为满足空间反射镜高面形精度、高轻量化率的要求,在外径700 mm圆反射镜的设计过程中引入拓扑优化方法,依据变密度法建立了SIMP模型。在反射镜光轴方向重力工况下,以结构整体柔度为设计约束,最小体积为设计目标进行迭代,优化设计出了RMS值为8.89 nm,轻量化率达82%的反射镜模型。在同等质量下,基于传统的三角形轻量化孔结构设计出的反射镜模型RMS值为11.75 nm,轻量化率为65%。在径向重力工况下,拓扑优化结构也能满足面形要求。计算结果表明,拓扑优化的轻量化形式在面形和轻量化率上都优于传统形式。
In order to satisfy the strict requirements of the surface-shapes and lightweight ratios for space mirrors, the topological method was introduced to design the reflect mirror with a Ф 700 mm. According to the density method, the Solid Isotropic Microstructure with Penalization(SIMP) model was established. In the condition of axial-oriented gravity, by taking the general flexibility as a design constraint, and the minimum volume as a design objective, a better structure with a RMS of 8.89 nm and a lightweight ratio of 82% was obtained after iterations. In the same weight, the conventional triangular lightweight structure shows its RMS in 11.75 nm and lightweight ratio in 65%. In the condition of radial-oriented gravity, the surface-shape of the topological structure also meets the requirements of the design. In the considerations of the surface-shape and lightweight ratio, the computational result shows that the topological optimization method is better than the conventional method.