远距离爆炸荷载作用下钢框架几何相似律研究

陈能翔; 钟巍; 王澍霏; 杨尚霖; 田宙; 欧翔; 黄怀纬; 姚小虎

doi:10.11883/bzycj-2021-0498

远距离爆炸荷载作用下钢框架几何相似律研究

doi: 10.11883/bzycj-2021-0498

陈能翔^1,,
钟巍^{2, 3},
王澍霏²,
杨尚霖¹,
田宙²,
欧翔¹,
黄怀纬^1, ,,
姚小虎¹

1.
华南理工大学土木与交通学院，广东广州 510641
2.
西北核技术研究所，陕西西安710024
3.
北京大学数学科学学院，北京100871

基金项目: 国家杰出青年科学基金（11925203）

详细信息

作者简介:
陈能翔（1996－　），男，硕士研究生，201920106515@mail.scut.edu.cn

通讯作者:
黄怀纬（1979－　），男，博士，副教授，cthwhuang@scut.edu.cn

中图分类号: O382.4
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- 被引次数: 0
出版历程
- 收稿日期: 2021-12-06
- 修回日期: 2022-04-12
- 网络出版日期: 2022-04-15
- 刊出日期: 2023-01-05

Study on geometric similarity law of steel frame under a far-field explosion load

1.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, Guangdong, China
2.
Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China
3.
School of Mathematical Sciences, Peking University, Beijing 100871, China

摘要

摘要: 根据Π定理推导了远距离爆炸荷载作用下钢框架原型结构与缩比模型的几何相似律表达式。基于已有的钢框架子结构爆炸实验，采用AUTODYN建立了钢框架子结构数值模型，验证了流固耦合方法在结构爆炸响应分析中的可靠性。在此基础上，对比了流固耦合方法和解析爆炸边界方法在钢框架远距离爆炸数值模拟中的准确性和计算效率，结果表明，解析爆炸边界方法可以合理地模拟远距离爆炸荷载作用下钢框架的动态响应，且计算效率较高。最后，采用该方法分析了具有不同相似比的两层三跨钢框架结构在远距离爆炸荷载作用下的动态响应及毁伤效应，结果表明：该结构的动态响应和毁伤效应符合几何相似规律。
- 相似律 /
- 钢框架 /
- 远距离爆炸 /
- 动态响应
Abstract: According to the Π principle, a similarity law was proposed between the prototype and the scaled-down models of the steel frame under a far-field explosion load. Based on the explosion experiments of steel frame substructures, a numerical model of the substructure was established by AUTODYN to verify the reliability, accuracy, and computational efficiency of the fluid-structure interaction method in the structural explosion response analysis and the analytical blast boundary method by comparing the numerical simulation results with the experiments of the steel frame under the far-field explosion load. The results show that the analytical blast boundary method can reasonably simulate the dynamic response of the steel frame under far-field explosion loads with high computational efficiency. Finally, the dynamic response and damage of a two-story three-span steel frame structure under a far-field explosion load were analyzed by the analytical blast boundary method using different scaling ratios. The results show that when the two-story three-span steel frame is fully scaled according to the geometric similarity ratio, the dynamic displacement responses of the prototype and the scaled-down models of the steel frame under the far-field explosion load are similar. And the damage effects of the prototype and the scaled-down models based on the assessment index of interlayer displacement angle are similar.
- similarity law /
- steel frame /
- far-field explosion /
- dynamic response

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图 1 几何特征量示意图

Figure 1. Schematic diagram of the geometric characteristic quantity

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图 2 钢框架子结构流固耦合数值模型

Figure 2. Numerical model of a steel frame substructure with fluid-structure interaction

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图 3 不同网格尺寸得到的特征点（应变片1）位移时程曲线比较

Figure 3. Comparison of displacement-time curves at the feature point (gauge 1) obtained by different mesh sizes

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图 4 失效模式对比

Figure 4. Comparison of the failure modes

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图 5 结构示意图

Figure 5. Schematic diagram of a steel structure

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图 6 中柱侧移对比

Figure 6. Comparison of the lateral displacement of the middle column

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图 7 钢框架在不同工况下的应变时程曲线

Figure 7. Strain history curves of the steel frame under different conditions

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图 8 钢框架各响应时程曲线

Figure 8. Response history curves of the steel frame

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图 9 钢框架结构模型应力云图

Figure 9. Stress contours of the steel frame models

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表 1 爆炸毁伤问题中变量的量纲幂次指数

Table 1. Dimensional power coefficients of variables in explosion damage problems

