Experiments on snap buckling, hysteresis and loop formation in twisted rods

Experimental Mechanics

Volumn 45, Issue 2, 2005, Pages 101-111

  Goss, V G A ^a,b   van der Heijden, G H M ^a   Thompson, J M T ^a   Neukirch, S ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b LONDON SOUTH BANK UNIVERSITY   (United Kingdom)

Author keywords

Bifurcation; Hockling; Loop formation; Nitinol; Rod experiments; Snap buckling; Snarling; Twisted rods; Welded boundary conditions

Indexed keywords

BENDING (FORMING); BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; BUCKLING; CALCULATIONS; GRAVITATIONAL EFFECTS; HYSTERESIS; KINEMATICS; NICKEL ALLOYS; TITANIUM ALLOYS;

DEFLECTION; HOCKLING; LOOP FORMATION; NITINOL; ROD EXPERIMENTS; SNAP BUCKLING; SNARLING; TWISTED RODS; WELDED BOUNDARY CONDITIONS;

WELDING RODS;

BIFURCATION; BUCKLING;

EID: 24144475221     PISSN: 00144851     EISSN: None     Source Type: Journal    
DOI: 10.1177/0014485105052318     Document Type: Article

References (27)

1. Coyne, J., "Analysis of the Formation and Elimination of Loops in Twisted Cable," IEEE Journal of Oceanic Engineering, 15 (2), 72-83 (1990).
2. Liu, F.E C., "Kink Formation and Rotational Response of Single and Multistrand Electromechanical Cables," Technical Note N-1403, Civil Engineering Lab, Naval Construction Batallion Center, Port Hueneme, CA (1975).
3. Rosenthal, E, "The Application of Greenhill's Formulae to Cable Hockling," ASME Journal of Applied Mechanics, 43, 681-683 (1976).
4. Tan, Z. and Witz, J.A., "Loop Formation of Marine Cables and Umbilicals During Installation," Proceedings of Behaviour of Offshore Structures (BOSS '92), London, UK, Vol. II, M.H. Patel and R. Gibbins (editors), BPP Technical Services, London, 1270-1285 (1992).
5. Yabuta, T, "Submarine Cable Kink Analysis," Bulletin of the Japanese Society of Mechanical Engineers, 27 (231), 1821-1828 (1984).
6. Hearle, J.W.S. and Yegin, A.E., "The Snarling of Highly Twisted Monofilaments," Journal of the Textile Institute, 63 (9), 477-489 (1972).
7. Swigon, D., "Configurations With Self-contact in the Theory of the Elastic Rod Model for DNA," Ph.D. Dissertation, Rutgers State University of New Jersey, NJ (1999).
8. Coleman, B.D. and Swigon, D., "Theory of Supercoiled Elastic Rings with Self-contact and Its Application to DNA Plasmids," Journal of Elasticity, 60, 173-221 (2000).
9. Calladine, C.R., Drew, H., Luisi, B., and Travers, A., Understanding DNA: The Molecule and How It Works, 3rd edition, Elsevier Academic, London (2004).
10. Born, M., "Untersuchungenüber die Stabilität der elastischen linie in Ebene und Raum," Ph.D. Thesis, University of Göttingen, Germany (1906).
11. Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, 4th edition, Cambridge University Press, Cambridge (1927).
12. Greenhill, A.G., "On the Strength of Shafting When Exposed Both to Torsion and to End Thrust," Proceedings of the Institute of Mechanical Engineers, London, April, 182-209 (1883).
13. 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, A452, 117-138 (1996).
14. Miyazaki, Y. and Kondo, K., "Analytical Solution of Spatial Elastica and Its Application to Kinking Problem," International Journal of Solids and Structures, 34 (27), 3619-3636 (1997).
15. Van der Heijden, G.H.M., Neukirch, S., Goss, V.G.A., and Thompson, J.M.T., "Instability and Contact Phenomena in the Writhing of Clamped Rods," International Journal of Mechanical Sciences, 45, 161-196 (2003).
16. Kauffman, G.B. and Mayo, I., "The Story of Nitinol: The Serendipitious Discovery of the Memory Metal and Its Applications," The Chemical Educator, 2 (2), 1-21 (1996).
17. Pemble, C.M. and Towe, B.C., "A Miniature Memory Alloy Pinch Valve," Sensors and Actuators, 77, 145-148 (1999).
18. Kujala, S., Pajala, A., Kallioinen, M., Pramila, A., Tuukkanen, J., and Ryhanen, J., "Biocompatibility and Strength Properties of Nitinol Shape Memory Alloy Suture in Rabbit Tendon," Biomaterials, 25, 353-358 (2004).
19. Kusy, R. P., "Orthodontic Biomaterials: From the Past to the Present," Angle Orthodontist, 72 (6), 501-502 (2002).
20. Gere, J.M. and Timoshenko, S.P., Mechanics of Materials, 2nd edition, Van Nostrand Reinhold, London (1987).
21. Rucker B.K. and Kusy, R.P., "Elastic Properties of Alternative Versus Single Stranded Leveling Archwires," American Journal of Orthodontics and Dentofacial Orthopedics, 122 (5), 528-541 (2002).
22. Drake, S.R., Wayne, D.M., Powers, J.M., and Asgar K., "Mechanical Properties of Orthodontic Wires in Tension, Bending, and Torsion," American Journal of Orthodontics, 82 (3), 206-210 (1982).
23. Antman, S.S., Nonlinear Problems of Elasticity, Springer-Verlag, New York (1995).
24. Kehrbaum, S. and Maddocks, J.H., "Elastic Bodies, Quarternians and the Last Quadrature," Proceedings of the Royal Society of London, A355, 2117-2136 (1997).
25. Shampine, L. W., Kierzenka, J., and Reichelt, M. W., "Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c," ftp://ftp.mathworks.com/pub/doc/papers/bvp/ (2000).
26. Euler L., "Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentes," Bousquent, Lausanne (1744). Reprinted in Opera Omnia I, 24, 231-297.
27. Zajac, E.E., "Stability of Two Planar Loop Elasticas," Transactions of the ASME Journal of Applied Mechanics, 29, 136-142 (1962).