Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On end rotation for open rods undergoing large deformations


Authors: G. H. M. van der Heijden, M. A. Peletier and R. Planqué
Journal: Quart. Appl. Math. 65 (2007), 385-402
MSC (2000): Primary 49N99, 51H99, 51N99, 74B20, 74K10
DOI: https://doi.org/10.1090/S0033-569X-07-01049-X
Published electronically: April 10, 2007
MathSciNet review: 2330564
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a careful discussion of end rotation in elastic rods, focusing on ambiguities that arise if arbitrarily large deformations are allowed. By introducing a closure and restricting to a class of deformations we show that a rigorous treatment of end rotation can be obtained. The results underpin various non-rigorous discussions in the literature and serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations. As an example we discuss the application to the model of a rod lying on the surface of a cylinder.


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Additional Information

G. H. M. van der Heijden
Affiliation: Centre for Nonlinear Dynamics and its Applications, University College London, Gower Street, London WC1E 6BT

M. A. Peletier
Affiliation: Technische Universiteit Eindhoven, Den Dolech 2, P.O. Box 513, 5600 MB Eindhoven

R. Planqué
Affiliation: Department of Mathematics, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam
Email: rplanque@few.vu.nl

DOI: https://doi.org/10.1090/S0033-569X-07-01049-X
Keywords: Rod theory, end rotation, twist, writhe, large deformations.
Received by editor(s): August 28, 2006
Published electronically: April 10, 2007
Additional Notes: This research was partly funded by the EPSRC under contract GR/R51698/01. The first author also thanks The Royal Society for continuing support. The authors are grateful to Jason Cantarella for many interesting discussions, and to Rubber Import Amsterdam BV for supplying us with ample experimental material.
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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