数据驱动的曲面构件形状⁃拓扑协同优化方法

doi:10.7527/S1000-6893.2023.28806

Abstract

Abstract:

Due to the extreme lightweight requirements of surface components in compact design space， this paper proposed a data-driven shape-topology optimization method of curved shells， which consists of three stages， namely the offline stage， the online stage and the update stage. First， in the offline stage， the Latin hypercube sampling method is used to extract the sample points from the design space， and the mesh deformation technique is used for modeling to obtain the mesh model corresponding to the sample points. Then， topology optimization was carried out on the mesh models to obtain the optimized strain energy. Based on the sample data obtained in the above steps， the radial basis function surrogate model is trained， where the shape design variable is the input and the strain energy after topology optimization is the output. In the online stage， optimization is carried out based on the surrogate model obtained in the offline stage， and the covariance matrix adaptive evolution strategy is adopted to improve the optimization efficiency. In the update stage， the real response of optimization results of the surrogate model is calculated and added to the sample dataset to update the surrogate model. Finally， the algorithm is verified by a simply supported beam and a spacecraft cabin door. The results show that compared with the topology optimization with the fixed shape， the strain energy obtained by the proposed method can be reduced by 20.08% and 37.93%， respectively， indicating that the proposed method has better design capability.

Key words: shape-topology optimization, mesh deformation, data driven, curved shell, radial basis function

CLC Number:

V214.4

Tianhe GAO, Kuo TIAN, Lei HUANG, Shu ZHANG, Zengcong LI. Data⁃driven shape⁃topology optimization method for curved shells[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(2): 428806.

Figures/Tables 15

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设计点	R²	RRMSE	a/mm	b/mm	质量/g	应变能/mJ
设计上限			15	5	1.4	0.020 7
设计下限			-15	-5	1.4	0.056 6
初始设计（仅拓扑优化）			0	0	1.4	0.024 9
形状⁃拓扑协同优化设计Ⅰ （15 代理模型样本+5 优化加点）	0.956 5	0.201 5	-7.838 6	1.610 1	1.4	0.019 9
形状-拓扑协同优化设计Ⅱ （19 代理模型样本+1 精细校核）	0.995 0	0.068 7	-5.891 5	1.610 1	1.4	0.020 7
形状-拓扑协同优化设计Ⅲ （无代理模型，20 CMA-ES迭代点）			11.533 6	1.707 7	1.4	0.024 3
形状-拓扑协同优化设计Ⅳ （15 代理模型FF样本+5 优化加点）	0.984 3	0.120 9	-12.226 9	1.610 1	1.4	0.019 6
形状-拓扑协同优化设计Ⅴ （无代理模型，100 CMA-ES迭代点）			5.634 1	1.796 8	1.4	0.021 7

结构	密度/（g·cm^-3）	弹性模量/GPa	泊松比
门体	1.780	42.2	0.3
门框	2.640	68.0	0.3

设计点	R²	RRMSE	c/mm	n	应变能/mJ
设计上限			100	3.000 0	15 040.0
设计下限			60	1.000 0	14 038.0
初始设计（仅拓扑优化）			80	2.000 0	11 983.0
形状⁃拓扑协同优化设计I （30 代理模型样本+15 优化加点）	0.931 0	0.674 3	100	1.465 4	7 437.4
形状-拓扑协同优化设计II （44 代理模型样本+1 精细校核）	0.937 8	0.774 7	100	1.381 2	7 519.4
形状-拓扑协同优化设计III （无代理模型，45 CMA-ES迭代点）			100	1.314 4	7 818.2

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Data⁃driven shape⁃topology optimization method for curved shells

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