基于材料-设计-制造融合的多相材料结构轻质化拓扑优化方法研究

The coupled effect between different scales is not considered in the traditional optimization methods with single scale and the corresponding optimal solution is difficult to be manufactured. In order to improve the static and dynamic characteristics and multiphyscial functions of engineering structures, the integrated topology optimization model of materials and structures with the static and dynamic characteristic constraints and manufacturing constraints is built by the research on the characterization method of the manufacturing constraint model based on the topology skeleton and the characterization model of material interface based on the restraint layer theory. The integrated optimization is executed by the feasible domain adjustment based topology optimization method, including projection, mergence and condensation of design variables, the low-pass, high-pass and band-pass filter methods and a adjoint variable method for the sensitivity analysis. Therefore the easy-to-manufactruing optimization solutions are obtained through above methods. An new platform is provided from viewpoint of the theory and method for the integrated optimization of design and manufacturing. The corresponding feasible engineering technical support and storage is supplied for the integrated design of multifunctional and multicharacteristic material and structure. The innovations lie in: (1) the characterization method is put forwarded for the manufacturing constraints based on the topology skeleton and the influence mechanism and law of the manufacturing constraints and material interfaces on the optimal solutions are discussed; (2) the feasible domain adjustment based topology optimization method is proposed so as to build the cross-scale lightweight optimization theory is developed for the design of structures with multi-phase materials considering the coupled effect of material, design and manufacturing.

鉴于传统拓扑优化方法获得的宏微观结构可制造性差且没考虑宏微观尺度间的耦合效应等缺点，为了提高工程结构在极端环境下的静动力学性能和多物理场功能，拟基于拓扑图形骨架的增材制造工艺约束和基于拘束层理论的材料界面数学模型表征方法研究，建立含制造约束和力学特性约束等多约束的宏微结构构型与材料分布的跨尺度拓扑优化模型，采用基于可行域调整的拓扑优化方法进行优化，包括设计变量映射、归并与缩减，低通、高通和带通过滤方法和灵敏度分析的伴随变量法，最终获得可制造的优化结果，从而在理论与方法上为设计-制造的协同优化建立集成平台，为多功能和性能材料结构一体化设计提供切实可行的工程优化技术支持和储备。本研究创新点在于：1.提出基于拓扑图形骨架的制造约束的数学模型表征方法，探究其与材料界面对优化解的影响机理和规律；2.提出基于可行域调整的拓扑优化方法，系统建立“材料-设计-制造”融合的多相材料结构跨尺度轻量化优化理论。

鉴于传统拓扑优化方法获得的宏微观结构可制造性差且没考虑宏微观尺度间的耦合效应等缺点，为了提高工程结构在极端环境下的静动力学性能和多物理场功能，以发展面向“材料-设计-制造”融合的复杂整体结构的高性能轻量化为研究背景，建立了基于图形拓扑骨架和结构物理场特征的增材制造工艺约束的数学模型表征方法以及多相材料界面模型的表征方法，发展了多尺度灵敏度分析方法及高效稳健的大规模拓扑变量拓扑优化算法，综合解决了涉及多相材料界面影响、温度变化影响、增材制造工艺约束和静动力特性等多约束的材料与结构一体化轻量化优化求解问题，发展了非线性结构强度拓扑优化设计方法和变刚度纤维增强复合结构优化设计方法，形成了具有良好结构功能和承载性能的材料与结构一体化拓扑优化新算法和自动化设计流程。