Helical and localized buckling in twisted rods: A unified analysis of the symmetric case

Nonlinear Dynamics

Volumn 21, Issue 1, 2000, Pages 71-99

  Van Der Heijden, G H M ^a   Thompson, J M T ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING MOMENTS; MATHEMATICAL MODELS; TENSILE STRESS; TORSIONAL STRESS;

ROD THEORY;

BUCKLING;

EID: 0033903070     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008310425967     Document Type: Article

References (27)

1. Antman, S. S., Nonlinear Problems of Elasticity, Springer-Verlag, Berlin, 1995.
2. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, 4th edn., Cambridge University Press, Cambridge, 1927.
3. Champneys, A. R. and Thompson, J. M. T., 'A multiplicity of localised buckling modes for twisted rod equations', Proceedings of the Royal Society of London A 452, 1996, 2467-2491.
4. Van der Heijden, G. H. M., Champneys, A. R., and Thompson, J. M. T., 'The spatial complexity of localised buckling in rods with non-circular cross-section', SIAM Journal on Applied Mathematics 59, 1999, 198-221.
5. Goldstein, H., Classical Mechanics, 2nd edn., Addison-Wesley, Reading, MA, 1980.
6. Antman, S. S. and Jordan, K. B., 'Qualitative aspects of the spatial deformation of non-linearly elastic rods', Proceedings of the Royal Society of Edinburgh A 73(5), 1974, 85-105.
7. Benham, C. J., 'An elastic model of the large-scale structure of duplex DNA', Biopolymers 18, 1979, 609-623.
8. Shi, Y. and Hearst, J. E., 'The Kirchhoff elastic rod, the nonlinear Schrödinger equation, and DNA supercoiling', Journal of Chemical Physics 101, 1994, 5186-5200.
9. Tobias, I., Coleman, B. D., and Olson, W. K., 'The dependence of DNA tertiary structure on end conditions: theory and implications for topological transitions', Journal of Chemical Physics 101, 1994, 10990-10996.
10. Thompson, J. M. T. and Champneys, A. R., 'From helix to localized writhing in the torsional post-buckling of elastic rods', Proceedings of the Royal Society of London A 452, 1996, 117-138.
11. Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, 2nd edn., McGraw-Hill, New York, 1961.
12. Coyne, J., 'Analysis of the formation and elimination of loops in twisted cable', IEEE Journal of Oceanic Engineering 15, 1990, 72-83.
13. Vigodsky, M., Matematicheskii Sbornik 16, 1945, 73-80.
14. Kauffman, L. H., Knots and Physics, World Scientific, Singapore, 1991.
15. Fuller, F. B., 'The writhing number of a space curve', Proceedings of the National Academy of Sciences of the United States of America 68, 1971, 815-819.
16. Cǎlugǎreanu, G., 'Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants', Czechoslovak Mathematical Journal 11, 1961, 588-625.
17. White, J. H., 'Self-linking and the Gauss integral in higher dimensions', American Journal of Mathematics 91, 1969, 693-728.
18. Moffatt, H. K. and Ricca, R. L., 'Helicity and the Cǎlugǎreanu invariant', Proceedings of the Royal Society of London A 439, 1992, 411-429.
19. Pohl, W. F., 'DNA and differential geometry', Mathematical Intelligencer 3, 1980, 20-27.
20. Fuller, F. B., 'Decomposition of the linking of a closed ribbon: a problem from molecular biology', Proceedings of the National Academy of Sciences of the United States of America 75, 1978, 3557-3561.
21. Tabor, M. and Klapper, I., 'The dynamics of knots and curves (Parts I and II)', Nonlinear Science Today 4(1), 1994, 7-13, 4(2), 1994, 12-18.
22. Tabor, M. and Klapper, I., 'The dynamics of knots and curves (Parts I and II)', Nonlinear Science Today 4(1), 1994, 7-13, 4(2), 1994, 12-18.
23. Alexander, J. C. and Antman, S. S., 'The ambiguous twist of Love', Quarterly of Applied Mathematics 40, 1982, 83-92.
24. Champneys, A. R., van der Heijden, G. H. M., and Thompson, J. M. T., 'Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature', Philosophical Transactions of the Royal Society of London A 355, 1997, 2151-2174.
25. Van der Heijden, G. H. M. and Thompson, J. M. T., 'Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods', Physica D 112, 1998, 201-224.
26. Van der Heijden, G. H. M., Champneys, A. R., and Thompson, J. M. T, 'Spatially complex localisation in twisted elastic rods constrained to lie in the plane', Journal of the Mechanics and Physics of Solids 47, 1999, 59-79.
27. Van der Heijden, G. H. M., 'The static deformation of a twisted elastic rod constrained to lie on a cylinder', Proceedings of the Royal Society A, submitted.