A finite element approach for cable problems

Abstract A finite element approach is proposed for the static and dynamic nonlinear analysis of cable structures. Starting from the stress equations of equilibrium, a variational formulation is derived in which the static and kinematic variables are measured in some previous configuration of the body. To discretize this variational form of equilibrium equations, Lagrangian functions are employed to interpolate the curved geometry of each element and only displacement continuity is enforced between element nodes. By introducing a separate interpolation for arclength, displacement patterns which leave element nodal arclengths constant are not allowed to induce strains in the element. The finite element matrices resulting from the operations of linearization and discretization are derived. By evaluating the stiffness matrix of the 2-node element, it is shown explicitly that the element stiffness matrix is independent of whether the initial configuration or the current configuration is used in the description of kinematic and static variables. Sample analyses are presented to demonstrate the utility and reliability of the proposed elements.