基于筋板式基结构的大口径空间反射镜构型设计的拓扑优化方法  

Topologic optimization for configuration design of web-skin-type ground structure based large-aperture space mirror

作　　者：刘书田[1] 胡瑞[1] 周平[2] 董志刚[2] 康仁科[2] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [2]大连理工大学精密与特种加工教育部重点实验室,辽宁大连116024

出　　处：《光学精密工程》2013年第7期1803-1810,共8页Optics and Precision Engineering

基　　金：国家973重点基础发展计划资助项目(No.2011CB013201,No.2011CB610304);国家自然科学基金资助项目(No.11172052)

摘　　要：针对大口径空间光学反射镜对轻量化的需求,提出了基于筋板式基结构的大口径空间反射镜构型设计的拓扑优化方法。该方法利用基结构拓扑优化的思想,将反射镜初始设计域限定为筋板式的反射镜基结构,通过各筋板的有无描述结构构型的变化。首先,借鉴连续体结构拓扑优化的思想,以壳单元离散筋板结构,以加筋板各单元的相对密度为设计变量(通过相对密度取1或0,描述该单元所在区域的筋板是否存在),以光轴竖直工况下镜面面形误差为设计约束,镜体的质量最小为优化目标,建立了镜体结构构型设计的拓扑优化模型;然后,以拓扑优化所得构型为基础,提取并形成结构概念构型;最后,采用有限元法进行动静刚度分析与光学性能分析,并对结构进行修正,形成性能更好、满足要求的反射镜轻量化结构创新构型。文中的设计实例得到的反射镜镜面面形误差PV值小于λ/10,RMS值小于λ/40,第一阶自振频率大于1 000Hz,轻量化率达到86.0%。得到的结果验证了本文方法的有效性。For the requirements of the mirror in a large-aperture spaceborne telescope for lightweight,a web-skin-typed ground structure based topology optimization method was presented for the configuration design of large-aperture mirror.Based on the idea of topology optimization,the ground structure in this method was restricted to be a web-skin-type structure composed of a surface（skin） stiffened by webs,and the change of the configuration was described by whether webs or parts of the webs were deleted from the ground structure or not.Firstly,the web-skin-type ground structure was discreted with shell elements,the relative densities of all the elements on the webs were taken as design variables（the relative density was taken as 1 or 0 to describe whether the webs or parts of webs were kept or not）.Then,by using optical aberration of the mirror in the load case of vertical optical axis as a design restraint,and the total weight of the structure as a optimized target,a topology optimization model was established.Furthermore,the concept configuration based on the structure obtained by topology optimization was extracted.Finally,the dynamic and static stiffnesses and optical performance of the mirror were analyzed using the finite element method,the mirror configuration was modified,and a lightweight mirror structural innovation configuration was obtained.It shows that the optical aberration PV and RMS of the mirror obtained by the design example are less than λ/10 and λ/40,respectively,the fundamental frequency is greater than 1 000 Hz and the lightweight ratio reaches 86.0%.The results demonstrate the validity of the proposed approach properly.

关 键 词：大口径空间望远镜 反射镜 构型设计 轻量化设计 拓扑优化 筋板式基结构 

分 类 号：TH743[机械工程—光学工程]