物理量	M	L	T
$l,{l_1},{l_2},{l_3},{H_{\text{c}}},h$	0	1	0
${M_{\text{b}}},{M_{\text{c}}}$	1	2	-2
${N_{\text{b}}},{N_{\text{c}}}$	1	1	-2
ρ	1	-3	0
E	1	1	-2
ν	0	0	0
σ_y	1	-1	-2
p	1	-1	-2
t	0	0	1

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表 2 爆炸毁伤问题中自变量相似准数

Table 2. Similar parameters of independent variables in explosion damage problems

$ {\varPi _1} $	$ {\varPi _2} $	$ {\varPi _3} $	$ {\varPi _4} $	$ {\varPi _5} $	$ {\varPi _6} $	$ {\varPi _7} $	$ {\varPi _8} $	$ {\varPi _9} $
$ \dfrac{{{l_1}}}{l} $	$ \dfrac{{{l_2}}}{l} $	$ \dfrac{{{l_3}}}{l} $	$\dfrac{{{H_{\text{c}}}}}{l}$	$ \dfrac{h}{l} $	$\dfrac{{{M_{\text{b}}}}}{{{\sigma _{\text{y}}}{l^3}}}$	$\dfrac{{{N_{\text{b}}}}}{{{\sigma _{\text{y}}}{l^2}}}$	$\dfrac{{{M_{\text{c}}}}}{{{\sigma _{\text{y}}}{l^3}}}$	$\dfrac{{{N_{\text{c}}}}}{{{\sigma _{\text{y}}}{l^2}}}$

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表 3 炸药的材料参数

Table 3. Material parameters of explosive

ρ_t / (kg∙m⁻³)	A / GPa	B / GPa	R₁	R₂	$ \omega $	D_CJ / (m∙s⁻¹)	P_CJ / GPa	E₀ / (kJ∙m⁻³)
1630	373.77	3.7471	4.15	0.9	0.35	6930	21	6×10⁶

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表 4 钢材J-C模型参数

Table 4. The J-C model parameters of steel

ρ / (kg∙m⁻³)	E / GPa	ν	B / MPa	C	n	m	$ {\dot \varepsilon _0}/{{\text{s}}^{ - 1}} $
7850	210	0.3	280	0.022	0.4	1.03	1

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表 5 钢框架材料属性

Table 5. Material properties of steel frame

子结构试件	$ {f_{\text{y}}} $/ MPa	$ {f_{\text{u}}} $/ MPa
梁翼缘	345	464
梁腹板	353	463
柱翼缘	420	529
柱腹板	407	539
端板	305	417

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表 6 钢框架不同工况下应变率计算

Table 6. Strain rate of the steel frame under different conditions

工况1	比例1/5	应变率计算值/s⁻¹	工况2	比例1/5	应变率计算值/s⁻¹
30 kg，5 m	m	0.5590	30 kg，6 m	m	0.3475
3750 kg，25 m	p	0.1038	3750 kg，30 m	p	0.0711

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表 7 钢框架缩比模型相似比

Table 7. The similarity ratios of the scaled steel-frame models

模型	原型	比例1/2	比例1/5	比例1/10	比例1/20
相似比	1	1/2	1/5	1/10	1/20

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表 8 与结构损伤状况相对应的层间位移角限制

Table 8. Interlayer displacement angle limit corresponding to structural damage

性能水平	损伤状态	层间位移角 / %
Ⅰ	完好	δ ≤ 0.2
Ⅱ	很轻微破坏	0.2 < δ ≤ 0.5
Ⅲ	轻微破坏	0.5 < δ ≤ 0.7
Ⅳ	中等破坏	0.7 < δ ≤ 1.5
Ⅴ	严重破坏	1.5 < δ ≤ 2.5
Ⅵ	很严重破坏	2.5 < δ ≤ 5.0
Ⅶ	倒塌	δ > 5.0

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