A cable finite element formulation based on exact tension field for static nonlinear analysis of cable structures

Abstract: This paper presents a numerically exact cable finite element model for static nonlinear analysis of cable structures. The model derives the exact expression of the tension field using the geometrically exact beam theory coupled with the fundamental mechanical characteristics of cables. The equations for the cable element are formulated by addressing the equilibrium conditions at the element boundaries and ensuring compatibility within the element. Unlike previous studies that typically provide explicit expressions for cable models, this study develops a formulation that emphasizes numerical precision and broad applicability. It achieves this by deriving linearized equations with implicit expressions incorporating integrals. The proposed model accurately computes internal forces and deformation states, and determines the unstrained length of the cable. Additionally, it accounts for the variability in cross-sectional stiffness along the cable's length. The paper discusses solution implementations using the complete tangent matrix and element internal iterations. The effectiveness of the proposed cable element is demonstrated through numerical examples.