负高斯曲率曲面薄壁管吸能特性研究

马梓鸿; 张慧乐; 孙泽玉; 陈慧敏; 岳晓丽

doi:10.11883/bzycj-2022-0146

负高斯曲率曲面薄壁管吸能特性研究

doi: 10.11883/bzycj-2022-0146

马梓鸿^1,,
张慧乐^{2, 3},
孙泽玉²,
陈慧敏¹,
岳晓丽^1, ,

1.
东华大学机械工程学院，上海 201620
2.
东华大学上海市轻质结构复合材料重点实验室，上海, 201620
3.
电子科技大学长三角研究院（湖州），浙江湖州 313000

基金项目: 上海市轻质结构复合材料重点实验室开放课题 (2232021A4-06)

详细信息

作者简介:
马梓鸿（1998－　），男，硕士研究生，jeffreymzh@foxmail.com

通讯作者:
岳晓丽（1968－　），女，博士，教授，xlyue@dhu.edu.cn

中图分类号: O347；TB331
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- 文章访问数: 779
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- 被引次数: 0
出版历程
- 收稿日期: 2022-04-07
- 修回日期: 2022-06-17
- 网络出版日期: 2022-07-07
- 刊出日期: 2022-11-18

Study on energy absorption characteristics of thin-walled tubes with negative Gaussian curvature

MA Zihong^1
,,
ZHANG Huile^{2, 3},
SUN Zeyu²,
CHEN Huimin¹,
YUE Xiaoli^{1
, ,}

1.
School of Mechanical Engineering, Donghua University, Shanghai 201620, China
2.
Shanghai Key Laboratory of lightweight structural composites, Donghua University, Shanghai 201620, China
3.
Yangtze Delta Research Institute, University of Electronic Science and Technology of China, Huzhou 313000, Zhejiang, China

摘要

摘要: 为设计出具备优良吸能特性的薄壁结构，提出一种新型负高斯曲率曲面圆形横截面薄壁管(negative Gaussian curvature surface circular tube, NGC-C)。利用经验证的有限元分析方法对其进行轴向动态冲击模拟，提取各项性能指标，借助复杂比例评估法(complex proportion assessment, COPRAS)将其与传统薄壁吸能结构进行了综合性能对比。采用拉丁超立方抽样法从设计空间中提取样本点并获取各样本点对应性能响应值，建立代理模型。基于该代理模型，借助改进非支配排序遗传算法(non-dominated sorting genetic algorithm, NSGA-Ⅱ)对其进行了多目标优化设计。结果表明：NGC-C综合性能优于传统薄壁吸能结构，经优化后比吸能提高了16.47%，有效压溃长度降低了12.40%，质量减少了20.18%。将负高斯曲率曲面形态引入薄壁管构型，能够提高薄壁管的耐撞性和轴向抗变形能力。
- 薄壁结构 /
- 负高斯曲率曲面 /
- 吸能特性 /
- COPRAS /
- NSGA-Ⅱ
Abstract: In order to design a lightweight thin-walled structure with high specific energy absorption and high stiffness, a new type of circular cross-section thin-walled tube with negative Gaussian curvature (negative Gaussian curvature surface circular tube, NGC-C) is proposed and studied in this paper. The finite element analysis method verified by previous experimental data is used to simulate the axial dynamic impact, and various performance indexes such as specific energy absorption and effective crushing length are extracted. The comprehensive performance of the thin wall energy absorption structure with zero Gaussian curvature and positive Gaussian curvature is compared with the complex proportional assessment method (complex proportion assessment, COPRAS). The Latin hypercube sampling method is used to extract 20 sample points from the design space and obtain the corresponding performance response values of each sample point, and the polynomial fitting method is used to establish the proxy model. Based on the agent model, the multi-objective optimization design is carried out by using the improved non dominated sorting genetic algorithm (non-dominated sorting genetic algorithm, NSGA-Ⅱ). The results show that the comprehensive performance of the thin-walled circular tube with negative Gaussian curvature is better than that of all kinds of non-negative Gaussian curvature thin-walled energy absorbing structures, especially in that it has the minimum effective crushing length. The goodness of fit of the established proxy models is higher than 98%, which can better reflect the relationship between structural design variables and performance response. After optimization, the specific energy absorption of thin-walled circular tubes with negative Gaussian curvature is increased by 16.47 %, the effective crushing length is reduced by 12.4 %, and the mass is reduced by 20.18 %. To sum up: introducing the negative Gaussian curvature surface shape into the thin-walled tube configuration can reduce the structural quality and improve the crashworthiness of the thin-walled tube, provide a new idea for the design of the thin-walled energy absorbing structure, and can be applied to the energy absorbing scenarios such as the automobile energy absorbing box.
- thin-walled structure /
- negative Gaussian curvature surface /
- energy absorption /
- COPRAS /
- NSGA-Ⅱ

HTML全文

图 1 有限元模型以及网格选择

Figure 1. Finite element model and element size selection

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图 2 能量变化情况

Figure 2. Energy change

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图 3 薄壁管变形模式的实验与模拟对比情况

Figure 3. Comparison of experiment and simulation of four kinds of thin-walled tube deformation modes

