Nonlinear response of elastic cables with flexural-torsional stiffness

• A nonlinear Cosserat model of flexible cables is proposed.
• The stresses within boundary layers are underestimated by approximate theories.
• The prestress regulates the boundary layer features, including the stress peaks.
• The model offers accuracy in boundary layers estimation also under dynamic loadings.

A geometrically exact mechanical formulation is proposed to describe three-dimensional motions of flexible cables without any restriction on the amplitude of such motions. The nonlinear equations of motion are formulated via an updated Lagrangian formulation taking the prestressed catenary equilibrium under gravity as the start configuration. By employing a single space coordinate parametrization, the kinematics feature finite displacement and rotation of the cable cross sections, assumed rigid in their own planes. The ensuing generalized strain parameters and curvatures retain the full geometric nonlinearities. By considering several case-study cables within the groups of taut and shallow cables, nonlinear equilibrium analyses are performed to investigate the effects of the cable bending and torsional stiffness for nontrivial boundary conditions. The full nonlinear formulation allows to estimate the size of the boundary layers as well as the stress states within them otherwise unknown adopting classical theories of purely stretchable cables.