## A two-strand ply hanging under its own weight

G.H.M. van der Heijden

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.
keywords: constraints, contact force, elastic rod, gravity, two-strand ply,
variational analysis

*Nonlinear Dynamics* **43**, 197-208 (2006)