A Two-Strand Ply Hanging Under Its Own Weight
- G. H. M. Van Der Heijden
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We consider an idealised model for a plied structure such as may form when a straight rod or filament is subjected to a high twisting moment. Examples are found in textile yarns, interwound DNA molecules and bacterial macrofibres. Plied structures, generally composed of more than two strands, are also used widely in engineering (mooring ropes, cables in lift shafts), although here the strands are often not intrinsically straight. The ply is assumed to consist of two strands of thin circular elastic rod winding around each other while touching on a straight line of contact. Each strand is therefore constrained to lie on a cylinder. Using a variational approach we give an unconstrained Hamiltonian formulation for this problem. We also derive an exact expression for the contact force acting between the two strands. We study the symmetry-breaking effect of gravity on the ply configuration as well as on the contact force.
- Costello, G. A., Theory of Wire Rope, 2nd edn., Springer-Verlag, New York, 1997.
- Parry, D. A. D. and Squire, J. M. (eds.), ‘Fibrous proteins’, Journal of Structural Biology 122(special issue), 1998.
- Hearle, J. W. S. and Yegin, A. E., ‘The snarling of highly twisted monofilaments. Part I: The load-elongation behaviour with normal snarling’, Journal of the Textile Institute 63, 1972, 477–489; ‘Part II: Cylindrical snarling’, Journal of the Textile Institute 63, 1972, 490–501.
- Treloar, L. R. G., ‘The geometry of multy-ply yarns’, Journal of the Textile Institute 47, 1956, T348–T368.
- Fraser, W. B. and Stump, D. M., ‘The equilibrium of the convergence point in two-strand yarn plying’, International Journal of Solids and Structures 35, 1998, 285–298. CrossRef
- Fraser, W. B. and Stump, D. M., ‘Twist in balanced-ply structures’, Journal of the Textile Institute 89, 1998, 485–497.
- Strick, T. R., Allemand, J. F., Bensimon, D., Bensimon, A., and Croquette, V., ‘The elasticity of a single supercoiled DNA molecule’, Science 271, 1996, 1835–1837.
- Mendelson, N. H., Chen, L., and Thwaites, J. J., ‘A new form of bacterial movement, dragging of multicellular aggregate structures over solid surfaces, is powered by macrofiber supercoiling’, Research in Microbiology 155, 2004, 113–127. CrossRef
- Tsuru, H. and Wadati, M., ‘Elastic model of highly supercoiled DNA’, Biopolymers 25, 1986, 2083–2096. CrossRef
- Hunt, N. G. and Hearst, J. E., ‘Elastic model of DNA supercoiling in the infinite-length limit’, Journal of Chemical Physics 95, 1991, 9329–9336.
- Yang, Y., Tobias, I., and Olson, W. K., ‘Finite element analysis of DNA supercoiling’, Journal of Chemical Physics 98, 1993, 1673-1686.
- Dichmann, D. J., Li, Y., and Maddocks, J. H., ‘Hamiltonian formulations and symmetries in rod mechanics’, in Mathematical Approaches to Biomolecular Structure and Dynamics, J. P. Mesirov, K. Schulten, and D. W. Sumners (eds.), Springer-Verlag, New York, 1996, pp. 71–113.
- Goriely, A. and Tabor, M., ‘The nonlinear dynamics of filaments’, Nonlinear Dynamics 21, 2000, 101–133. CrossRef
- Coleman, B. D. and Swigon, D., ‘Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids’, Journal of Elasticity 60, 2000, 173–221. CrossRef
- Thompson, J. M. T., van der Heijden, G. H. M., and Neukirch, S., ‘Supercoiling of DNA plasmids: Mechanics of the generalized ply’, Proceedings of the Royal Society of London A 458, 2002, 959–985.
- 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.
- van der Heijden, G. H. M., Thompson, J. M. T., and Neukirch, S., ‘A variational approach to loaded ply structures’, Journal of Vibration and Control 9, 2003, 175–185. CrossRef
- 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 of London A 457, 2001, 695–715.
- van der Heijden, G. H. M., Neukirch, S., Goss, V. G. A., and Thompson, J. M. T., ‘Instability and self-contact phenomena in the writhing of clamped rods’, International Journal of Mechanical Sciences 45, 2003, 161–196.
- Klapper, I., ‘Biological applications of the dynamics of twisted elastic rods’, Journal of Computational Physics 125, 1996, 325–337. CrossRef
- Neukirch, S. and van der Heijden, G. H. M., ‘Geometry and mechanics of uniform n-plies: From engineering ropes to biological filaments’, Journal of Elasticity 69, 2002, 41–72. CrossRef
- Antman, S. S., Nonlinear Problems of Elasticity, Springer-Verlag, Berlin, 1995.
- Doedel, E. J., Champneys, A. R., Fairgrieve, T. R., Kuznetsov, Yu. A., Sandstede, B., and Wang, X. J., ‘AUTO97: Continuation and bifurcation software for ordinary differential equations’, 1997. Available by anonymous ftp from ftp://ftp.cs.concordia.ca/pub/doedel/auto.
- A Two-Strand Ply Hanging Under Its Own Weight
Volume 43, Issue 1-2 , pp 197-208
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- Kluwer Academic Publishers
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- contact force
- elastic rod
- two-strand ply
- variational analysis
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- Author Affiliations
- 1. Centre for Nonlinear Dynamics, Civil Engineering Building, University College London, Gower Street, London, WC1E 6BT, U.K.