Trade-off analysis for structural design of high-precision space reflector using multiobjective optimization method

This study investigates the robustness of a space reflector structure consisting of radial ribs and hoop cables by using the multiobjective optimization method. The radial ribs are deformed into a parabola shape by cable tensions applied to the hoop cables that are arranged concentrically around the central hub and to the tie cables that are connected to the deployable structure. The design problem is to achieve the ideal deformation shape for the radial rib under the prescribed cable tensions through the determination of the rib height distribution. In addition, the ability to adjust the shape by changing the cable tension is required for handling uncertainty under actual environment condition. A simplified structural model with only one radial rib is used for structural design, where the cables are replaced by equivalent tensions. This study adopts the multiobjective optimization method to verify the structural design by investigating the trade-off between the deformation error and its sensitivity with respect to the cable tensions. Robustness corresponds to lower value of sensitivity, that the RMS error is difficult to deteriorate by changing the cable tension. On the other hand, design with higher value of sensitivity is called adjustability, because such a design is easy to adjust the deformation shape by the cable tension. The primary objective of the design problem is to minimize the RMS error between the ideal and the deformation shape of the rib under the prescribed cable tension in terms of the rib dimensions. The other two objectives are to accomplish the robustness and the adjustability of the rib deformation shape by adjusting the cable tension using the tie cable and the outermost hoop cable. This multiobjective optimization problem is evaluated by the satisficing trade-off method (STOM). Through investigating Pareto solutions obtained from the two-objective and then the three-objective function problems, the effects of cable tension variations on the surface shape error and the robustness are discussed.