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
计量
- 文章访问数: 663
- HTML全文浏览量: 101
- PDF下载量: 117
- 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

下载: 全尺寸图片幻灯片

图 2 能量变化情况

Figure 2. Energy change

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 6 冲击过程中力-位移曲线

Figure 6. Force-displacement curve during impact

下载: 全尺寸图片幻灯片

图 7 NGC-S剖切面示意图

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

下载: 全尺寸图片幻灯片

图 8 触发结构

Figure 8. Trigger structure

下载: 全尺寸图片幻灯片

图 9 变形模式对比

Figure 9. Comparison of deformation modes

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 12 COPRAS法流程图

Figure 12. Process flow chart of COPRAS method

下载: 全尺寸图片幻灯片

图 13 各组优选模型结果比较

Figure 13. Comparison of optimal model results of each group

下载: 全尺寸图片幻灯片

图 14 NGC-C与ZGC-O结构的应变情况

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

下载: 全尺寸图片幻灯片

图 15 Pareto解集

Figure 15. Pareto solution set

下载: 全尺寸图片幻灯片

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

参考文献(22)

[1]	KARL F G. 关于曲面的一般研究[M]. 陈惠勇, 译. 哈尔滨: 哈尔滨工业大学出版社, 2016: 47–83.
[2]	郭佳民, 刘欣丹, 鲁青青, 等. 一种负高斯曲率索穹顶: CN104631620A[P]. 2015-05-20.
[3]	陈昕, 沈世钊. 负高斯曲率单层网壳的刚度及整体稳定性研究 [J]. 哈尔滨建筑工程学院学报, 1990(2): 80–89. CHEN X, SHEN S Z. Study on stiffness and global stability of single-layer reticulated shells with negative Gaussian curvature [J]. Journal of Harbin Institute of Architectural Engineering, 1990(2): 80–89.
[4]	李松晏, 郑志军. 高速列车吸能结构设计和耐撞性分析 [J]. 爆炸与冲击, 2015, 35(2): 164–170. DOI: 10.11883/1001-1455(2015)02-0164-0. LI S Y, ZHENG Z J. Energy absorbing structure design and crashworthiness analysis of high-speed trains [J]. Explosion and Shock Waves, 2015, 35(2): 164–170. DOI: 10.11883/1001-1455(2015)02-0164-0.
[5]	KARAGIOZOVA D, NURICK G N, KIM C Y, et al. Energy absorption of aluminium alloy circular and square tubes under an axial explosive load [J]. Thin-Walled Structures, 2004, 43(6): 956–982. DOI: 10.1016/j.tws.2004.11.002.
[6]	YAMASHITA M, HATTORI T, NISHIMURA N, et al. Quasi-static and dynamic axial crushing of various polygonal tubes [J]. Key Engineering Materials, 2007, 340: 1399–1404. DOI: 10.4028/www.scientific.net/kem.340-341.1399.
[7]	LI J, LIU J, LIU H, et al. A precise theoretical model for laterally crushed hexagonal tubes [J]. Thin-Walled Structures, 2020, 152: 106750. DOI: 10.1016/j.tws.2020.106750.
[8]	ALAVI NIA A. , PARSAPOUR M. Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular, square, hexagonal and octagonal sections [J]. Thin-Walled Structures, 2014, 74: 155–165. DOI: 10.1016/j.tws.2013.10.005.
[9]	PIRMOHAMMAD S, ESMAEILI-MARZDASHTI S. Multi-objective crashworthiness optimization of square and octagonal bitubal structures including different hole shapes [J]. Thin-Walled Structures, 2019, 139: 126–138. DOI: 10.1016/j.tws.2019.03.004.
[10]	MAMALIS A, MANOLAKOS D, IOANNIDIS M, et al. Finite element simulation of the axial collapse of metallic thin-walled tubes with octagonal cross-section [J]. Thin-Walled Structures, 2003, 41(10): 891–900. DOI: 10.1016/s0263-8231(03)00046-6.
[11]	MAMALIS A G, MANOLAKOS, D E BALDOUKAS A K, et al. Energy dissipation and associated failure modes when axially loading polygonal thin-walled cylinders [J]. Thin-Walled Structures, 1991, 12(1): 17–34. DOI: 10.1016/0263-8231(91)90024-d.
[12]	AL GALIB D, LIMAM A. Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes [J]. Thin-Walled Structures, 2004, 42(8): 1103–1137. DOI: 10.1016/j.tws.2004.03.001.
[13]	路国运, 段晨灏, 雷建平, 等. 金属圆柱壳受大质量低速冲击的屈曲变形 [J]. 爆炸与冲击, 2015, 35(2): 171–176. DOI: 10.11883/1001-1455(2015)02-0171-06. LU G Y, DUAN C H, LEI J P, et al. Dynamic buckling of the cylindrical shell impacted by large mass with low velocity [J]. Explosion and Shock Waves, 2015, 35(2): 171–176. DOI: 10.11883/1001-1455(2015)02-0171-06.
[14]	张宗华, 刘书田. 多边形薄壁管动态轴向冲击的耐撞性研究[C]//2007中国汽车工程学会年会论文集.2007: 449–455.
[15]	GUILLOW S R, LU G, GRZEBIETA R H. Quasi-static axial compression of thin-walled circular aluminium tubes [J]. International Journal of Mechanical Sciences, 2001, 43(9): 2103–2123. DOI: 10.1016/S0020-7403(01)00031-5.
[16]	ZAREI H R, KRÖGER M. Multiobjective crashworthiness optimization of circular aluminum tubes [J]. Thin-Walled Structures, 2006, 44(3): 301–308. DOI: 10.1016/j.tws.2006.03.010.
[17]	HOU S J, HAN X, SUN G Y, et al. Multiobjective optimization for tapered circular tubes [J]. Thin-Walled Structures, 2011, 49(7): 855–863. DOI: 10.1016/j.tws.2011.02.010.
[18]	MARZBANRAD J, EBRAHIMI M R. Multi-objective optimization of aluminum hollow tubes for vehicle crash energy absorption using a genetic algorithm and neural networks [J]. Thin-Walled Structures, 2011, 49(12): 1605–1615. DOI: 10.1016/j.tws.2011.08.009.
[19]	PALANIVELU S, VAN PAEPEGEM W, DEGRIECK J, et al. Parametric study of crushing parameters and failure patterns of pultruded composite tubes using cohesive elements and seam, part I: central delamination and triggering modelling [J]. Polymer Testing, 2010, 29(6): 729–741. DOI: 10.1016/j.polymertesting.2010.05.
[20]	HA N S, PHAM T M, CHEN W S, et al. Crashworthiness analysis of bio-inspired fractal tree-like multi-cell circular tubes under axial crushing [J]. Thin-Walled Structures, 2021, 169: 108315. DOI: 10.1016/j.tws.2021.108315.
[21]	WIERZBICKI T. Crushing analysis of metal honeycombs [J]. International Journal of Impact Engineering, 1983, 1(2): 157–174. DOI: 10.1016/0734-743x(83)90004-0.
[22]	孔祥韶, 杨豹, 周沪, 等. 基于响应面法的纤维金属层合板抗弹性能优化设计 [J]. 爆炸与冲击, 2022, 42(4): 043301. DOI: 10.11883/bzycj-2021-0146. KONG X S, YANG B, ZHOU H, et al. Optimal design of ballistic performance of fiber-metal laminates based on the response surface method [J]. Explosion and Shock Waves, 2022, 42(4): 043301. DOI: 10.11883/bzycj-2021-0146.