具有吸波和承载功能的多场耦合结构与周期微材料协同优化方法研究

The coupled and collaborative effect between different scales is not considered in traditional optimizations with single scale, i.e., either macrostructure optimization or microstructure material optimization. The functional optimization to absorb electromagnetic wave and that to bear mechanical load are independently implemented in traditional case. In order to improve the monolithic functions of structure-type absorbing material, multiple averaging method and two-scale asymptotic expansion method are used to predict stiffness, dynamic characteristics, permittivity and permeability of macrostructure with periodic microstructure material, to describe the corresponding scale effect and coupled relationship. The collaborative optimization model with dual functions is bulit. The collaborative optimization is executed by global coordination and hierarchical optimization strategies. To reduce computational works, the design variables are constructed on basis of variable density function method where their exponents are determined by statistical analysis, domain decomposition method and linking-grouping method, and an analytical adjoint variable method is used for sensitivity analysis. Then the robust optimization solutions are obtained through above methods.The innovations of the project lie in: (1) the innovation design method is put forward to optimize the topology configuration of material microstructure so as to achieve some specified electromagnetic performances; (2) the collaborative optimization theory with multiscale and coupled multi-field is developed for the design of microstructure material and macrostructure to absorb electromagnetic wave and bear mechanical load. An new platform of collaborative optimization is provided for the prestudy of structure-type absorbing material. The feasible engineering technique is supplied for the integrated design of multifunctional material and structure.

鉴于传统宏微观结构单尺度优化没有考虑尺度间的耦合协同效应而且吸波和承载功能优化均是独立实施等缺点，为了提高结构型吸波材料吸波和承载整体性能，拟基于多重平均化法和双尺度渐进展开法对周期微材料结构宏观刚度、动力特性、介电常数和磁导率等性能的预测、尺度效应和耦合关系数学描述方法研究，建立其合理的协同优化模型，采用全局协调和分层优化策略进行协同优化，其中通过设计变量变密度函数法与指数统计分析法、区域分解法与关联分组法以及灵敏度分析的伴随变量法以减少优化计算量，最终获得鲁棒的优化结果。本研究创新点在于：1. 提出特定电磁性能的材料微结构拓扑构型创新设计方法；2. 发展具有承载和吸波功能的多尺度多场耦合微材料/结构协同优化理论。从而其在理论与方法上为结构型吸波材料预研提供新的协同优化集成平台，为多功能材料与结构一体化设计提供切实可行的工程技术支持和技术储备。

传统结构与材料的两尺度设计（结构设计和材料设计）是独立实施进行的，并没有充分考虑到其相互耦合产生的协同效应，为了提升结构的静动力学性能以及特定的物理功能，本研究基于均匀化理论，结合各向同性材料插值模型，根据势能和动能相等原则，建立了周期性微结构材料单胞的等效弹性模量和质量密度，进一步推导了宏观结构刚度矩阵和质量矩阵分别与单胞弹性模量和质量密度的关系式；分析了宏观结构静力学（宏观刚度，柔顺度）和动力学特性（固有频率，动力可靠性以及动荷载下的响应）以及电磁性能随周期微结构几何参数和物理参数的变化关系，并通过构建微观和宏观层次广义设计变量，利用伴随变量法进行了力学特性的灵敏度分析，形成了多物理场下超轻材料微结构和宏观构型创新优化设计并行的协同优化方法，为多功能材料/结构一体化优化设计提供切实可行的工程技术支持和技术储备。本研究创新点在于：（1）研究了宏微观不同层次的多尺度（跨尺度）建模及协同优化算法（2）研究了多场耦合（多功能）建模及协同优化算法（3）研究了加工制造约束下连续体结构的宏观拓扑优化算法（4）对功能性材料的吸波性能进行了深入分析研究。