类向日葵夹芯圆柱壳的准静态轴向吸能特性与优化

牛林耕; 闫栋; 王根伟; 宋辉; 郭美卿

doi:10.11858/gywlxb.20230637

类向日葵夹芯圆柱壳的准静态轴向吸能特性与优化

doi: 10.11858/gywlxb.20230637

牛林耕^{1, 2,},
闫栋³,
王根伟^{2, 4,*, ,},
宋辉^{1, 2},
郭美卿^{1, 2}

1.
太原理工大学机械与运载工程学院，山西太原　030024
2.
太原理工大学材料强度与结构冲击山西省重点实验室，山西太原　030024
3.
湖北三江航天红阳机电有限公司工艺技术中心，湖北孝感　432000
4.
太原理工大学航空航天学院，山西晋中　030600

基金项目: 国家自然科学基金（11872265）；山西省科技重大专项（202101120401007）

详细信息

作者简介:
牛林耕（1997－），男，硕士研究生，主要从事轻质吸能结构研究. E-mail：niulingeng2022@163.com

通讯作者:
王根伟（1974－），男，博士，副教授，主要从事冲击动力学、新能源汽车轻量化及安全防护研究. E-mail：gwang@tyut.edu.cn

中图分类号: O347
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出版历程
- 收稿日期: 2023-04-06
- 修回日期: 2023-04-17
- 录用日期: 2023-04-24
- 刊出日期: 2023-09-01

Quasi-Static Axial Energy Absorption Characteristics and Optimization of Sunflower-Like Sandwich Cylindrical Shells

NIU Lingeng^{1, 2
,},
YAN Dong³,
WANG Genwei^{2, 4,*
, ,},
SONG Hui^{1, 2},
GUO Meiqing^{1, 2}

1.
College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
2.
Shanxi Key Laboratory of Material Strength and Structure Impact, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
3.
Hongyang Electromechanical Company, Process Technology Center, Xiaogan 432000, Hubei, China
4.
College of Aeronautics and Astronautics, Taiyuan University of Technology, Jinzhong 030600, Shanxi, China

摘要

摘要: 采用实验、理论和数值模拟方法研究了类向日葵夹芯圆柱壳在准静态轴向加载下的吸能特性。首先，对3种内径的夹芯圆柱壳及其构件进行了准静态轴向压缩实验和数值模拟。结果表明：所有夹芯圆柱壳的比吸能和压溃力效率都大于其各个组成构件以及构件之和；芯壳的波浪形结构比圆柱壳结构具有更好的能量吸收能力；圆柱壳和波浪形曲线芯壳的联合使用可以有效地提高薄壁金属结构的吸能效率。其次，基于简化的超级折叠单元理论，推导了夹芯圆柱壳的轴向平均压溃力的理论公式。理论预测的平均压溃力与实验结果及数值模拟结果间的相对误差均在10%以内。最后，以比吸能最大和峰值压溃力最小为目标，进行了类向日葵夹芯圆柱壳吸能特性的多目标优化设计，得到了夹芯圆柱壳比吸能和峰值压溃力的Pareto前沿，优化后的夹芯圆柱壳的比吸能和平均压溃力均有提高，与此同时，质量减小。
- 夹芯圆柱壳 /
- 吸能特性 /
- 夹芯设计 /
- 理论预测 /
- 多目标优化
Abstract: Experiments, theoretical analysis, and numerical simulations were conducted to investigate the energy absorption characteristics of sunflower-like sandwich cylindrical shells under quasi-static axial loading. Firstly, quasi-static axial compression experiments and numerical simulations were conducted for sandwich cylindrical shells with three inner diameters and for their components. It was found that the specific energy absorptions and crushing force efficiencies of all sandwich cylindrical shells are greater than those of their individual components, and those of the sums of the individual components. The combination of cylindrical shell and corrugated core shell can effectively improve the energy absorption efficiency of thin-walled metal structure. Then, the theoretical formula of the axial average crushing force for the sandwich cylindrical shell was derived based on the simplified super folding element theory. The axial average crushing force predicted by the theoretical model was compared with the experimental and simulation results. It was found that the errors are within 10%. Finally, a multi-objective optimization design, with the objectives of maximum specific energy absorption and minimum peak crushing force for the sunflower-like sandwich cylindrical shell, was carried out. The Pareto front of specific energy absorption and peak crushing force of the sandwich cylindrical shell was obtained. The optimized sandwich cylindrical shell structure was improved in terms of specific energy absorption, average crushing force, and mass.
- sandwich cylindrical shell /
- energy absorption characteristics /
- sandwich design /
- theoretical prediction /
- multi-objective optimization

