Keywords: inflatable membranes, deployment, energy minimization, contact and self-contact.

Inflatable structures are an attractive means to build some large spacecraft appendages. Compared to the structures deployed by electromechanical systems, the membrane structures have the advantage, in addition to their lightness, to be packed up during the launching phase. The dimensions of these appendages can be increased considerably and reach unequalled performance for a drastically reduced launching coast. Nevertheless, the control of the deployment of the inflatable structures remains more delicate than rigid structures. Some experiments, the like inflatable antenna experiment [3], were already undertaken successfully in space. Nevertheless, without gravity, the deployment is often carried out in chaotic way and can potentially fail. Numerical simulation of the deployment is an interesting means to achieve better knowledge of this phenomenon. This challenge gathers many non-linearities, which causes various numerical difficulties and often makes computer codes fail.

This paper presents experimental and numerical results on the vertical deployment of tubes simply folded and inflated with air. The study is intended to validate computer codes on the simulation of the deployment of membranous structures under quasi-static conditions. The values chosen for the loading parameters are rather weak and approach the values used in space applications. The experimented specimens are hermetic tubes of 80cm length with different diameters. They are simply folded at their middle. The bottom edge can pivot around an horizontal axis, and their top is fixed to an airborne carriage that slides on vertical stainless stem. The deployment is constrained by various values of dead loads placed on the airborne carriage. We use numerical models specifically developed for inflated membranes to simulate the quasi-static deployment of the tubes. It is based on the finite element discretization and uses the minimization approach of the total potential energy. A robust contact algorithm and self-contact of pressurized membranes in case of large transformations is developed and validated. The Saint-Venant-Kirchhoff potential energy is used to describe the hyperelastic behaviour of the material. We used the penalty method for the implementation of the contact and self-contact. The minimum energy formulation requires the system to be conservative, thus the contact is presumed to be without friction. Earlier works shows that the first order minimization method of total potential energy is very efficient for the resolution of pressurized membranes problems without contact [1].

We took particular care in the design of the experimental device. Frictions of the carriage were reduced to values lower than 0.2N. We tested various diameters of tube and various dead loads. The obtained results are presented as evolution curves of the carriage displacement according to the inflation pressure, supposed constant in the whole tube. We present here only the results obtained for two diameters: 15cm and 20cm.

The experimental results are used to validate the code in complicated simulation conditions. Indeed, such a problem gathers many non-linearities: large transformations, following forces like the inflation pressure, contact in the case of large transformations, and structural instabilities. The simulations are done by volume control with the help of Lagrange multipliers representing the inflation pressure [2,4]. The very good correlation between the experiment and simulation results demonstrates the reliability of this numerical approach and lets imagine an interesting future works about more complicated inflatable structure.

1

R. Bouzidi and A. Le Van, "Numerical solution of hyperelastic membranes by energy minimization", Computer and structures, 82, 1961-1969, 2004. doi:10.1016/j.compstruc.2004.03.057

2

K. A. Brakke, "Surface evolver manual", Manual Version 2.17, 2002.

3

R.E Freeland and G.R Veal, "Significance of the inflatable antenna experiment technology",Proceeding of the 39 th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference and exhibit, Long Beach, 1998.

4

Y. Zhang and B. Tabarrok, "Generation of surfaces via equilibrium of forces", Computers and structures, 70, 599-613, 1999. doi:10.1016/S0045-7949(98)00207-7

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