From helix to localized writhing in the torsional post-buckling of elastic rods

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1944, 1996, Pages 117-138

  Thompson, J M T ^a   Cliampneys, A R ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000111802     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0007     Document Type: Article

References (29)

1. Alexander, J. C. & Antman, S. S. 1982 The ambiguous twist of Love. Q. appl. Math. 40, 83-92.
2. Antman, S. S. 1995 Nonlinear problems of elasticity. New York: Springer.
3. Antman, S. S. fc Kenney, C. S. 1981 Large buckled states of nonlinearly elastic rods under torsion, thrust and gravity. Arch, ration. Mech. Analysis 76, 289-338.
4. Bauer, W. R., Crick, F. H. C. & White, J. H. 1980 Supercoiled DNA. Scient Am. 243, 118-133.
5. Buffoni, B., Champneys, A. R. & Toland, J. F. 1994 Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system. Mathematics preprint, 94/05, School of Mathematical Sciences, University of Bath.
6. Calladine, C. R. 1980 Toroidal elastic supercoiling of DNA. Biopolymers 19, 1705-1713.
7. Calladine, C. R. & Drew, H. R. 1992 Understanding DNA. London: Academic.
8. Champneys, A. R. & Spence, A. 1993 Hunting for homoclinic orbits in reversible systems: a shooting technique. Adv. comput. Math. 1, 81-108.
9. Champneys, A. R. & Thompson, J. M. T. 1995 A multiplicity of localized buckling modes for twisted rod equations. Proc. R. Soc. Land. A (submitted).
10. Champneys, A. R. & Toland, J. F. 1993 Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems. Nonlinearity 6, 665-721.
11. Cottrell, A. H. 1964 The mechanical properties of matter. New York: Wiley.
12. Coy ne, J. 1990 Analysis of the formation and elimination of loops in twisted cable. IEEE J. ocean. Engng 15, 72-83.
13. Davies, M. A. & Moon, F. C. 1993 3D spatial chaos in the elastica and the spinning top: Kirchhoff analogy. Chaos 3, 93-99.
14. Fuller, F. B. 1971 The writhing number of a space curve. Proc. natn. Acad. Sci. U.S.A. 68, 815-819.
15. Hunt, G. W., Bolt, H. M. & Thompson, J. M. T. 1989 Structural localization phenomena and the dynamical phase-space analogy. Proc. R. Soc. Land. A 425, 245-267.
16. Hunt, G. W. & Neto, E. L. 1991 Localized buckling in long axially-loaded cylindrical shells. J. Mech. Phys. Solids 39, 881-894.
17. Hunt, G. W. & Neto, E. L. 1993 Maxwell critical loads for axially loaded cylindrical shells. J. appl. Mech. 60, 702-706.
18. Hunt, G. W. & Wadee, M. K. 1991 Comparative Lagrangian formulations for localized buckling. Proc. R. Soc. Land. A 434, 485-502.
19. Ikeda, K., Providencia, P. & Hunt, G. V. 1993 Multiple equilibria for unlinked and weakly-linked cellular structural forms. Int. J. Solids Struct. 30, 371-384.
20. Kauffman, L. H. 1991 Knots and physics. Singapore: World Scientific.
21. Love, A. E. H. 1927 A Treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press.
22. Mansfield, E. H. 1965 The instability of buckle pattern in cylindrical shells under axial compression. Aeronaut. Q. 16, 275-281.
23. Mielke, A. & Holmes, P. 1988 Spatially complex equilibria of buckled rods. Arch, ration. Mech. Analysis 101, 319-348.
24. Tan, Z. & Witz, J. A. 1992 Loop formation of marine cables and umbilicals during installation. In BOSS 92 (ed. M. H. Patel & R. Gibbins), pp. 1270-1285. London: BPP Technical Services.
25. Thompson, J. M. T. 1979 Stability predictions through a succession of folds. Phil. Trans. R. Soc. Land. A 292, 1-23.
26. Thompson, J. M. T. & Virgin, L. N. 1988 Spatial chaos and localization phenomena in nonlinear elasticity. Phys. Lett. 126A, 491-496
27. Timoshenko, S. P. & Gère, J. M. 1961 Theory of elastic stability. New York: McGraw-Hill.
28. van der Meer, J. 1985 The Hamiltonian Hopf bifurcation (Lecture Notes in Mathematics 1160). Berlin: Springer.
29. Ziegler, H. 1968 Principles of structural stability. Waltham, MA: Blaisdell.