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Integrated topology optimization of structures and lattice material microstructures to maximize structural fundamental frequency considering the connectivity between lattice materials |
Received:May 20, 2022 Revised:September 30, 2022 |
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DOI:10.7511/jslx20220520001 |
KeyWord:topology optimization numerical homogenization natural frequency microstructure optimization integrated topology optimization of structure and microstructures |
Author | Institution |
罗潇 |
中国航发湖南动力机械研究所, 株洲 |
刘湃 |
大连理工大学 工业装备结构分析优化与CAE软件全国重点实验室, 大连 |
曾雨琪 |
中国航发湖南动力机械研究所, 株洲 |
李坚 |
中国航发湖南动力机械研究所, 株洲 |
徐友良 |
中国航发湖南动力机械研究所, 株洲 |
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Abstract: |
Lattice materials have broad application prospects in aerospace engineering 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 a gradient-based algorithm.Numerical examples show that the optimization method proposed in this paper can effectively ensure the connectivity between the microstructures of different lattice materials in the optimized two-scale structural designs and enhance the manufacturability of the optimized designs. |
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