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图 1 夹芯圆柱壳的截面形状

Figure 1. Cross-section of sandwich cylindrical shell

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图 2 夹芯圆柱壳的组成

Figure 2. Composition of sandwich cylindrical shell

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图 3 AA6061铝合金的应力-应变曲线

Figure 3. Stress-strain curve of AA6061 aluminum alloy

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图 4 夹芯圆柱壳及其构件

Figure 4. Sandwich cylindrical shells and its components

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图 5 准静态压缩实验平台

Figure 5. Quasi-static compression experiment platform

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图 6 实验获得的夹芯圆柱壳及其构件的力-位移曲线

Figure 6. Experimental force-displacement curves of sandwich cylindrical shells and its components

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图 7 内径为25 mm的夹芯圆柱壳在轴向压缩下的有限元模型

Figure 7. Finite element model of sandwich cylindrical shell with a inner diameter of 25 mm under axial compression

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图 8 有限元模型的网格敏感性分析

Figure 8. Mesh sensitivity analysis of finite element model

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图 9 动能与内能的比较

Figure 9. Comparison of kinetic energy and internal energy

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图 10 实验和有限元模拟获得的内径为25 mm的夹芯圆柱壳及其构件的变形过程

Figure 10. Deformation processes of sandwich cylindrical shell with the inner diameter of 25 mm and its components obtained by experiment and simulation

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图 11 实验和有限元模拟获得的内径为25 mm夹芯圆柱壳及其构件的力-位移曲线

Figure 11. Force-displacement curves of the experiment and finite element simulation for the sandwich cylindrical shells with an inner diameter of 25 mm and its components

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图 12 实验和有限元模拟获得的内径为25 mm夹芯圆柱壳及其构件的能量吸收-位移曲线

Figure 12. Energy absorption-displacement curves of the experiment and finite element simulation for the sandwich cylindrical shell with an inner diameter of 25 mm and its components

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图 13 数值模拟获得的夹芯圆柱壳及其构件的力-位移曲线

Figure 13. Simulated force-displacement curves of sandwich cylindrical shells and its components

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图 14 有限元模拟得到的夹芯圆柱壳及其构件的能量吸收-位移曲线

Figure 14. Simulated energy absorption-displacement curves of sandwich cylindrical shells and its components

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图 15 有限元模拟得到的夹芯圆柱壳及其构件的比能量吸收-位移曲线

Figure 15. Simulated specific energy absorption-displacement curves of sandwich cylindrical shells and its components

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图 16 有限元模拟得到的不同内径的夹芯圆柱壳及其构件的SEA

Figure 16. Simulated SEA of sandwich cylindrical shells and its components with different inner diameters

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图 17 内径为25 mm的夹芯圆柱壳及其构件在31.5 mm位移处的变形

Figure 17. Deformation of sandwich cylindrical shell with the inner diameter of 25 mm and its components at a displacement of 31.5 mm

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图 18 基本折叠单元的理想折叠过程

Figure 18. Ideal folding process of a basic folding element

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图 19 角单元类型

Figure 19. Types of corner element

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图 20 4面板单元的简化过程

Figure 20. Simplify process of 4-panel element

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图 21 夹芯圆柱壳的最优解集的Pareto前沿

Figure 21. Pareto front of the optimal solution set for sandwich cylindrical shells

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图 22 优化前后的力-位移曲线对比

Figure 22. Comparison of force-displacement curves before and after optimization

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表 1 AA6061铝合金的材料属性

Table 1. Material properties of AA6061 aluminium alloy

Density/(kg·m⁻³)	Young’s modulus/GPa	Initial yield stress/MPa	Ultimate strength/MPa	Poison’s ratio
2.7×10³	68.2	227	282	0.3

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表 2 夹芯圆柱壳及其构件的壁厚和质量

Table 2. Wall thickness and mass of sandwich cylindrical shells and its components

Item	t/mm			m/kg
Item	R_I=15 mm	R_I=25 mm	R_I=35 mm	R_I=15 mm	R_I=25 mm	R_I=35 mm
SCS	1.00	1.08	1.11	0.102	0.103	0.103
IS	0.96	0.98	1.04	0.010	0.018	0.025
CS	0.96	1.04	1.10	0.058	0.046	0.037
OS	0.92	1.06	1.08	0.029	0.032	0.032

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表 3 实验和有限元模拟获得的夹芯圆柱壳及其构件的SEA对比

Table 3. SEA comparison of experiments and finite element simulaitons of sandwich cylindrical shells and its components

