Caltech Young Investigators Lecture
Simulation of Quasi-static Folding and Deployment of Tape Spring Flexures Using an Efficient Geometrically Nonlinear Unified Beam Formulation
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. She joined Imperial College London in March 2019, just before receiving her PhD in April 2019. Prior to that, she worked as a postgraduate researcher at the University of Strathclyde, in 2018, and at the Laboratory of Composite Materials and Adaptive Structures (CMASLab) at ETH, in 2017.
Soltani's primary research is focused on developing efficient but robust tools for the geometrically nonlinear finite element analysis and optimum design of compliant and deployable structures.
This talk is part of the Caltech Young Investigators Lecture Series, sponsored by the Division of Engineering and Applied Science.
Contact: Kate Jackson firstname.lastname@example.org