We show how an energy analysis can be used to derive the equilibrium equations and boundary conditions for an end-loaded variable ply much more efficiently than in previous works. Numerical results are then presented for a clamped balanced ply approaching lock-up. We also use the energy method to derive the equations for a more general ply made of imperfect anisotropic rods and we briefly consider their helical solutions.
Champneys, A.R., van der Heijden, G.H.M., and Thompson, J.M.T., 1997, “Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature”, Philosophical Transactions of the Royal Society of London, Series A355, 2151-2174.
2.
Coleman, B.D., and Swigon, D., 2000, “Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids”, Journal of Elasticity60, 173-221.
3.
Fraser, W.B. and Stump, D.M., 1998, “The equilibrium of the convergence point in two-strand yarn plying”, International Journal of Solids and Structures35, 285-298.
4.
Pierański, P., 1998, “In search of ideal knots”, in Ideal Knots, A. Stasiak, V. Katritch and L.H. Kauffman, eds., Series on Knots and Everything, Vol. 19, pp. 20-41, World Scientific, Singapore.
5.
Stasiak, A., and Maddocks, J.H., 2000, “Best packing in proteins and DNA”, Nature406, 251-253.
6.
Thompson, J.M.T., van der Heijden, G.H.M., and Neukirch, S., 2002, “Supercoiling of DNA plasmids: mechanics of the generalized ply”, Proceedings of the Royal Society of London, Series A458, 959-985.
7.
Van der Heijden, G.H.M., 2001, “The static deformation of a twisted elastic rod constrained to lie on a cylinder”, Proceedings of the Royal Society of London, Series A457, 695-715.
8.
Van der Heijden, G.H.M. and Thompson, J.M.T., 1998, “Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods”, Physica D112, 201-224.
