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| 考虑微结构连接性的双尺度结构自然频率拓扑优化 |
| Integrated topology optimization of structures and lattice material microstructures to maximize structural fundamental frequency considering the connectivity between lattice materials |
| 投稿时间：2022-05-20 修订日期：2022-06-07 |
| DOI： |
| 中文关键词: 拓扑优化 数值均匀化 自然频率 微结构设计 结构与材料一体化设计 |
| 英文关键词:opology optimization numerical homogenization natural frequency microstructure optimization integrated topology optimization of structure and microstructures |
| 基金项目:国家自然科学基金项目（11902064）和中国航发集团自主创新专项资金项目（ZZCX-2021-025）资助. |
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| 中文摘要: |
| 多孔材料因具有轻量化、高孔隙率、减振/散热等优良多物理特性，在航空航天等领域具有广阔应用前景。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，有助于获得具有优良力学性能的结构设计。然而，传统逆均匀化微结构设计方法无法确保不同多孔材料微结构之间的连接性，设计结果不具备可制造性。本文面向含多种多孔材料的双尺度结构基频最大化设计问题，考虑不同微结构之间的连接性，协同设计多孔材料的微结构构型及其在宏观尺度下的布局。采用均匀化方法计算多孔材料的宏观等效力学性能，通过对不同多孔材料微结构单胞的边界区域采用相同的拓扑描述确保双尺度优化过程中任意空间排布下不同微结构的连接性，并通过优化算法确定微结构间的连接形式及微结构拓扑。在宏观尺度，提出结合离散材料插值模型和RAMP插值模型（Rational Approximation of Material Properties, RAMP）的多孔材料各向异性宏观等效刚度及质量插值模型，获得清晰的多孔材料宏观尺度布局并减轻优化过程中伪振动模态的影响。建立以双尺度结构基频最大化为目标，以材料用量为约束的优化列式，推导灵敏度表达式，并基于梯度优化算法求解双尺度结构拓扑优化问题。数值算例表明，采用多种多孔材料的双尺度结构设计的振动基频优于采用单一多孔材料的结构设计，并且本文所提优化方法能够有效确保不同多孔材料微结构之间的连接性，增强优化设计结果的可制造性。 |
| 英文摘要: |
| Lattice materials have broad application prospects in aerospace and other fields due to their excellent properties such as light weight, high porosity, and vibration reduction/heat dissipation. Considering a structure composed of several lattice materials, the integrated design of the structural and material microstructural configuration with topology optimization is helpful to obtain structure designs with excellent mechanical properties. However, the conventional inverse-homogenization-based microstructure design cannot ensure the connectivity between the microstructures of different lattice materials, and the design results are not manufacturable. This paper focuses on the fundamental frequency maximization design problem of two-scale structures composed of multiple lattice materials, considers the connectivity between different microstructures, and synergistically design the microstructure configuration of lattice materials and their layout at the macroscale. The homogenization method is used to calculate the macroscopic equivalent mechanical properties of the lattice materials, and the same topology description is used for the boundary regions of the microstructure unit cells of different lattice materials to ensure the connectivity with any spatial arrangement in the two-scale optimization process. The form of connections between the microstructures is determined by the optimization algorithm. At the macroscopic scale, an anisotropic macroscopic equivalent performance interpolation model of lattice materials combining discrete material interpolation model and RAMP interpolation model (Rational Approximation of Material Properties, RAMP) is proposed to obtain a clear macroscale layout of lattice materials and reduce the effects of spurious vibration modes in the optimization process. The optimization formulation with the objective of maximizing the fundamental frequency of the two-scale structure and the material consumption as the constraint is established, and the sensitivity expression is derived. The topology optimization problem of the two-scale structure is solved using the gradient-based algorithm. Numerical examples show that the vibration fundamental frequency of the two-scale structure design using multiple lattice materials is better than that of the structure design using a single lattice material, and the optimization method proposed in this paper can effectively ensure the connectivity between the microstructures of different lattice materials and enhance the manufacturability of the optimized designs. |
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