Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 370767, 21 pages
Nonlinear Modeling of Cables with
1Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli studi di Roma la Sapienza, Via Eudossiana, 00184 Rome, Italy
2Ecole Nationale des Travaux Publics de L'Etat, Laboratoire des Séomatériaux, 69120 Vaulx-En-Velin, France
Received 14 November 2007; Accepted 28 March 2008
Academic Editor: Paulo Gonçalves
Copyright © 2008 Walter Lacarbonara and Arnaud Pacitti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A geometrically exact formulation of cables suffering axis stretching and flexural curvature is
presented. The dynamical formulation is based on nonlinearly viscoelastic constitutive laws
for the tension and bending moment with the additional constitutive nonlinearity accounting
for the no-compression condition. A continuation method, combined with a mixed finite-difference
spatial discretization, is then employed to path-follow the static responses of cables subject to
forces or support displacements. These computations, conducted in the quasistatic regime, are
based on cables with linearly elastic material behaviors, whereas the nonlinearity is in the geometric
stiffness terms and the no-compression behavior. The finite-difference results have been
confirmed employing a weak formulation based on quadratic Lagrangian finite elements.
The influence of the flexural stiffness on the nonlinear static responses is assessed comparing the
results with those obtained for purely extensible cables. The properties of the frequencies of the
linear normal modes of cables with flexural stiffness are also investigated and compared with those
of purely extensible cables.