横向爆炸载荷下泡沫铝夹芯管的动态响应与多目标优化

武钰朋; 张天辉; 刘志芳; 雷建银; 李世强

doi:10.11858/gywlxb.20230634

横向爆炸载荷下泡沫铝夹芯管的动态响应与多目标优化

doi: 10.11858/gywlxb.20230634

太原理工大学机械与运载工程学院应用力学研究所，山西太原　030024

基金项目: 国家自然科学基金（12272254，12072219）；山西省自然科学基金（202203021211170）

详细信息

作者简介:
武钰朋（1998－），男，硕士研究生，主要从事冲击动力学研究. E-mail：wuyvpeng5@163.com

通讯作者:
刘志芳（1971－），女，博士，教授，主要从事冲击动力学研究. E-mail：liuzhifang@tyut.edu.cn

中图分类号: O347
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出版历程
- 收稿日期: 2023-03-31
- 修回日期: 2023-05-17
- 录用日期: 2023-06-08
- 刊出日期: 2023-09-01

Dynamic Response and Multi-Objective Optimization of Aluminum Foam-Filled Sandwich Tube under Lateral Blast Loading

Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 基于动力显式有限元法，研究了泡沫铝夹芯管在横向爆炸载荷下的动态响应，以芯层能量吸收及外管刚度为目标，对结构的抗爆性能进行了多目标优化设计。系统研究了泡沫铝夹芯管结构的几何参数、泡沫铝芯层相对密度和爆炸加载条件等对其变形规律和能量吸收性能的影响。结果表明：横向爆炸载荷下，泡沫铝夹芯管的变形区域集中在跨中位置，内外管通过跨中位置塑性变形和变形区域左右两端的弯曲变形吸收能量，泡沫铝芯层主要依靠芯层压缩吸收能量；减小外管壁厚或泡沫铝芯层相对密度能有效提高结构的比吸能，但会影响泡沫铝夹芯管内外管的变形程度；外管几何参数对结构吸能性能和内外管变形的影响程度远大于内管；基于泡沫铝夹芯管的数值模拟结果，构造了响应面模型并对其进行了多目标优化，给出了Pareto前沿图，可根据实际工程应用来确定泡沫铝夹芯管结构中内外管的壁厚与芯层的相对密度。
- 泡沫铝夹芯管 /
- 爆炸载荷 /
- 动态响应 /
- 多目标优化
Abstract: The dynamic response of aluminum foam-filled sandwich tubes subjected to lateral blast loading was investigated numerically using the dynamic explicit finite element method. Based on numerical simulation, the structural blast resistance was optimized with the core energy absorption and outer tube stiffness as the optimization objectives. The effects of structural geometric parameters, the relative density of the aluminum foam core layer, and blast loading conditions on the deformation patterns and energy absorption properties of aluminum foam-filled sandwich tube have been systematically investigated. The study results indicate that the deformation region of the aluminum foam-filled sandwich tube under lateral blast loading is mainly concentrated in the middle span. Energy absorption occurs through plastic deformation in the middle of the span and bending deformation at the left and right ends of the deformed region for both the inner and outer tubes. In contrast, the energy absorption of the aluminum foam core layer relies primarily on core compression. Reducing of the thickness of the outer tube or the relative density of the aluminum foam core layer can effectively improve the specific energy absorption of the structure and increase the deformation of the inner and outer tubes. The effect of the geometry parameters of the outer tube on the energy absorption properties of the structure and the deformation of the inner and outer tubes is much larger than that of the inner tube. A response surface model is constructed based on the numerical simulation results of aluminum foam-filled sandwich tube. Subsequently, multi-objective optimization is performed and the resulting Pareto front graph is provided. The determination of the wall thickness of the inner and outer tubes, together with the relative density of the aluminum foam core layers in the aluminum foam-filled sandwich tube, can be based on the specific engineering application requirements.
- aluminum foam-filled sandwich tube /
- blast loading /
- dynamic response /
- multi-objective optimization

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图 1 泡沫铝夹芯管

Figure 1. Aluminum foam-filled sandwich tube

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图 2 有限元模型

Figure 2. Finite element model

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图 3 爆炸载荷假设^[13]

Figure 3. Blast load assumption^[13]

