Nonlinear Spatial Equilibria and Stability of Cables Under Uni-axial Torque and Thrust

[+] Author and Article Information
C.-L. Lu, N. C. Perkins

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Appl. Mech 61(4), 879-886 (Dec 01, 1994) (8 pages) doi:10.1115/1.2901571 History: Received July 19, 1993; Online March 31, 2008


Low tension cables subject to torque may form complex three-dimensional (spatial) equilibria. The resulting nonlinear static deformations, which are dominated by cable flexure and torsion, may produce interior loops or kinks that can seriously degrade the performance of the cable. Using Kirchhoffrod assumptions, a theoretical model governing cable flexure and torsion is derived herein and used to analyze (1) globally large equilibrium states, and (2) local equilibrium stability. For the broad class of problems described by pure boundary loading, the equilibrium boundary value problem is integrable and admits closed-form elliptic integral solutions. Attention is focused on the example problem of a cable subject to uni-axial torque and thrust. Closed-form solutions are presented for the complex three-dimensional equilibrium states which, heretofore, were analyzed using purely numerical methods. Moreover, the stability of these equilibrium states is assessed and new and important stability conclusions are drawn.

Copyright © 1994 by The American Society of Mechanical Engineers
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