Damage characteristics of cylindrical shell structures subject to double UNDEX
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摘要:
目的 旨在充分研究多种毁伤元对目标毁伤模式，分析双爆源水下爆炸对圆柱壳结构的毁伤效应。 方法 首先，建立圆柱壳有限元模型，采用任意拉格朗日−欧拉（ALE）方法对单/双爆源水下爆炸下圆柱壳的毁伤特性开展研究。然后，从破口面积、最大垂向位移和塑性应变区域面积等特征参数评价结构毁伤效果。 结果 计算结果表明，以500 kg TNT装药为例，对于间距为1 m的双爆源水下爆炸，等当量的双爆源相比单爆源的爆炸对圆柱壳外板会造成更严重的毁伤，但对圆柱壳内板的毁伤不如单爆源。对于间距大于3 m的双爆源水下爆炸，随着间距的增加，爆炸对圆柱壳结构的毁伤效果越弱。 结论 通过计算不同初始参数下水下爆炸对圆柱壳结构的毁伤，获取了单、双爆源水下爆炸对圆柱壳结构的毁伤规律，结果可为增强水下作战武器威力提供参考。 Abstract:Objective This paper aims to study the damage modes of the target simultaneously caused by multiple damage elements, and analyze the damage effect of the cylindrical shell subjected to the double underwater explosion (UNDEX). Methods First, a finite element model of cylindrical shell is established, and arbitrary Lagrangian-Eulerian（ALE） method is used to investigate the damage characteristics of cylindrical shell under underwater explosion of single or double explosion sources, and the damage effect is evaluated from the structural fracture area, the maximum vertical displacement of the structure and the area of the plastic strain area. Results Take 500 kg TNT charge as an example, the calculation results show that, when the spacing between two explosive sources is 1 m, the damage to the outer plate of the cylindrical shell is more serious when the double explosive source is equal to that of the single explosive source, but the damage to the inner plate of the cylindrical shell is less than that of the single explosive source. At the same time, with the increase of the distance between the two charges, especially when the distance is greater than 3 m, the damage effect on the cylindrical shell structure becomes weaker. Conclusions By calculating the damage to cylindrical shell structures by underwater explosion under different initial parameters, the general rules of damage to cylindrical shell structures by single and double explosion sources are given, which can provide reference for enhancing the power of underwater combat weapons. -
Key words:
- underwater explosion /
- structural damage /
- bubble /
- shockwave /
- dual explosive sources
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图 3 ALE方法计算的水下爆炸气泡脉动数值结果
Figure 3. Numerical simulation results of UNDEX bubble pulsation by ALE method
图 4 ALE方法与Zhang方程[25]的气泡脉动时历曲线对比
Figure 4. Comparison of bubble pulsation time history between ALE and Zhang's equation
图 8 单爆源水下爆炸作用下典型时刻下圆柱壳结构等效应力云图
Figure 8. The equivalent stress contours of cylindrical shell at typical moments under single UNDEX
图 9 单爆源水下爆炸下圆柱壳外板毁伤云图
Figure 9. The damage contour plots of cylindrical shell plate under single UNDEX
图 10 单爆源水下爆炸下圆柱壳板间骨架毁伤云图
Figure 10. The damage contour plots of framing structure of cylindrical shell under single UNDEX
图 11 单爆源水下爆炸下圆柱壳内板毁伤云图
Figure 11. The damage contour plots of inner plate of cylindrical shell under single UNDEX
图 12 双爆源水下爆炸工况1时的圆柱壳结构毁伤响应过程
Figure 12. Structural damage of cylindrical shell under double UNDEX in case 1
图 13 双爆源水下爆炸工况3时圆柱壳结构毁伤响应过程
Figure 13. Structural damage of cylindrical shell under double UNDEX in case 3
图 14 双爆源水下爆炸不同工况下的圆柱壳外板塑性应变
