Form Finding of Planar Cables Considering Bending Stiffness Using Geometrically Exact Beam Theory

The bending stiffness of cables is an important influencing parameter in the analysis of cable structures, and the modeling of cables with bending stiffness has always been a key concern. This paper proposes an accurate beam formulation for planar cables with bending stiffness, in which the deformation–strain relationship is accurately described, thus enabling the geometrically exact form finding of planar cables. After the kinematics of the cable geometry are described, the strong- and weak-form equilibrium equations of the cable are derived, and then the finite element implementations are presented. Three typical examples of cable structures are also presented; the numerical results demonstrate that the presented beam formulation shows stable and accurate numerical performance. The proposed formulation achieves rapid convergence when the number of elements reaches 20. The analysis of a suspension bridge shows that considering bending stiffness has little influence on the completed bridge state, with the error between the calculated hanger forces and the design values remaining within 1.5%. However, in the free cable state, considering bending stiffness causes a saddle pre-offset variation of approximately 5 cm, while the sag difference reaches approximately 1 m. The results demonstrate that the proposed formulation is of significant importance for planar cable form finding problems.