时域动载荷作用下多微结构多尺度并行动力学拓扑优化

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摘要采用拓扑优化方法对含多种多孔材料的结构进行结构与材料微结构构型一体化设计，可以获得具有优良力学性能的结构设计。本文面向多晶胞双尺度结构的时域动刚度最优设计问题，考虑不同晶胞间的可连接性，并行设计微结构的构型及其宏观布局。首先，引入双Helmholtz平滑-分块投影方案，识别不同多孔材料的宏观结构域。其次，通过均匀化方法计算多孔材料的宏观等效力学性能，利用有序SIMP方法优化不同微观结构的宏观布局。同时，为了保证不同晶胞间的可连接性，在不同多孔材料微结构的边界区域设置为相同拓扑描述的可设计连接域。然后，基于先离散-后微分的伴随敏度分析方法，实现了时空离散动力系统的一致性敏度计算。最后，以双尺度结构动柔度最小化为目标，以材料用量为约束条件，提出了时域动载荷作用下多微结构多尺度并行动力学拓扑优化方法。数值算例结果表明，提出的优化方法能够实现多晶胞结构的构型与宏观布局设计，充分提高了多孔结构的承载性能，同时保证不同晶胞之间的几何连续性，研究结果可为高承载多孔材料结构设计提供理论参考。

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	江旭东1
	吴昊1
	滕晓艳2
	熊冶平3

关键词 ：多尺度并行拓扑优化, 多晶胞结构, 瞬态动力学, 微结构连接性, 数值均匀化

Abstract：Topology optimization is an effective tool to perform the structure-material integrated design of a lattice structure with multiple microstructures for improving its mechanical performances. This paper aims to propose the concurrent design method for the lattice structure at both macro- and micro-scales considering the connectivity between neighboring microstructures for the dynamic stiffness maximization problem. Firstly, the double Helmholtz smoothing and piecewise projection scheme is introduced to identify the spatial distribution of multiple microstructure blocks at macroscale. Then, we optimize the spatial distribution of various microstructures by ordered SIMP method following the effective mechanical properties obtained by homogenization method. Meanwhile, the different microstructural unit cells share the same topology description within their boundary regions to ensure the connectivity. Subsequently, we implement the sensitivity analysis by adjoint variable method based on the “discretize-then-differentiate” approach, such that the consistent sensitivities are obtained on the space-time discretized system. Finally, we formulate the dynamic compliance minimization problem under the constraint of material volume fractions, and present the multiscale concurrent topology optimization method for structures periodically filled with multiple microstructures. Numerical examples demonstrate that this approach has the potential to perform the concurrent microscopic design of multiple unit-cells and their macroscopic layout for improving the load-carrying capacity and ensuring the geometrical connectivity between neighboring unit-cells. This method offers a theoretical reference for design of highly loading porous structures.

Key words： multi-scale concurrent topology optimization multiple cellular structure transient dynamics connectable microstructures numerical homogenization

收稿日期: 2023-06-26 出版日期: 2024-06-28

引用本文:

江旭东1，吴昊1，滕晓艳2，熊冶平3. 时域动载荷作用下多微结构多尺度并行动力学拓扑优化[J]. 振动与冲击, 2024, 43(12): 53-64.
JIANG Xudong1，WU Hao1，TENG Xiaoyan2，XIONG Yeping3. Multiscale concurrent topology optimization for cellular structures with multiple microstructures subjected to dynamic load. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(12): 53-64.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I12/53

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