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图 4 S-1模型实验与数值模拟变形模式对比

Figure 4. Comparison of experiment and simulation deformation modes of S-1 model

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图 5 S-1模型实验与数值模拟力-位移曲线对比

Figure 5. Comparison of force-displacement curves between experiment and simulation of S-1 model

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图 6 冲击过程中力-位移曲线

Figure 6. Force-displacement curve during impact

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图 7 NGC-S剖切面示意图

Figure 7. Schematic diagram of section plane of NGC-S

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图 8 触发结构

Figure 8. Trigger structure

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图 9 变形模式对比

Figure 9. Comparison of deformation modes

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图 10 3类高斯曲率情况下的模型力位移曲线

Figure 10. Force-displacement curves of model under three kinds of Gaussian curvature

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图 11 3类高斯曲率情况下的模型性能指标比较

Figure 11. Comparison of model performance indexes under three kinds of Gaussian curvature

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图 12 COPRAS法流程图

Figure 12. Process flow chart of COPRAS method

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图 13 各组优选模型结果比较

Figure 13. Comparison of optimal model results of each group

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图 14 NGC-C与ZGC-O结构的应变情况

Figure 14. Strain of NGC-C and ZGC-O structure

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图 15 Pareto解集

Figure 15. Pareto solution set

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表 1 材料参数

Table 1. Material parameters

材料	杨氏模量/GPa	泊松比	屈服强度/MPa
A6060-T5	69.5	0.33	264

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表 2 有限元验证模型尺寸参数^[16]

Table 2. Finite element verification model size parameters^[16]

模型	长度/mm	直径/mm	厚度/mm	撞击初速度/(m·s⁻¹)	冲击墙质量/kg
S-1	180	40	1.0	4.3	104.5
S-3	180	40	2.0	5.9	104.5
S-5	180	40	2.5	6.6	104.5
S-6	180	50	3.0	10.7	91.0

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表 3 实验与数值模拟结果对比

Table 3. Comparison of experimental and simulation numerical results

模型	总吸能/J			平均压溃力/kN
模型	实验	数值模拟	误差/%	实验	数值模拟	误差/%
S-1	998	958	4.18	13.03	12.39	5.17
S-3	1 858	1 835	1.25	46.40	45.79	1.33
S-5	2260	2197	2.88	42.30	41.02	3.12
S-6	5081	4996	1.70	86.00	84.03	2.34

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表 4 指标$\delta、l、{F_0}、\eta $ 的权衡赋分过程及其权重因子$w_j $

Table 4. Weighing and scoring process of four indicators ($\delta,{\text{ }}l,{\text{ }}{F_0},{\text{ }}\eta $) and their weighting factors ($w_j $)

指标	$\delta - l$	$\delta - {F_{\text{0}}}$	$\delta - \eta $	$l - {F_{\text{0}}}$	$l - \eta $	${F_{\text{0}}} - \eta $	${w_j}$
$\delta $	2	3	3				0.333
$l$	2			3	3		0.333
F₀		1		1		1	0.126
$\eta $			1		1	3	0.208

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表 5 各结构COPRAS法相关计算值

Table 5. Relevant calculated values of COPRAS method for each structure

结构	$S + $	$S - $	${Q_i}$	${U_i}$	排名
NGC-S	0.020	0.034	0.237	90.54	11
NGC-H	0.021	0.031	0.243	92.76	6
NGC-O	0.020	0.035	0.238	90.96	9
NGC-C	0.034	0.031	0.262	100.00	1
PGC-S	0.041	0.034	0.242	92.37	7
PGC-H	0.043	0.047	0.258	98.46	3
PGC-O	0.039	0.060	0.234	89.37	12
PGC-C	0.042	0.052	0.249	95.26	4
ZGC-S	0.040	0.056	0.239	91.39	8
ZGC-H	0.050	0.039	0.237	90.69	10
ZGC-O	0.054	0.053	0.262	99.98	2
ZGC-C	0.060	0.063	0.247	94.39	5

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表 6 样本点及其响应

Table 6. Sample points and responses

样本点	T/mm	G/mm	R/mm	δ/(J·g⁻¹)	l/mm
1	2.31	−0.55	80.77	19.12	77.4
2	4.92	1.25	96.63	8.03	19.6
3	2.44	−2.99	69.24	23.23	78.3
4	2.88	2.57	86.08	13.68	53.3
5	3.20	9.85	76.66	12.02	37.2
6	4.30	0.88	75.14	11.36	25.8
7	4.78	4.20	71.32	10.31	21.1
8	2.73	−1.90	66.34	20.12	61.9
9	1.15	−8.37	82.49	27.73	146.2
$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $
18	3.23	8.60	62.27	14.63	41.3
19	4.51	−3.49	64.50	13.86	23.6
20	3.67	7.92	73.80	11.43	30.9

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表 7 数值模拟与代理模型预测结果对比

Table 7. Comparison of simulation and agent model prediction results

项目	δ/(J·g⁻¹)	l/mm
预测结果	26.24	69.29
数值模拟结果	27.21	73.37
误差/%	3.56	4.19

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