For the development of a large-aperture space telescope, one of the key techniques is the method for designing the flexures for mounting the primary mirror, as the flexures are the key components. In this paper, a topology-optimization-based method for designing flexures is presented. The structural performances of the mirror system under multiple load conditions, including static gravity and thermal loads, as well as the dynamic vibration, are considered. The mirror surface shape error caused by gravity and the thermal effect is treated as the objective function, and the first-order natural frequency of the mirror structural system is taken as the constraint. The pattern repetition constraint is added, which can ensure symmetrical material distribution. The topology optimization model for flexure design is established. The substructuring method is also used to condense the degrees of freedom (DOF) of all the nodes of the mirror system, except for the nodes that are linked to the mounting flexures, to reduce the computation effort during the optimization iteration process. A potential optimized configuration is achieved by solving the optimization model and post-processing. A detailed shape optimization is subsequently conducted to optimize its dimension parameters. Our optimization method deduces new mounting structures that significantly enhance the optical performance of the mirror system compared to the traditional methods, which only focus on the parameters of existing structures. Design results demonstrate the effectiveness of the proposed optimization method.