Figure 14. Plastic strain of outer plate of cylindrical shell under double UNDEX in different cases
图 15 双爆源水下爆炸不同工况下的圆柱壳外板垂向位移
Figure 15. Vertical displacement of outer plate of cylindrical shell under double UNDEX in different cases
图 16 双爆源不同间距水下爆炸后圆柱壳外板最大垂向位移和塑性变形面积
Figure 16. Max vertical displacement and plastic strain area of outer plate of cylindrical shell under double UNDEX in different spacing of the two explosion sources
图 17 双爆源不同工况水下爆炸下的圆柱壳板间骨架塑性应变
Figure 17. Plastic strain of framing structure of cylindrical shell under double UNDEX in different cases
图 18 双爆源不同工况水下爆炸下的圆柱壳板间骨架垂向位移
Figure 18. Vertical displacement of framing structure of cylindrical shell under double UNDEX in different cases
图 19 双爆源不同间距下板间骨架最大垂向位移和塑性变形面积
Figure 19. Max vertical displacement and plastic strain area of framing structure of cylindrical shell under double UNDEX in different spacing of the two explosion sources
图 20 双爆源不同工况水下爆炸下的圆柱壳内板塑性应变
Figure 20. Plastic strain of inter plate of cylindrical shell under double UNDEX in different cases
图 21 双爆源不同工况水下爆炸下的圆柱壳内板垂向位移
Figure 21. Vertical displacement of inter plate of cylindrical shell under double UNDEX in different cases
图 22 双爆源不同间距时水下爆炸圆柱壳内板最大垂向位移和塑性变形面积
Figure 22. Max vertical displacement and plastic strain area of inter plate of cylindrical shell under double UNDEX in different spacing of the two explosion sources
表 1 水状态方程参数
Table 1. EOS parameters of water
参数 数值 ρw/（kg·m−3） 1 000 c/m·s−1 1 480 S1 2.56 S2 −1.98 6 S3 0.226 8 γ0 0.5 α 2.67 E/（J·m−3） 30 700 V 1 
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表 2 空气状态方程参数
Table 2. EOS parameters of air
参数 数值 ρa/（kg·m−3） 1 C0=C1=C2=C3=C6 0 C4 0.4 C5 0.4 E/（J·m−3） 222 500 V 1
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表 3 TNT炸药JWL状态方程参数
Table 3. JWL EOS parameters of TNT explosive
参数 数值 ρTNT/（kg·m−3） 1 630 D/（m·s−1） 6 930 Pcj/GPa 21 A/GPa 371.2 B/GPa 3.21 R1 4.15 R2 0.95 ω 0.3 E/（GJ·m−3） 7.0
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表 4 不同网格尺寸下冲击波载荷ALE方法计算峰值与Zhang方程[25]理论峰值对比
Table 4. Comparison of calculated shockwave peak loads by different element sizes with ALE and Zhang’s equation[25]
网格尺寸
/mALE方法计算峰值
/MPaZhang方程[25]理论峰值
/MPa相对误差
/%0.10 56.12 56.40 0.50 0.15 55.16 1.61 0.20 51.18 9.26 0.40 18.16 13.8
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表 5 ALE方法与Zhang方程[25]计算的冲击波载荷峰值对比
Table 5. Comparison of shockwave peak loads calculated by ALE and Zhang's equation
爆距
/m冲击波载荷峰值/MPa 相对误差
/%Zhang 方程[25] ALE方法 7 66.64 65.23 2.12 8 56.40 55.49 1.61 9 48.09 46.25 3.83 10 42.35 40.39 4.63
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表 6 试验结果与ALE计算结果比对
Table 6. Results comparison of the experiment and ALE simulation
装药类型 装药/g 爆距/m 加筋板变形挠度/mm 相对误差
/%试验结果[28] ALE结果 TNT 110 0.7 15.79 15.22 3.61
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表 7 计算模型结构参数
Table 7. Structural parameters of calculation model
内壳 外壳 环肋 纵骨 舱壁 平台 板厚/mm 30 10 20 20 14 7
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表 8 单爆源水下爆炸下圆柱壳毁伤特征参数
Table 8. Characteristic parameters of damage of cylindrical shell under single UNDEX
破口纵向
直径/m破口横向
直径/m垂向最大
位移/m塑性变形
面积/m2外板 5.28 5.86 4.16 48.32 板间骨架 6.36 5.26 9.50 47.31 内板 7.36 6.74 5.74 53.94
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