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Self-contact for rods on cylinders

Van der Heijden, G.H.M.; Peletier, M.A.; Planqué, R.; (2006) Self-contact for rods on cylinders. Archive for Rational Mechanics and Analysis , 182 (3) pp. 471-511. 10.1007/s00205-006-0011-y.

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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.

Title:Self-contact for rods on cylinders
Publisher version:http://dx.doi.org/10.1007/s00205-006-0011-y
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Civil, Environmental and Geomatic Engineering

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