Caltech Young Investigators Lecture
Tape spring flexures are a commonly-proposed component of deployable structures due to their ability to combine self-deployment, via a release of stored strain energy, with locking into a relatively stiff geometric configuration with a curved cross section. They may also be coupled with additional tape springs to achieve improvements in deployed stiffness. A common manifestation of this is the tube flexure, famously employed on the MARSIS boom on the Mars Express spacecraft. Currently, finite element (FE) analysis of tapes springs in commercial solvers requires a large number of finite elements to resolve the highly-localized flexure fold region accurately, and a robust solver to enable the capture of complex post-buckling behaviour. Consequently the computational requirements are significant. For tape spring flexure design methodologies requiring computational optimization, and hence numerous simulations, there is a strong motivation to seek efficient and robust alternatives.
In this talk, I will present a transition unified beam finite element formulation capable of matching different refinements in different cross sections. The main advantage of this formulation is that it enables the localized refinement of regions such as the fold where greater discretization is required whilst retaining the computational efficiency offered by the technique. In other words, in this formulation, different refinements are inferred as different numbers of transverse degrees of freedom at each node along the beam axis. Moreover, the independent discretization between the beam axis and over the cross section leads to a very well banded stiffness matrix, which benefits from a significant reduction in the storage requirement and the computation time.
Another difficulty in conventional FE analysis of tape spring is the capabilities to simulate the highly nonlinear folding behaviour of tape springs under bending loading — which is a combination of geometric nonlinearity, post-buckling, and (in the case of tube flexures) internal contact. This is crucial for simulating deployment behavior of tape springs that cannot be easily measured in experimental tests. In spite of versatility of finite element methods in structural analysis, typical load increment and displacement increment methods are not suitable for capturing the critical points during bending, in which the tape spring cannot support an increase of the external moment and instabilities occur. In this work, using the arc-length method, an automatic increment technique is employed to choose sufficiently small arc-length, in particular at turning points. This enables simulation of the unstable fold localization process accurately, efficiently, and robustly.
To summarize, the significant reduction in degrees of freedom for no loss of accuracy and the ability to resolve unstable equilibrium regions, in addition to the advantage of the banded stiffness matrix, means that the present formulation offers a significantly higher computational efficiency in comparison with the traditional FE formulation for rapid and robust nonlinear analysis of tape spring flexures. This will enable confident design of the next generation of deployable structures.
Zahra Soltani is currently a Research Associate in the Aerospace Structures group in the Department of Aeronautics, Imperial College, London. She studied Aerospace Engineering for her bachelor's and master's degrees at Sharif University of Technology, from where she also obtained a PhD in Aerospace Structures in 2019. She spent one year as a visiting researcher in the Laboratory of Composite Materials and Adaptive Structures (CMASLab) at ETH in 2017 as part of her PhD study. Upon finishing her PhD, she joined Imperial College in 2019. Zahra's research background is mainly related to developing efficient and robust tools for the nonlinear and/or instability analysis of compliant structures and their optimum design. Her research interests include soft materials, geometrically nonlinear analysis, composite structures, deployable structures, adaptive mechanisms, Bayesian optimization, and machine learning.
This talk is part of the Caltech Young Investigators Lecture Series, sponsored by the Division of Engineering and Applied Science.