A Rigid-Body-Qualified Truss Element for Nonlinear Analysis of Cable Structures

Cable analysis need not rely on the catenary theory, but can be performed using a rigid-body-qualified truss element. This paper presents a rigorous formulation of the truss element for nonlinear analysis of cable structures based on the updated Lagrangian (UL) approach. Starting from the virtual work principle, the exact stiffness equations are derived for the truss element that incorporates five stiffness components. The stiffness components are not separate, but must appear in conjugate pairs to collectively address the effects of rigid rotations and stretching. Inadvertent omission of some of the higher-order stiffness terms may result in violation of the rigid body rule, which is harmful to nonlinear analysis. The incremental–iterative algorithm based on the Newton–Raphson method is composed of the predictor, corrector, and equilibrium checking stages. While the predictor can be approximate, the corrector needs to be as exact as possible, especially for large-displacement problems. In the four well-designed examples, it was validated that using complete stiffnesses in the corrector is essential for reliable accuracy; incomplete stiffnesses lead to non-removable errors. Thus, the rigid-body rule must be fully satisfied for truss elements in nonlinear cable analysis.