Name	E_SA for R_I=15 mm			E_SA for R_I=25 mm			E_SA for R_I=35 mm
Name	Exp./(J·g⁻¹)	Sim./(J·g⁻¹)	Error/%	Exp./(J·g⁻¹)	Sim./(J·g⁻¹)	Error/%	Exp./(J·g⁻¹)	Sim./(J·g⁻¹)	Error/%
SCS	34.82	31.70	−8.95	37.14	37.87	1.93	32.91	30.50	−7.91
IS	30.43	29.69	−2.43	21.16	22.93	7.73	18.54	18.89	1.84
OS	15.23	15.01	−1.46	16.49	16.14	−2.17	15.48	16.45	5.93
CS	21.18	24.44	13.36	26.12	28.10	7.05	23.85	22.63	−5.39

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表 4 内径为25 mm的夹芯圆柱壳及其构件的能量吸收性能指标

Table 4. Energy absorption performance indicators of sandwich cylindrical shell with the inner diameter of 25 mm and its components

Item	m/kg	E_A/kJ	E_SA/(J·g⁻¹)	p_p/kN	η_c
SCS	0.106	4.02	37.87	217.36	0.59
IS	0.018	0.40	22.93	33.27	0.38
OS	0.032	0.51	16.14	57.10	0.28
CS	0.047	1.69	28.11	92.15	0.45

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表 5 理论预测与实验及模拟结果的对比

Table 5. Comparison of theoretical predictions with experiments and simulations

R_I/mm	t/mm	p_m/kN			Error/%
R_I/mm	t/mm	Theory	Sim.	Exp.	Theory relative to simulation	Theory relative to experiment
15	1.00	109.1	106.8	112.2	2.15	−2.76
25	1.08	115.1	121.2	121.2	−5.03	−5.03
35	1.11	116.5	114.2	107.7	2.01	8.17

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表 6 夹芯圆柱壳的样本点及响应值

Table 6. Sample points and response values of sandwich cylindrical shells

No.	R_I/mm	R_O/mm	t/mm	p_p/kN	E_SA/(J·g⁻¹)
1	23.05	37.05	0.816	154.1	43.7
2	23.58	46.00	1.079	273.3	41.6
3	32.00	38.11	0.763	129.5	40.4
4	27.79	36.53	0.711	119.2	41.9
5	26.74	43.37	0.974	217.1	42.5
6	31.47	42.32	0.868	170.9	40.5
7	28.32	44.42	1.500	360.6	58.7
8	28.84	44.95	0.658	142.6	34.7
9	22.00	38.63	1.237	269.4	52.7
10	22.53	41.79	0.921	208.2	40.6
11	30.95	41.26	1.289	262.3	53.8
12	25.16	39.68	0.553	104.7	33.3
13	24.63	43.89	0.605	132.9	30.4
14	29.89	37.58	1.184	213.8	51.7
15	25.68	36.00	1.342	249.7	60.6
16	29.37	40.74	0.500	91.6	30.7
17	30.42	45.47	1.132	258.8	47.3
18	24.11	42.84	1.395	337.4	52.7
19	27.26	40.21	1.447	307.0	62.0
20	26.21	39.16	1.026	203.3	48.0

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表 7 夹芯圆柱壳近似模型的预测精度评估

Table 7. Evaluation of prediction accuracy of the approximation models for sandwich cylindrical shell

Model	R²		P		Q
Model	p_p	E_SA	p_p	E_SA	p_p	E_SA
KRG	0.9742	0.9687	0.0458	0.0520	0.1501	0.1354
RBF	0.9951	0.9737	0.0198	0.0476	0.0683	0.1088
RSM	0.9993	0.9718	0.0076	0.0494	0.0171	0.1137

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表 8 NSGA-Ⅱ算法参数设置

Table 8. Parameters of NSGA-Ⅱ algorithm

Population size	Number of iterations	Crossover probability	Crossover distribution index	Mutation distribution index
12	40	0.9	10	20

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表 9 优化获得的PCF和 SEA 与有限元结果对比

Table 9. PCF and SEA comparison between optimization results and finite element results

p_p/kN		E_SA/(J·g⁻¹)		Error/%
Optimization	Simulation	Optimization	Simulation	p_p	E_SA
204.1	206.2	53.7	52.2	1.0	2.9

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表 10 优化前后模拟结果的对比

Table 10. Comparison of simulation results before and after optimization

Case	p_p/kN	E_SA/(J·g⁻¹)	p_m/kN	m/kg
Before optimization	203.3	48.0	140.0	0.092
After optimization	206.2	52.2	146.2	0.088
Change/%	1.43	8.75	4.43	−4.35

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