprint arXiv:math-ph/0411007},
year = {2009}
}
Comments
42 pages, 11 figures