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图 4 实验^[13]与数值模拟结果的对比

Figure 4. Comparison of experimental^[13] and numerical simulation results

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图 5 网格敏感性验证

Figure 5. Grid sensitivity verification

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图 6 外管直径和壁厚对泡沫铝夹芯管内外管跨中挠度的影响

Figure 6. Effects of outer tube diameter and wall thickness on mid-span deflection of inner and outer tubes of aluminum foam-filled sandwich tubes

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图 7 内管直径和壁厚对泡沫铝夹芯管内外管跨中挠度的影响

Figure 7. Effects of inner tube diameter and wall thickness on mid-span deflection of inner and outer tubes of aluminum foam-filled sandwich tubes

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图 8 泡沫铝相对密度对泡沫铝夹芯管内外管跨中挠度的影响

Figure 8. Effect of relative density of aluminum foam on mid-span deflection of inner and outer tubes of aluminum foam-filled sandwich tubes

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图 9 不同相对密度泡沫铝夹芯管的轴向变形轮廓

Figure 9. Axial deformation profiles of aluminum foam-filled sandwich tubes with different relative densities

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图 10 炸药起爆距离和炸药质量对泡沫铝夹芯管内外管跨中挠度的影响

Figure 10. Effect of explosive initiation distance on mid-span deflection of inner and outer tubes of aluminum foam-filled sandwich tubes

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图 11 优化方法流程

Figure 11. Flowchart of the optimization method

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图 12 Pareto前沿

Figure 12. Pareto front

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表 1 泡沫铝材料参数^[18]

Table 1. Material parameters for aluminum foam^[18]

ρ^*/%	ρ/(g·cm⁻³)	E/MPa	μ	μ_c	μ_p
10	0.27	48	0	1.41	0.17
15	0.40	71	0	1.12	0.29
20	0.54	143	0	1.10	0.30

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表 2 理论冲量与实验冲量的对比

Table 2. Comparison of impulse between theoretical solution and experiment

Test piece	W_s/g	R/mm	D/mm	H/mm	m/kg	p₀/MPa	I_E/(N·s)	I_T/(N·s)	$\dfrac{ {I{_{ \rm{T } } }-I{_{ \rm{E} } } } }{ {I{_{ \rm{E} } } } }\Big/$%
No.1	30	40	76	0.7	96.8	27.7	7.1	7.4	4.2
No.2	50	40	76	0.7	96.7	45.8	12.9	12.2	−5.4

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表 3 试件几何参数

Table 3. Geometric parameter of specimens

Test piece	D/mm	d/mm	H/mm	h/mm	L/mm	m/g
NS01	101	76	0.7	0.7	280	1 242.62
NS02	101	65	0.7	0.7	280	1 326.02
NS03	101	54	0.7	0.7	280	1 388.13
NS04	90	54	0.7	0.7	280	1 150.28
NS05	79	54	0.7	0.7	280	933.72
NS06	101	76	0.8	0.7	280	1 312.19
NS07	101	76	0.9	0.7	280	1 381.75
NS08	101	76	0.7	0.8	280	1 294.97
NS09	101	76	0.7	0.9	280	1 347.31

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表 4 外管直径和壁厚的影响

Table 4. Effect of outer tube diameter and wall thickness

Test piece	E_t/J	m/g	E_a/(J·g⁻¹)	w_o/mm	w_i/mm
NS03	539.878	1 388.13	0.389	10.78	1.95
NS04	442.605	1 150.28	0.385	9.06	2.21
NS05	354.622	933.72	0.380	8.88	2.87
NS01	542.923	1 242.62	0.437	10.06	2.45
NS06	456.645	1 312.19	0.348	7.61	2.16
NS07	388.472	1 381.75	0.281	5.81	1.76

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表 5 内管直径和壁厚的影响

Table 5. Effect of inner tube diameter and wall thickness

Test piece	E_t/J	m/g	E_a/(J·g⁻¹)	w_o/mm	w_i/mm
NS01	542.923	1 242.62	0.437	10.06	2.45
NS02	546.692	1 326.02	0.412	10.39	2.32
NS03	539.878	1 388.13	0.389	10.78	1.95
NS08	542.470	1 294.97	0.419	9.92	2.16
NS09	542.161	1 347.31	0.402	9.81	1.92

