DEPLOYMENT DYNAMICS OF THIN-SHELL STRIPS WITH ELASTIC FOLDS
2.8 Conclusion
This chapter has presented a study of the dynamic deployment of rectangular space frames composed of interconnected, ultralight thin-shell longerons. The structures were initially folded by forming two elastic folds, and were then deployed by releasing the stored elastic energy. An experimental setup was designed to symmetrically fold 1.125-m-long structural prototypes, which were supported by a cord suspension system and deployed against gravity with the assistance of two edge masses. Digital Image Correlation was used to measure the deformation of the structure during deployment, and an algorithm was developed to track the location and angle of the elastic folds, robust against noisy and incomplete point clouds. The algorithm, implemented in MATLAB, can be easily adapted to different shell geometries and to point clouds obtained from different measurement techniques, and is available to the interested reader at the following link https://github.com/apedivel/
thin_shell_localized_folds.git.
Deployment experiments have shown that a symmetrically folded structure remains essentially symmetric during the deployment process. For the particular experiments presented in the chapter, the elastic folds did not move along the longerons, behaving as non-linear elastic hinges. In other experiments, with different initial locations for the elastic folds (very close to the center or to the ends of the strips) and not presented in this chapter, the folds did move, although they were often constrained by the battens to remain within one bay of the structure.
The present simulation method can be used to predict the effects of different loading and boundary conditions on the deployment of the structure, which can be significant.
For example, Fig. 2.37 compares the evolution of the elastic folds𝜃(𝑠) for the strip without membrane, if the end masses are replaced with constant force retractors.
This plot shows that free deployment in 0 g would be almost twice as fast as the benchmark case studied in this chapter (deployment with gravity and suspension system with 50-g end masses), with a deployment time of 144 ms vs. 282 ms. Also, the angle of the folds monotonically decreases during free deployment, whereas it oscillates in the final part of deployment for the benchmark case. The oscillation
0 100 200 300 400 500 Time [ms]
-45 -30 -15 0 15 30 45
[deg]
Cords with 50 g end masses 5 N constant force retractor Free deployment - 0g
Figure 2.37: Effect of boundary conditions and gravity on the deployment of a strip.
in the fold angle is due to the inertia of the end masses. This was confirmed by simulating a variant of the suspension system, where the counterweights are replaced by a constant force spring retractor with negligible inertia, providing the same amount of cord tension (5 N) as the benchmark suspension system. The results for this case (yellow lines in Fig. 2.37) show that the fold angle is the same as the suspension system with counterweights for the first 110 ms of deployment, but it decreases much faster afterwards and remains monotonic. The deployment time for this case is 175 ms, only 20% slower than free deployment in 0 g.
These results indicate that, although the suspension system presented in this chapter offers a relatively simple implementation and can be accurately characterized ex- perimentally and modeled in simulations, alternative suspension concepts may be devised that provide a closer approximation to deployment under zero-g conditions.
The effect of air on the deployment dynamics of these structures has been exper- imentally characterized for the first time. It has been shown that the interaction with air significantly slows down the deployment of a strip prototype supporting a thin membrane. However, this effect becomes negligible in the absence of the membrane.
A finite element model of deployment has been developed. Quasi-static deployment simulations were able to correctly predict the steady-state moment of the strip pro- totypes, but significantly overpredicted the peak moment at the end of deployment.
This discrepancy was attributed to the longerons being sensitive to geometric imper- fections, such as local variations of the flange radius and angle. Such imperfections were not considered in this chapter, and require further work to be experimentally characterized and included in simulations. As far as the dynamic deployment sim-
ulations are concerned, they correctly capture the initial equilibrium configuration in the folded state, and accurately predict the evolution of the fold angles during deployment, with less than 5 % error on the deployment time. A simple model to estimate the added mass of air from the geometry of the structure, as well as an air drag model based on drag coefficients from literature, has been proposed.
Simulations made with this model closely match the deployment behavior observed in experiments, both qualitatively and quantitatively. Although the present study has considered initial folding angles of about 45◦, it would be interesting to investigate the deployment of fully folded strips, which would require a different suspension system.
In conclusion, it has been shown that the packaging and deployment of space frames consisting of thin-shell longerons can self-deploy in a reliable and repeatable fashion. This represents a promising path forward to the application of thin-shell technologies to novel lightweight solar array concepts and other applications.
C h a p t e r 3