| With the continuous improvement of the imaging quality requirement of the space optical system,the large-aperture mirror becomes the research focus in the development of the space telescope.However,the increase of the aperture of the space mirror will increase the weight of the whole structural system,thus resulting in high launch cost.Furthermore,the structural deformation induced by self-gravity and temperature shift will also degrade the mirror surface shape accuracy.Actually,the structural configuration of the mirror substrate is one of the key factors affecting the weight and surface shape accuracy of the mirror.Therefore,the design method of the mirror substrate is of great importance to acquire a large-aperture space mirror with light weight and high surface shape accuracy.Additionally,as a key component of the large-aperture space mirror support structure system,the flexible support is used to achieve the best matching on stiffness and flexibility between the mirror and support structure,whose structural form also has an important effect on the mirror surface shape accuracy.Hence,it is of great significance to study the design method of flexible support structure for improving the surface shape accuracy of space mirror.Motivated by two mentioned demands,two kinds of design methods based on topology optimization with web-skin-type ground structure and 3D solid structure are investigated for the most typical open back mirror form;A new bidirectional multi-arch configuration for large-aperture space mirror is proposed,and a design of the new configuration is conducted;For the closed back mirror with high manufacturing difficulty,the topology optimization-based design method considering the manufacturability constraints for the closed back mirror is presented.Finally,the design method of flexible support structure for improving the surface shape accuracy of space mirror is studied based on topology optimization.The main research contents and achievements are listed as follows:(1)Design method based on topology optimization for open back mirror with web-skin-type ground structure.Inspired by the topology optimization of discrete truss-like structures,the web-skin-type mirror ground structure is selected as the design domain of topology optimization,and the structural configuration is determined by properly deciding webs or parts of the webs deleted from the ground structure.The topology optimization model of the web-skin-type mirror ground structure is established by taking the minimum weight of the mirror as the objective and setting the mirror surface shape error as the constraint.Considering the practical manufacturing process,the method to extract the conceptual configuration of the mirror is presented.In the design example,an optimized open back web-skin-type mirror is obtained,whose surface shape accuracy and lightweight ratio are greatly improved compared with the initial ground structure.Furthermore,the design of a non-circular off-axis mirror is successfully improved using the proposed method.The mirror surface accuracy is improved and the weight of the mirror is reduced,thus showing the universality and feasibility of the proposed design method.(2)Design method for open back mirror through topology optimization of 3D solid structure.By setting the initial solid mirror model as the design domain,the distribution and the heights of the stiffeners on the mirror back can be concurrently optimized by introducing an explicit parameterization considering casting constraint.The topology optimization model of the open back mirror for designing the stiffeners on the mirror back is established with the purpose of improving the mirror surface shape accuracy.An optimized mirror configuration is achieved using the proposed design method.Compared with the classical flat back mirror and double arch mirror with hexagonal lightweight hole,the optimized mirror has great superiority on the mirror surface shape accuracy with the same weight.Furthermore,the validity and universality of the proposed method are verified by the successful application to some other mirror design examples.(3)Design of a new bidirectional multi-arch large-aperture space mirror.For the large-aperture space mirror,a new bidirectional multi-arch configuration is proposed composing multi-arches arranged radially and circumferentially.The structural characteristics of the new bidirectional multi-arch mirror configuration are described in detail.Through reasonable arranging of the grooves in the mirror substrate,the shape of the substrate is changed along the radial and circumferential direction of the mirror using the rationality of arch,which improved the structural specific stiffness consequently.According to the proposed new configuration,a detailed design of a 2 m large-aperture space mirror is carried out,and then a bidirectional multi-arch lightweight mirror is obtained with excellent performance.(4)Topology optimization-based design method of closed back mirror structure considering manufacturability constraints.Aiming at the closed back mirror with higher specific stiffness and more difficulty to be manufactured,the design of vertical stiffening webs inside the mirror core is obtained by introducing extrusion constraints;Moreover,a simply connected constraint based on the virtual temperature method is considered to avoid enclosed voids in the structures,which ensures the structural manufacturability.The topology optimization model for the closed back mirror is established with the objective of improving the mirror surface shape accuracy.In addition,a size optimization model is implemented to adjust the thicknesses of the stiffening webs in detail.In the design example,the optimized closed back mirror shows significant superiorities on the optical performance and the lightweight ratio,which demonstrates the effectiveness of the proposed method for designing the closed back mirror.(5)Topology optimization-based design method of the flexible support structure for improving the surface shape accuracy of space mirror.Considering the structural performances of the mirror system under multiple loads including the static gravity,thermal loads as well as the dynamic vibration responses,the topology optimization model of the flexible support structure for improving the mirror surface shape accuracy is established by treating the mirror surface shape error as the objective function and by setting both the first order natural frequency of the mirror structural system and the pattern repetition manufacturability as the constraints.The sub-structure analyzing technique is also used to condense the degrees of freedom of all the nodes of the mirror system,except for those from the flexible support,thus reducing the computation effort for accurately calculating the responses of the complex mirror system and optimization iteration.In addition,a detailed shape optimization model is established to optimize its dimension parameters.The design results show that topology optimized flexible support has great superiorities on improving the surface shape accuracy than the conventional cruciform and universal joint flexible supports designed by parameter optimization,which demonstrates the effectiveness of the proposed optimization design method for the flexible support structure of space mirrors. |
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