Self-contact for rods on cylinders

G.H.M. Heijden, van der, M.A. Peletier, R. Planqué

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

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 ordinary differential equation 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.
Original languageEnglish
Pages (from-to)471-511
JournalArchive for Rational Mechanics and Analysis
Volume182
Issue number3
DOIs
Publication statusPublished - 2006

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