Self-Contact for Rods on Cylinders |
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| Authors: | G H M van der Heijden M A Peletier R Planqué |
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| Institution: | (1) Centre for Nonlinear Dynamics, University College London, Gower Street, London, WC1E 6BT, England;(2) Dept. of Mathematics and Computing Science, Technical University Eindhoven, PO Box 513, 5600, MB, Eindhoven, The Netherlands;(3) Department of Computer Science, University of Bristol, Woodland Road, Bristol, BS8 1UB, England |
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| 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. |
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