Mode change and evolution of thin deployable space structures in small and large displacement regimes

Predicting the dynamic response of thin-walled deployable space structures, such as tape springs, remains a major challenge due to severe geometric nonlinearities. Classical 1D beam models miss essential cross-sectional morphing. Consequently, analyzing these architectures typically requires the use of computationally expensive 3D solid elements. To overcome this limitation, this study employs the 1D Carrera Unified Formulation (CUF) to investigate the modal evolution of a tape spring subjected to large axial tensile loads. By solving the generalized eigenvalue problem around distinct equilibrium states, the pre-stress field is explicitly incorporated via the geometric stiffness matrix Kσ. Comparing linear and non-linear analyses reveals that a linear assumption yields an unmitigated stress-stiffening effect, causing unrealistic frequency spikes and chaotic modal shifts. The non-linear analysis, however, successfully captures cross-section deformation, which significantly mitigates artificial stiffening and stabilizes modal evolution. These findings highlight that combining high-fidelity non-linear equilibrium analysis with advanced modal tracking (MAC) is essential to correctly interpret these complex structural dynamics.