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表 6 泡沫铝相对密度的影响

Table 6. Effect of relative density of aluminum foam

ρ^*/%	p₀/MPa	E_t/J	m/g	E_a/(J·g⁻¹)	w_o/mm	w_i/mm
10	36.8	614.301	1 116.12	0.550	14.77	4.99
15	36.8	542.923	1 242.62	0.437	10.06	2.45
20	36.8	379.921	1 378.86	0.276	4.82	2.35

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表 7 爆炸加载条件的影响

Table 7. Effect of blast loading conditions

R/mm	W_s/g	p₀/MPa	E_t/J	E_a/(J·g⁻¹)	w_o/mm	w_i/mm
37	30	34.9	935.594	0.753	14.96	4.34
40	30	27.7	542.923	0.437	10.06	2.45
40	35	32.3	776.974	0.625	12.60	3.62
40	40	36.8	1058.910	0.852	16.20	4.98
43	30	22.4	312.212	0.251	5.92	1.54

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表 8 泡沫铝夹芯管组成部分的吸能百分比

Table 8. Energy absorption percentage of aluminum foam-filled sandwich tube components

Test piece	$\rho ^* $/%	R/mm	W_s/g	p₀/MPa	Energy absorption percentage/%
Test piece	$\rho ^* $/%	R/mm	W_s/g	p₀/MPa	Outer tube	Foam core	Inner tube
NS01	15	40	30	27.7	59.9	32.0	8.1
NS02	15	40	30	27.7	62.6	30.5	6.9
NS03	15	40	30	27.7	61.8	33.7	4.5
NS04	15	40	30	27.7	62.4	30.7	6.9
NS05	15	40	30	27.7	59.7	32.3	8.0
NS06	15	40	30	27.7	64.0	28.1	7.9
NS07	15	40	30	27.7	66.3	25.6	8.2
NS08	15	40	30	27.7	59.5	32.4	8.0
NS09	15	40	30	27.7	59.2	32.9	7.9
NS01	10	40	30	27.7	79.8	17.5	2.7
NS01	20	40	30	27.7	52.0	32.2	15.8
NS01	15	37	30	34.9	61.7	31.0	7.3
NS01	15	43	30	22.4	61.5	29.6	8.9
NS01	15	40	35	32.3	62.0	30.5	7.5
NS01	15	40	40	36.8	61.5	31.2	7.3

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表 9 最佳设计点

Table 9. Optimum design point

Design point	H/mm	h/mm	$\,\rho ^ * $/%	w_o			E_CSA
Design point	H/mm	h/mm	$\,\rho ^ * $/%	FEM/mm	RSM/mm	Error/%	FEM/(J·g⁻¹)	RSM/(J·g⁻¹)	Error/%
Op1	0.70	0.76	13.7	0.457	0.505	−9.5	10.50	11.14	−5.7
Op2	1.78	1.75	18.8	0.051	0.056	−8.9	0.64	0.59	8.5
Op3	0.84	1.76	20.0	0.194	0.205	−5.4	2.85	2.83	0.7

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参考文献(20)

