The design of the mirror body and its supporting structure exert an important influence on the system imaging quality. It is necessary to reduce the structural mass as much as possible, improve the surface shape accuracy of the mirror as much as possible, and ensure the dynamic and static stiffness and thermal dimensional stability of the system to reduce the transmission cost. Meanwhile, this has always been a difficult point in designing spatial optical machine structures. Reasonable flexible support design can solve the contradiction of mirror surface shape decline caused by temperature load and assembly stress on the premise of satisfying the mirror support stiffness. Computer-aided design/computer-aided engineering (CAD/CAE) technology is employed to predict and optimize the parameters of the flexible structure, and the direction and amount of parameter correction are determined according to the simulation results before design iteration. It is an efficient design solution for mirror support systems. In recent years, compared with traditional materials, the additive manufacturing lattice structure has been widely applied in space remote sensing cameras due to its excellent characteristics such as higher lightweight efficiency, specific stiffness/strength, and mechanical properties that can be designed. The complex lattice structures result in huge analysis and calculation amounts. At present, scholars at home and abroad mostly adopt the equivalent homogenization analysis method for lattice structures, and an urgent problem is to predict the mechanical properties of lattice filled structures quickly and effectively. To this end, a mechanical simulation technique based on accurate finite element modeling is proposed.

Based on the size optimization technique, we build a parametric finite element model of a rectangular reflective mirror and a multi-parameter optimization model of biaxial circular cut-out flexure hinge support. First, the feasible direction method and adaptive response surface optimization algorithm are applied respectively to obtain the thickness parameters of the mirror plate and the rib plate (Table 3) and the geometric size parameters of the flexible hinge support (Table 4). The influence of independent variables on the installation angle (Fig. 6) and the installation axial position (Fig. 7) of the flexible support is analyzed by the parametric test method. Second, a simulation optimization method of lattice structure design based on three-dimensional point cloud reconstruction is studied. Lattice filling and point cloud generation (Fig. 10) are utilized to reconstruct the grid of point clouds generated by the lattice structure envelope (Fig. 11), which can ensure the continuity and authenticity of the lattice structure model and obtain the backplane support parameters (Table 5). Finally, finite element modeling (Fig. 13) and simulation verification (Table 6) are carried out for the mirror assembly.

The optimization results show that when the installation angle β is 20°, the installation position is 13 mm±0.5 mm, and the geometric parameter r/t/b is 1/2/3 mm (Table 4), the composite surface shape of the mirror reaches the optimal value (0.018λ) (Table 6). When the skin and lattice structure parameter R/a/T of the backplane support is 0.8/6/4.5 mm (Table 5), the rigid body displacement of the mirror reaches the optimal value (0.007 mm). At the same time, the first order fundamental frequency and component mass meet the design requirements.

We propose a simulation optimization method for lattice structure design based on three-dimensional point cloud reconstruction. The results show that the simulation optimization method is reasonable and feasible, and can meet the design requirements of mirror support structures with similar structural forms.