| Summary: | Deployable structures serve a large number of space missions. They are vital since spacecraft are launched by placing them inside launch vehicle payload fairings of limited volume. Traditional spacecraft design often involves large components. These components could have power, communication, or optics applications and include booms, masts, antennas, and solar arrays. Different stowing methods are used in order to reduce the overall size of a spacecraft. Some examples of stowing methods include simple articulating, more complex origami inspired folding, telescoping, and rolling or wrapping. Wrapping of a flexible component could reduce the weight by eliminating joints and other components needed to enable some of the other mechanisms. It also is one of the most effective methods at reducing the compaction volume of the stowed deployable. In this study, a generic unfurlable structure is optimized for maximum natural frequency at its fully deployed configuration and minimal strain energy in its stowed configuration. The optimized stowed structure is then deployed in simulation. The structure consists of a rectangular panel that tightly wraps around a central cylindrical hub for release in space. It is desired to minimize elastic energy in the fully wrapped panel and hinge to ensure minimum reaction load into the spacecraft as it deploys in space, since that elastic energy stored at the stowed position transforms into kinetic energy when the panel is released and induces a moment in the connected spacecraft. It is also desired to maximize the fundamental frequency of the released panel as a surrogate for the panel having sufficient stiffness. Deployment dynamic analysis of the finite element model was run to ensure satisfactory optimization formulation and results. === Master of Science === Spacecraft, or artificial satellites, do not fly from earth to space on their own. They are launched into their orbits by placing them inside launch vehicles, also known as carrier rockets. Some parts or components of spacecraft are large and cannot fit in their designated space inside launch vehicles without being stowed into smaller volumes first. Examples of large components on spacecraft include solar arrays, which provide power to the spacecraft, and antennas, which are used on satellite for communication purposes. Many methods have been developed to stow such large components. Many of these methods involve folding about joints or hinges, whether it is done in a simple manner or by more complex designs. Moreover, components that are flexible enough could be rolled or wrapped before they are placed in launch vehicles. This method reduces the mass which the launch vehicle needs to carry, since added mass of joints is eliminated. Low mass is always desirable in space applications. Furthermore, wrapping is very effective at minimizing the volume of a component. These structures store energy inside them as they are wrapped due to the stiffness of their materials. This behavior is identical to that observed in a deformed spring. When the structures are released in space, that energy is released, and thus, they deploy and try to return to their original form. This is due to inertia, where the stored strain energy turns into kinetic energy as the structure deploys. The physical analysis of these structures, which enables their design, is complex and requires computational solutions and numerical modeling. The best design for a given problem can be found through numerical optimization. Numerical optimization uses mathematical approximations and computer programming to give the values of design parameters that would result in the best design based on specified criterion and goals. In this thesis, numerical optimization was conducted for a simple unfurlable structure. The structure consists of a thin rectangular panel that wraps tightly around a central cylinder. The cylinder and panel are connected with a hinge that is a rotational spring with some stiffness. The optimization was solved to obtain the best values for the stiffness of the hinge, the thickness of the panel, which is allowed to vary along its length, and the stiffness or elasticity of the panel's material. The goals or objective of the optimization was to ensure that the deployed panel meets stiffness requirement specified for similar space components. Those requirements are set to make certain that the spacecraft can be controlled from earth even with its large component deployed. Additionally, the second goal of the optimization was to guarantee that the unfurling panel does not have very high energy stored while it's wrapped, so that it would not cause large motion the connected spacecraft in the zero gravity environments of space. A computer simulation was run with the resulting hinge stiffness and panel elasticity and thickness values with the cylinder and four panels connected to a structure representing a spacecraft. The simulation results and deployment animation were assessed to confirm that desired results were achieved.
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