Spatially complex localisation in twisted elastic rods constrained to lie in the plane

Equilibrium configurations are considered of a long rod constrained to lie in a plane subject to end conditions constituting a wrench. Using the Cosse rat theory, a formulation of the problem is proposed using a reduced angula r description of the director basis. On the assumption of an isotropic cros s-section, it is found that flexure and torsion decouple so that the rod bu ckles like a planar elastica. For rods held under gravity, a condition is d erived for the applied end loads required for lift-off of the localised mod e under tension. For anisotropic rods, flexure and torsion are coupled and additional more complex equilibrium shapes are possible including multi-loo p localised modes. Using specially adapted numerical shooting techniques su ch solutions, which are mathematically represented by homoclinic orbits to a periodic solution, are computed, and conditions for lift-off of the singl e-loop solutions are calculated as a function of the applied loads and an a nisotropy parameter. (C) 1998 Elsevier Science Ltd. All rights reserved.