THE MECHANICS OF HIGHLY-EXTENSIBLE CABLES

Abstract The mechanics of highly extensible cables are studied numerically. The governing equations for the cable motion are reformulated using Euler parameters and we employ a nonlinear stress–strain relation. Also, bending–stiffness terms are included to ensure a well-posed problem when tension becomes very low. Thus, the singularity associated with Euler–angle formulation is removed and the model allows for shock formation, while it can accommodate zero or negative tension along the cable span. Implicit time integration and non-uniform grid along the cable are adopted for the numerical solution of the governing equations. The model is employed to investigate (1) the dynamical behaviour of the breaking and post-breaking of an initially taut cable; and (2) the dynamic response of a tethered near-surface buoy subject to wave excitation. For a breaking cable we find that the speed of snapback, which can have potentially catastrophic effects, is proportional to the initial strain level, but the principal parameter controlling the cable behaviour is the time it takes for the cable to fracture. In the case of a tethered buoy in waves, we find that beyond a threshold wave amplitude the system begins to exhibit first zero tension, then followed by snapping response, while the buoy performs chaotic motion.