泡沫铝填充薄壁金属圆管吸能特性的预测及优化方法

doi:10.12382/bgxb.2023.0366

摘要/Abstract

摘要：

为提高泡沫铝填充薄壁金属圆管的吸能特性并进行高效率结构设计,基于均匀拉丁超立方试验设计方法和径向基函数神经网络,构建轴向冲击下泡沫铝填充铝管吸能特性的近似模型,并将近似模型嵌入遗传算法中实现构件的结构优化。研究结果表明:基于径向基函数神经网络构建的近似模型的拟合优度大于0.99、均方根误差小于0.08,且近似模型的计算耗时仅为数值计算的0.56%;近似模型在保证较高精度的同时可大幅提高计算效率;对泡沫铝填充铝管的结构优化发现,通过增大圆管半径和壁厚、减小高度可使泡沫铝填充铝管的平均压缩力最大化,反之,可使泡沫铝填充铝管的峰值压缩力最小化;基于遗传算法的多目标优化显著提高了泡沫铝填充铝管的吸能特性;该研究成果可为泡沫铝填充薄壁金属圆管的快速设计和优化提供参考。

关键词: 泡沫铝, 吸能特性, 径向基函数神经网络, 近似模型, 结构优化

Abstract:

In order to improve the energy absorption characteristics of aluminum foam-filled thin-walled metal circular tube and realize high-efficiency structural design, an approximate model of the energy absorption characteristics of aluminum foam-filled aluminum tube under axial impact is established based on the uniform Latin hypercube design method and radial basis neural network, and it is embedded into the genetic algorithm to realize the structural optimization of components. The results show that the goodness of fit of the approximate model based on the radial basis neural network is greater than 0.99, the root mean square error is less than 0.08, and the calculation time of the approximate model is only 0.56% of the numerical calculation. The approximate model can greatly improve the calculation efficiency while ensuring higher accuracy. Through the optimization of the structure of aluminum foam-filled aluminum tube, it is found that the average compression force of aluminum foam-filled aluminum tube can be maximized by increasing the radius and wall thickness of the circular tube and reducing the height, and on the contrary, its peak compression force can be minimized. The multi-objective optimization based on the genetic algorithm significantly improves the energy absorption characteristics of aluminum foam-filled aluminum tube. The research results can provide a reference for the rapid design and optimization of aluminum foam-filled thin-walled metal circular tube.

Key words: aluminum foam, energy absorption characteristics, radial basis function neural network, approximate model, structure optimization

中图分类号:

U270.1

严松, 姜毅, 邓月光, 文享华. 泡沫铝填充薄壁金属圆管吸能特性的预测及优化方法[J]. 兵工学报, 2024, 45(6): 1954-1964.

YAN Song, JIANG Yi, DENG Yueguang, WEN Xianghua. Prediction and Optimization Method of Energy Absorption Characteristics of Thin-walled Metal Circular Pipe Filled with Aluminum Foam[J]. Acta Armamentarii, 2024, 45(6): 1954-1964.

图/表 21

图1 近似模型构造及预测框架

Fig.1 Construction of approximate model and prediction framework

图2 泡沫铝填充铝管的有限元模型

Fig.2 Finite element model of aluminum foam-filled aluminum tube

表1 各部件的材料参数

Table 1 Material parameters of each component

部件	密度/(kg·m^-3)	弹性模量/MPa	泊松比
铝管	2700	68200	0.33
泡沫铝	330	80	0.01
上、下压块	7800	210000	0.30

图3 铝合金的应力-应变曲线[27]

Fig.3 Stress-strain curve of aluminum alloy[27]

图4 泡沫铝的应力-应变曲线[27]

Fig.4 Stress-strain curve of aluminum foam[27]

图5 有限元计算结果与试验结果对比

Fig.5 Comparison between finite element calculation results and experimental results

图6 准静态压缩结果对比

Fig.6 Comparison of quasi-static compression results

图7 轴向冲击结果对比

Fig.7 Comparison of axial impact results

图8 RBF神经网络的结构

Fig.8 Framework of RBF neural network

表2 3个参数的取值范围

Table 2 Value ranges of three parametersmm

输入参数	取值下限	取值上限
r	10	30
T	1	5
H	20	100

图9 试验设计点分布

Fig.9 Design points distribution

图10 峰值压缩力近似模型误差分析

Fig.10 Error analysis of approximate model for peak compressive force

图11 平均压缩力近似模型误差分析

Fig.11 Error analysis of approximate model for average compressive force

图12 最大压缩距离近似模型误差分析

Fig.12 Error analysis of approximate model for maximum compressive distance

表3 近似模型误差分析

Table 3 Error analysis of approximate model

输出参数			E_MA	R²
F_max	0.0442	0.0061	0.1465	0.9980
F_m	0.0705	0.0011	0.2098	0.9949
d	0.0735	0.0346	0.3275	0.9945

表4 近似模型与有限元计算的效率对比

Table 4 Calculation efficiency comparison of approximate model and finite element min

近似模型	有限元计算
0.5	90

图13 遗传算法流程图

Fig.13 Flowchart of genetic algorithm

表5 泡沫铝填充铝管的单目标最优解

Table 5 Single-objective optimal solutions ofaluminum foam-filled aluminum tube

目标函数	r/mm	T/mm	H/mm	F_m/kN	F_max/kN
minF_m	10	1	100	9.952	13.550
maxF_max	30	5	20	169.749	186.806

图14 多目标最优解集和有限元计算结果对比

Fig.14 Comparison between multi-objective optimal solution set and finite element calculation results

表6 10组数据样本及对应的有限元解

Table 6 10 groups ofdata samples and corresponding finite element solutions

编号	r/mm	T/mm	H/mm	F_m/kN	F_max/kN	CFE/%
1	16.08	1.32	72.16	17.667	27.226	64.89
2	25.13	1.42	43.90	29.128	46.802	62.23
3	17.79	2.47	35.66	42.477	60.033	70.71
4	23.75	2.51	46.41	58.624	79.274	73.95
5	19.84	3.51	83.42	86.253	95.173	90.63
6	29.83	2.95	78.31	103.753	115.622	89.73
7	21.97	4.30	89.76	113.283	128.900	87.88
8	23.48	4.68	79.79	130.093	149.039	87.29
9	25.72	4.89	72.78	149.259	170.360	87.61
10	27.98	4.92	85.68	157.298	180.722	87.03

图15 优化前与优化后的压缩力效率对比

Fig.15 Comparison of compression force efficiencies before and after optimization

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