A mixed formulation for nonlinear analysis of cable structures

This paper proposes a general finite-element procedure for the nonlinear analysis of cables based on a mixed variational formulation in curvilinear coordinates with finite deformations. The formulation accounts for nonlinear elasticity and inelasticity, overcoming the limitation of recent numerical approaches which integrate explicitly the global balance of linear momentum for a linear elastic material with infinitesimal deformations. The formulation uses a weak form of the catenary problem and of the strain-displacement relation to derive a new family of cable finite elements with a continuous or discontinuous axial force field. Several examples from the literature on nonlinear cable analysis are used to validate the proposed formulation for St. Venant-Kirchhoff elastic materials and neo-Hookean materials. These studies show that the proposed formulation captures the displacements and the axial force distribution with high accuracy using a small number of finite elements.