[1]	MIRFENDERESKI L, SALIMI M, ZIAEIRAD S. Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings [J]. International Journal of Mechanical Sciences, 2008, 50(6): 1042–1057. doi: 10.1016/j.ijmecsci.2008.02.007
[2]	ZHANG J X, DU J L, MIAO F X, et al. Plastic behavior of slender circular metal foam-filled tubes under transverse loading [J]. Thin-Walled Structures, 2022, 171: 108768. doi: 10.1016/j.tws.2021.108768
[3]	苏兴亚, 敬霖, 赵隆茂. 爆炸载荷下分层梯度泡沫铝夹芯板的失效模式与抗冲击性能 [J]. 爆炸与冲击, 2019, 39(6): 063103. doi: 10.11883/bzycj-2018-0198 SU X Y, JING L, ZHAO L M. Failure modes and shock resistance of sandwich panels with layered-gradient aluminum foam cores under air-blast loading [J]. Explosion and Shock Waves, 2019, 39(6): 063103. doi: 10.11883/bzycj-2018-0198
[4]	FAN Z H, LU G X, RUAN D, et al. Dynamic lateral crushing of empty and sandwich tubes [J]. International Journal of Impact Engineering, 2013, 53: 3–16. doi: 10.1016/j.ijimpeng.2012.09.006
[5]	HALL I W, GUDEN M, CLAAR T D. Transverse and longitudinal crushing of aluminum-foam filled tubes [J]. 2002, 46(7): 513−518.
[6]	SONG K J, LONG Y, JI C, et al. Plastic deformation of metal tubes subjected to lateral blast loads [J]. Mathematical Problems in Engineering. 2014, 2014: 250379.
[7]	YUEN S C K, NURICK G N, BRINCKMANN H B, et al. Response of cylindrical shells to lateral blast load [J]. International Journal of Protective Structure. 2013, 4(3): 209−230.
[8]	WIERZBICKI T, HOOFATT M S. Damage assessment of cylinders due to impact and explosive loading [J]. International Journal of Impact Engineering, 1993, 13(2): 215–241. doi: 10.1016/0734-743X(93)90094-N
[9]	JING L, WANG Z H, ZHAO L M. Dynamic response of cylindrical sandwich shells with metallic foam cores under blast loading-numerical simulations [J]. Composite Structures, 2013, 99: 213–223. doi: 10.1016/j.compstruct.2012.12.013
[10]	JING L, WANG Z H, ZHAO L M. An approximate theoretical analysis for clamped cylindrical sandwich shells with metallic foam cores subjected to impulsive loading [J]. Composites Part B: Engineering, 2014, 60: 150–157. doi: 10.1016/j.compositesb.2013.12.047
[11]	JING L, WANG Z H, SHIM V P W. An experimental study of the dynamic response of cylindrical sandwich shells with metallic foam cores subjected to blast loading [J]. International Journal of Impact Engineering, 2014, 71: 60–72. doi: 10.1016/j.ijimpeng.2014.03.009
[12]	HOO FATT M S, SURABHI H. Blast resistance and energy absorption of foam-core cylindrical sandwich shells under external blast [J]. Composite Structures, 2012, 94(11): 3174–3185. doi: 10.1016/j.compstruct.2012.05.013
[13]	LIU Z F, ZHANG T H, LI S Q, et al. Experiment and numerical simulation on the dynamic response of foam-filled tubes under lateral blast loading [J]. Acta Mechanica Solida Sinica, 2021, 34(6): 937–953. doi: 10.1007/s10338-021-00285-1
[14]	BAROUTAJI A, GILCHRIST M D, SMYTH D, et al. Crush analysis and multi-objective optimization design for circular tube under quasi-static lateral loading [J]. Thin-Walled Structures, 2015, 86: 121–131. doi: 10.1016/j.tws.2014.08.018
[15]	BAROUTAJI A, GILCHRIST M D, SMYTH D, et al. Analysis and optimization of sandwich tubes energy absorbers under lateral loading [J]. International Journal of Impact Engineering, 2015, 82: 74–88. doi: 10.1016/j.ijimpeng.2015.01.005
[16]	QI C, YANG S, YANG L J, et al. Blast resistance and multi-objective optimization of aluminum foam-cored sandwich panels [J]. Composite Structures, 2013, 105: 45–57. doi: 10.1016/j.compstruct.2013.04.043
[17]	LI S Q, YU B L, KARAGIOZOVA D, et al. Experimental, numerical, and theoretical studies of the response of short cylindrical stainless steel tubes under lateral air blast loading [J]. International Journal of Impact Engineering, 2019, 124: 48–60. doi: 10.1016/j.ijimpeng.2018.10.004
[18]	LI S Q, WANG Z H, WU G Y, et al. Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading [J]. Composites Part A: Applied Science and Manufacturing, 2014, 56: 262–271. doi: 10.1016/j.compositesa.2013.10.019
[19]	GOEL M D, MATSAGAR V A, GUPTA A K, et al. An abridged review of blast wave parameters [J]. Defence Science Journal, 2012, 62(5): 300–306. doi: 10.14429/dsj.62.1149
[20]	李磊, 马宏昊, 沈兆武. 基于正交设计方法的双锥罩结构优化设计 [J]. 爆炸与冲击, 2013, 33(6): 567–573. doi: 10.3969/j.issn.1001-1455.2013.06.002 LI L, MA H H, SHEN Z W. Optimal design of biconical liner structure based on orthogonal design method [J]. Explosion and Shock Waves, 2013, 33(6): 567–573. doi: 10.3969/j.issn.1001-1455.2013.06.002