Model order reduction technique for variable-length beams based on arbitrary Lagrangian–Eulerian description

Dynamic analysis of variable-length beams in multibody systems (e.g., deployable space structures) via Arbitrary Lagrangian–Eulerian (ALE) formulations encounters significant computational challenges due to time-varying configurations and geometric nonlinearities. This paper proposes a Model Order Reduction (MOR) framework integrating the ALE description with a dimensionless beam element formulation. By deriving dynamic equations for normalized elements, we establish a length-independent reduction basis that avoids recomputing basis functions for varying beam lengths. To capture geometric nonlinearities, the MOR combines low-order linear vibration modes (VMs) and modal derivatives (MDs), extending our prior ALE-RNCF method to enable parametric model reduction in multibody systems. Numerical experiments on three beam element types demonstrate that the proposed method substantially reduces the degrees of freedom compared to full-order ALE models while maintaining tip displacement errors below one percent. Computational efficiency improves several times, enabling real-time simulation of complex deployment dynamics. This advancement provides a critical tool for designing adaptive structures in aerospace and robotic applications.