Self-Contact for Rods on Cylinders

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


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.

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • G. H. M. van der Heijden
    • 1
  • M. A. Peletier
    • 2
  • R. Planqué
    • 3
  1. 1.Centre for Nonlinear DynamicsUniversity College LondonLondonEngland
  2. 2.Dept. of Mathematics and Computing ScienceTechnical University EindhovenEindhovenThe Netherlands
  3. 3.Department of Computer ScienceUniversity of BristolBristolEngland

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