High-fidelity arbitrary Lagrangian–Eulerian absolute nodal coordinate formulation considering rotational inertia in deployment and retrieval of slender structures

• Rotational inertia added to GDBE-ANCF without computing moving frames • Tangent-based formulation reduces computational complexity • Novel co-moving node scheme suppresses ALE numerical disturbances • CPU and FLOPs analyses confirm efficiency gains • Improved fidelity for deployment and retrieval simulations Slender flexible structures, such as cables and booms, are widely employed in mechanical engineering; however, their complex deformation requires high-fidelity simulation for reliable operation. This paper presents a simulation framework for deployment and retrieval of variable-length slender structures utilizing a gradient-deficient Bernoulli–Euler beam based on an arbitrary Lagrangian–Eulerian absolute nodal coordinate formulation (GDBE-ALE-ANCF). The study offers three key contributions. First, a high-fidelity formulation that efficiently incorporates cross-sectional rotational inertia is proposed. Unlike conventional GDBE-ANCF models, which rarely account for rotational inertia, the proposed approach requires only the tangent vector and its time derivative, eliminating the need for moving frames. Numerical results show that this method captures rotational inertia accurately while improving computational efficiency by nearly twenty times. Computational efficiency is further validated through a theoretical floating-point operation (FLOPs) comparison. Second, a novel co-moving node scheme enhances the robustness of the ALE description for variable-length structures. Conventional methods, such as node deletion or uniform node operations, often cause numerical disturbances. The proposed scheme advances adjacent nodes with the driving node using a smooth trigonometric acceleration profile, reducing numerical disturbances.