面向空间展开与无皱设计的薄膜结构拓扑优化方法研究

With the advantages of light weight, large deformation, easy of stowing and folding, thin membranes are very useful for many space structures, such as deployable antennas and solar sails. However, most of the existing designs for space thin membrane structures were obtained by empirical means or size optimization methods, which will make them difficult to keep the optimum state under in-orbit operation. By using the relative density penalization model and the geometrically nonlinear finite element analysis, a wrinkle-free constraint definition is proposed based on the principal stress-principal strain criterion for membranes in wrinkled and taut states. Then, a wrinkle-free topology optimization model for the design of geometrically nonlinear membranes is proposed. In order to make the problem computationally tractable, an equivalent strategy for regularizing wrinkle-free constraints and the relaxed method for enlarging the narrow feasible domain are developed. Further, for the space-deployable and wrinkle-free design of membrane-support structures considering requirements on lightweight, low energy consumption and high surface precision, a two-material topology optimization theory and corresponding methods are investigated in this project. At last, topology optimizations by using the abovementioned model, numerical simulations and experimental tests on the ground for typical space thin membrane structures are performed. This project will greatly enrich the theory and method of topology optimization, give guidance to the design of space membrane structures and provide a reasonable and reliable solution for the novel connected material distribution of membranes and supports in the space engineering. The achievements in this project will form a solid theoretical foundation and provide rich technical reserves for future space environment tests.

薄膜具备重量轻、大变形、易于展开/折叠等优势，适用于可展开天线、太阳帆等航天空间结构。然而，现有设计大多局限于经验性手段或尺寸优化方法，难以实现空间薄膜结构在轨运行中的最佳状态。本项目基于相对密度惩罚模型和几何非线性有限元分析，结合描述薄膜张拉和褶皱状态的主应力-主应变准则，提出无皱化约束定义，建立几何非线性薄膜无皱化拓扑优化模型，发展无皱化约束的正则化等效策略和狭窄可行域松弛策略。进一步考虑轻量化、低能耗和薄膜形面高精度的要求，研究面向空间展开与无皱设计的薄膜-支撑双材料拓扑优化理论模型和求解方法，开展典型空间薄膜结构的优化设计、数值仿真和地面实验验证。项目研究将丰富和发展拓扑优化理论，指导空间薄膜结构的拓扑设计工作，为航天空间工程提供更为合理、可靠的薄膜-支撑材料最优联合布局设计方案。项目成果将为未来在轨空间运行提供理论基础和技术储备。

本项目以航天柔性薄膜结构拓扑优化设计为研究背景，结合描述薄膜拉伸和褶皱状态的主应力-主应变准则，建立了几何非线性薄膜无皱化拓扑优化模型，发展无皱化约束的正则化等效策略和狭窄可行域松弛策略。进一步考虑轻量化、低能耗和薄膜表面高精度的要求，研究面向空间展开与无皱设计的薄膜-支撑双材料拓扑优化理论模型和高效kriging代理模型优化算法，开展了典型空间薄膜结构的优化设计、数值仿真和地面实验验证。并首次揭示了初始缺陷不确定性对薄膜褶皱行为的影响机理。此外，本项目还原创性提出材料场级数展开拓扑优化降维新方法和复杂问题非梯度拓扑优化通用方案。在本项目资助下，课题组在本领域国内外权威期刊上共发表与本项目研究内容相关的高水平学术论文20篇（已标注），包括封面论文2篇，中科院一区论文6篇，中科院二区论文11篇。获批软件著作权1项，授权发明专利3项，其中PCT国际专利2项。以第二完成人获2020年度高等学校科学研究优秀成果奖（科学技术）自然科学一等奖，入选辽宁省“兴辽英才计划”青年拔尖人才。培养毕业博士2人，1人获大连理工大学优秀博士学位论文。