轻质热弹性点阵材料/结构尺度关联的并发多尺度优化设计研究

It is one of the most important issues of light weight design for the thermal protection structure of high speed vehicles. It is one of the most important possible solutions for the design task with the concurrent optimization technique of ultra-light lattice materials and structures. However, the existed studies mostly are carried out based on the assumption of separation of sizes of lattice materials and structures, which means it is a high order infinitesimal for the size of a representative volume element of the lattice material compared with the size of the macro structure. It is still not enough for the research work with size-related effects, which is more applied oriented and theoretically challenged. And the structural compliance which is an evaluation of the mean structural stiffness is the only focus of most of the existed research work..It is relatively rare observations for the study of singularity caused possibly by the strength and local buckling constraints, which is related with topology designs. Based on the above background, the present project aims at the light weight design of the lattice material used for the load bearing structure of the vehicle with thermal and mechanical loading conditions. And a new multi-scale FE model and a corresponding sensitivity analysis will be developed to analyze the thermal deformation and stress of the lattice structure. And the size effect of the microstructure of lattice materials is researched for its influence on the deformation and stress. A concurrent multi-scale optimization model which can consider the size-related effect will be developed to optimize the configuration of material microstructure of the lattice material and its distribution in the structural design domain. The numerical technique will be established to effectively cope with the singular difficulty in concurrent multi-scale optimization issues through the regularity of the design space. The multi-scale optimization design will be deepened and extended in this project. And this project will also provide scientific and technical base for the light weight design of thermal elastic structures of aircraft with high speed.

新一代高速飞行器研制必须解决能够有效实现热防护的轻量化结构设计问题。采用轻质点阵材料并与结构进行一体化并发设计是解决上述问题的一个重要途径。以往相关工作大都是在尺度可分离（即点阵材料代表体元尺寸相比结构宏观尺寸为高阶无限小）的假设下开展的，而对于更有应用背景和理论难度的尺度关联问题关注不够。另外，已有工作大多仅考虑了结构柔顺性等整体响应，有关包含强度、局部稳定性等可能导致奇异最优解的拓扑相关约束的并发设计问题研究还相对空白。基于上述背景，本项目将致力于建立考虑微结构尺寸效应以及热力共同作用的多尺度并发拓扑优化模型；基于多尺度有限元框架发展高效的多尺度结构响应和灵敏度分析方法；通过对设计空间实施正则化处理，研究能够有效处理奇异性并发优化设计问题的数值技术。本项目工作是对多尺度优化设计研究的深化和拓展，同时亦可为高速飞行器轻质热防护结构设计提供科学基础，具有重要意义。

航空航天结构的轻量化是提高相关运载装备性能的关键技术途径，而随着运载装备飞行速度的不断提高，气动热环境给运载装备的轻量化设计提出了苛刻的挑战。具有微观周期性结构特征的轻质点阵材料成为新一代高速飞行的运载装备结构最具潜力的承载材料。本项目针对机械力/热载荷联合作用下的热弹性结构，发展适应复杂结构构型、边界/载荷条件下的点阵结构宏观均匀化、细观局部化的精细化多尺度建模和分析理论，进而研究宏观结构与材料微结构尺寸关联条件下，微结构尺寸效应对热变形和热应力等结构性能的影响规律。基于扩展多尺度有限元方法(EMsFEM)和可移动变形组件法(MMC)开展了热弹性结构优化设计的研究。主要研究内容包括：1. 选择宏微观两尺度独立的设计变量，建立考虑微结构尺寸效应以及热力耦合的多尺度并发拓扑优化模型，深入研究对比热柔顺性和应变能两种目标函数对点阵结构优化结果的影响规律，基于多尺度有限元框架，发展高效的多尺度结构灵敏度分析方法；2. 在上述多尺度分析理论和方法的基础上，考虑热弹性点阵材料微结构的尺寸关联效应，实现了由多种材料构成的热弹性复合点阵结构多尺度优化；3. 针对特定载荷与约束作用下轻质热弹性点阵材料受力状态不同的特点，引入人工智能机器学习领域聚类方法，实现基于微观结构应变能的高效分组的多尺度团簇优化设计，突破了经典多尺度优化PAMP方法均一点阵微结构的假设，提高了结构/材料的利用效率；4. 针对高承载零膨胀点阵材料优化设计问题，通过综合运用拓扑优化和形状优化技术，设计多相材料及截面尺寸在离散基结构中的分布，获得了超高比刚度零膨胀点阵材料的微观结构形式；5. 采用可移动变形组件法（MMC）对热弹性结构的拓扑优化问题及散热结构的拓扑优化问题进行了研究，并分别讨论了不同目标函数的物理意义及适用范围，结果发现可移动变形组件法能够有效改善结构拓扑边界不清晰的优化难题。发表SCI检索论文10篇，获2019年度国家自然科学二等奖。