横向爆炸载荷下泡沫铝填充管的动态响应

张春云; 刘志芳

doi:10.11858/gywlxb.20210752

横向爆炸载荷下泡沫铝填充管的动态响应

doi: 10.11858/gywlxb.20210752

张春云,
刘志芳^*, ,

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（11772216）

详细信息

作者简介:
张春云（1993－），男，硕士研究生，主要从事冲击动力学研究. E-mail：1748867532@qq.com

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

中图分类号: O347.3
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出版历程
- 收稿日期: 2021-03-23
- 修回日期: 2021-04-16

Dynamic Response of Aluminum Foam Filled Pipes under Lateral Explosive Load

ZHANG Chunyun,
LIU Zhifang^{*
, ,}

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

摘要

摘要: 采用数值模拟与理论分析相结合的方法，研究横向爆炸载荷下泡沫铝填充管的动态响应。利用有限元软件ABAQUS/EXPLICIT对横向爆炸载荷下泡沫铝填充管的塑性变形进行了数值模拟研究，分析了泡沫铝的相对密度、外管的直径与壁厚等因素对结构动态响应的影响。基于理想刚塑性地基梁模型，结合模态分析法，建立了预测横向爆炸载荷下泡沫铝填充管跨中挠度的理论分析模型，并进行了无量纲分析，给出了跨中无量纲挠度随无量纲冲量的变化规律。泡沫铝填充管跨中挠度的理论预测与数值模拟结果的误差在20%以内，表明所建立的理论分析模型合理可行。泡沫铝相对密度对横向爆炸载荷下填充管的跨中挠度有较大的影响，随着泡沫铝相对密度的增大，填充管跨中挠度减小。随着外管直径与壁厚的增大，跨中挠度减小。理论分析中，假设的两种模态函数对填充管跨中挠度的影响较小。
- 地基梁 /
- 横向爆炸载荷 /
- 泡沫铝填充管 /
- 模态解
Abstract: A combination of numerical simulation and theoretical analysis is used to study the dynamic response of foamed aluminum filled pipes under lateral explosion loads. The finite element software ABAQUS/EXPLICIT was used to carry out a numerical simulation study on the plastic deformation of the aluminum foam-filled tube under lateral explosive load, and the influence of the relative density of the foam aluminum, the diameter and wall thickness of the outer tube and other factors on the dynamic response of the structure was analyzed. Based on the ideal rigid-plastic foundation beam model, combined with the modal analysis method, a theoretical analysis model for predicting the mid-span deflection of the foamed aluminum filled pipe under lateral explosive load is established, and a dimensionless analysis is carried out. The change of the dimensionless deflection of the mid-span with the elementary impulse is obtained. The error between the theoretical prediction and the numerical simulation result of the foamed aluminum filled pipe mid-span deflection is within 20%, indicating that the established theoretical analysis model is reasonable and feasible. The relative density of foamed aluminum has a great influence on the mid-span deflection of the filled pipe under lateral explosive load. As the relative density of foamed aluminum increases, the mid-span deflection of the filled pipe decreases. As the diameter and wall thickness of the outer tube increase, the mid-span deflection decreases. The two modal functions assumed in the theoretical analysis have little effect on the mid-span deflection of the filled pipe.
- beam-on-founding /
- transverse explosion load /
- aluminum foam filled pipe /
- modal solution

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图 1 爆炸载荷下填充管的几何模型

Figure 1. Geometry of the tube filling with aluminum foam under blast loading

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图 2 网格尺寸对跨中挠度的影响

Figure 2. Influence of mesh size on the deflection of the mid-span

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图 3 爆炸载荷下填充管刚塑性地基梁

Figure 3. Rigid-plastic beam-on-foundation of the tube filling with aluminum foam under blast loading

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图 4 无量纲挠度-无量纲量λ曲线

Figure 4. Curves of non-dimensional deflection vs. the non-dimensional quantity λ

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图 5 无量纲挠度-无量纲量η曲线

Figure 5. Curves of non-dimensional deflection vs. the non-dimensional quantity η

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图 6 不同无量纲冲量下无量纲挠度的理论解与数值模拟结果的对比

Figure 6. Comparison of the non-dimensional deflection of the theoretical results and numerical results under different value of I_n

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图 7 无量纲挠度-无量纲冲量曲线

Figure 7. Curves of non-dimensional deflection vs. the non-dimensional impulse

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图 8 爆炸载荷峰值-衰减常数曲线

Figure 8. Curves of peak explosive load ${p_0}$ vs. characteristic time constant $\tau $

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表 1 泡沫铝参数^[17]

Table 1. The parameters of aluminum foam^[17]

Relative density/%	Density/(kg·m⁻³)	$\mu $	${\sigma {_ {\rm{s}}} }$/MPa	E/GPa
8	220.8	0.33	2.81	0.9
12	331.2	0.33	4.52	1.9
20	552.0	0.33	7.99	5.7

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表 2 实心泡沫铝填充管跨中挠度的模态解与数值模拟结果对比

Table 2. Comparison of mid-span deflection of foamed aluminum filled tubes of modal solutions and numerical simulation results

d₁/mm	h/mm	Relative density/%	W_theor/mm	W_sim/mm	$\dfrac{W{_{ {\rm{sim} } } }-W{_{ {\rm{theor} } } } }{W{_{ {\rm{theor} } } } } \Big/\text{%}$
76	0.7	8	3.0	3.1	3
		12	1.6	1.7	6
		20	0.7	0.8	14
	0.8	8	2.8	2.9	4
		12	1.4	1.5	7
		20	0.6	0.7	17
89	0.7	8	2.5	2.7	8
		12	1.3	1.4	8
		20	0.5	0.6	20
	0.8	8	2.3	2.3	0
		12	1.2	1.2	0
		20	0.5	0.5	0

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表 3 两种模态函数跨中挠度的对比

Table 3. Comparison of mid-span deflection corresponding to two modal functions

d₁/mm	h/mm	Relative density/%	W/mm		Relative error/%
d₁/mm	h/mm	Relative density/%	${ {\phi^*{_2} }(x)=1-2x/L}$	${\phi^*{_2}(x)={\rm{cos} }(\text{π}x/L)}$	Relative error/%
76	0.7	8	3.0	2.8	−7
		12	1.6	1.4	−13
		20	0.7	0.6	−14
	0.8	8	2.8	2.6	−7
		12	1.4	1.4	0
		20	0.6	0.6	0
89	0.7	8	2.5	2.4	−4
		12	1.3	1.2	−8
		20	0.5	0.5	0
	0.8	8	2.3	2.2	−4
		12	1.2	1.1	−8
		20	0.5	0.5	0

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