A Two-Strand Ply Hanging Under Its Own Weight
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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.
Key Wordsconstraints contact force elastic rod gravity two-strand ply variational analysis
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