Optimal Design, Nonlinear Analysis and Shape Control of Deployable Mesh Reflectors

This thesis presents the research on optimal design, nonlinear analysis and shape control of the perimeter truss deployable mesh reflector (DMR) as a type of state-of-the-art space structures, all three portions of which construct the Active Shape Control architecture.;To design the shape of DMR, a new mesh generation approach is developed to automatically determine the mesh geometry of the working surface of DMRs, which is among very few of pseudo-geodesic mesh geometry design methods. Once the desired geometry of the mesh facets is generated, the optimal design method is presented to determine the structural parameters such as undeformed length of members and the external loads so that not only the mesh facets are deformed onto the desired working shape exactly but also the best tension distribution is assured in the reflector structure. In the academic literature such method is the first to include the external loads as the design variables to design deployable trusses.;The nonlinear static analysis is carried out based on a new static truss model using a nonlinear programming solving technique formulated in the thesis. Since the static model does not need the initial configuration of the reflector, both the initial shape and the deformed shape are obtained by the solving approach. The natural frequencies and the mode shapes are addressed on the linearized dynamics derived at the nonlinear static equilibrium solution and this linear dynamic system is used in the following shape control study.;As the final part of the architecture, both the static and dynamic shape control strategies are proposed in the thesis. The static shape control approach provides one of few thermal compensation solutions regarding the fully nonlinear statics of reflector structures. The dynamic shape control use the feedback of the nodal coordinates and is the first feedback shape control on DMRs. Both shape control methods have demonstrated their advancements on improving the surface accuracy of DMRs for the space thermal environment in orbiting missions.