Acta Armamentarii ›› 2024, Vol. 45 ›› Issue (1): 69-84.doi: 10.12382/bgxb.2023.0487
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FU Yaoyu1, GUI Xincheng1, ZHOU Yunbo2,*(), LIU Jiazhi2, SHI Hao1, WANG Zheng1
Received:
2023-05-23
Online:
2024-01-30
Contact:
ZHOU Yunbo
CLC Number:
FU Yaoyu, GUI Xincheng, ZHOU Yunbo, LIU Jiazhi, SHI Hao, WANG Zheng. Protection Performance Analysis and Optimization Design of Vehicle Roof Sandwich Plateunder Air Explosion Condition of Fragment Warhead[J]. Acta Armamentarii, 2024, 45(1): 69-84.
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ρ/(kg·m-3) | C0/MPa | C4/MPa | C5/MPa | E0/(kJ·m-3) | μ |
---|---|---|---|---|---|
1.225 | -0.1 | 0.4 | 0.4 | 253 | 1 |
Table 1 Air parameters
ρ/(kg·m-3) | C0/MPa | C4/MPa | C5/MPa | E0/(kJ·m-3) | μ |
---|---|---|---|---|---|
1.225 | -0.1 | 0.4 | 0.4 | 253 | 1 |
参数 | 数值 | 参数 | 数值 |
---|---|---|---|
pC-J/MPa | 21000 | R1 | 4.15 |
爆速v/(m·s-1) | 6930 | R2 | 0.9 |
ρ/(kg·m-3) | 1630 | ω | 0.35 |
A/MPa | 37377 | ETNT/(J·m-3) | 6000 |
B/MPa | 37347 | V | 1 |
Table 2 Explosive parameters
参数 | 数值 | 参数 | 数值 |
---|---|---|---|
pC-J/MPa | 21000 | R1 | 4.15 |
爆速v/(m·s-1) | 6930 | R2 | 0.9 |
ρ/(kg·m-3) | 1630 | ω | 0.35 |
A/MPa | 37377 | ETNT/(J·m-3) | 6000 |
B/MPa | 37347 | V | 1 |
ρ/(kg·m-3) | E/MPa | A/MPa | B/MPa | c | n | m |
---|---|---|---|---|---|---|
7800 | 210 | 1342 | 415 | 0.03 | 0.121 | 0.689 |
Table 3 Fragment parameters
ρ/(kg·m-3) | E/MPa | A/MPa | B/MPa | c | n | m |
---|---|---|---|---|---|---|
7800 | 210 | 1342 | 415 | 0.03 | 0.121 | 0.689 |
ρ/ (kg·m-3) | A/ MPa | B/ MPa | c | n | m | D1 | D2 | D3 | D4 |
---|---|---|---|---|---|---|---|---|---|
7850 | 1310 | 500 | 0.002 | 0.86 | 0.96 | 0.15 | 3.3 | -420 | 0.52 |
Table 4 Material parameters of sandwich plate
ρ/ (kg·m-3) | A/ MPa | B/ MPa | c | n | m | D1 | D2 | D3 | D4 |
---|---|---|---|---|---|---|---|---|---|
7850 | 1310 | 500 | 0.002 | 0.86 | 0.96 | 0.15 | 3.3 | -420 | 0.52 |
类型 | ta/ mm | tb/ mm | te/ mm | tf/ mm | bc/ mm | hc/ mm | 总质量/ kg |
---|---|---|---|---|---|---|---|
单层 | 8.9 | ||||||
I型 | 3.2 | 3.2 | 3.0 | 36 | 25 | ||
V型 | 3.2 | 3.2 | 1.8 | 36 | 25 | 18.5 | |
Y型 | 3.1 | 3.1 | 1.8 | 36 | 25 | ||
I-V型 | 2.7 | 2.7 | 1.9 | 1.8 | 36 | 25 | |
I-Y型 | 2.5 | 2.5 | 1.8 | 1.8 | 36 | 25 |
Table 5 Dimension parameters of six typical structures
类型 | ta/ mm | tb/ mm | te/ mm | tf/ mm | bc/ mm | hc/ mm | 总质量/ kg |
---|---|---|---|---|---|---|---|
单层 | 8.9 | ||||||
I型 | 3.2 | 3.2 | 3.0 | 36 | 25 | ||
V型 | 3.2 | 3.2 | 1.8 | 36 | 25 | 18.5 | |
Y型 | 3.1 | 3.1 | 1.8 | 36 | 25 | ||
I-V型 | 2.7 | 2.7 | 1.9 | 1.8 | 36 | 25 | |
I-Y型 | 2.5 | 2.5 | 1.8 | 1.8 | 36 | 25 |
工况 | 起爆方式 | 起爆点 |
---|---|---|
1 | 单点起爆 | 1 |
2 | 单点起爆 | 2 |
3 | 单点起爆 | 3 |
4 | 单点起爆 | 4 |
5 | 单点起爆 | 5 |
6 | 多点起爆 | 1,5 |
7 | 多点起爆 | 2,4 |
8 | 线起爆 |
Table 6 Modes of explosive initiation
工况 | 起爆方式 | 起爆点 |
---|---|---|
1 | 单点起爆 | 1 |
2 | 单点起爆 | 2 |
3 | 单点起爆 | 3 |
4 | 单点起爆 | 4 |
5 | 单点起爆 | 5 |
6 | 多点起爆 | 1,5 |
7 | 多点起爆 | 2,4 |
8 | 线起爆 |
工况 | ta/ mm | tb/ mm | te/ mm | tf/ mm | bc/ mm | hc/ mm | 总质量/ kg |
---|---|---|---|---|---|---|---|
1 | 1.5 | 3.5 | 1.8 | 1.8 | 36 | 25 | |
2 | 2.0 | 3.0 | 1.8 | 1.8 | 36 | 25 | |
3 | 2.5 | 2.5 | 1.8 | 1.8 | 36 | 25 | 18.5 |
4 | 3.0 | 2.0 | 1.8 | 1.8 | 36 | 25 | |
5 | 3.5 | 1.5 | 1.8 | 1.8 | 36 | 25 |
Table 7 Size parameters of five different structures
工况 | ta/ mm | tb/ mm | te/ mm | tf/ mm | bc/ mm | hc/ mm | 总质量/ kg |
---|---|---|---|---|---|---|---|
1 | 1.5 | 3.5 | 1.8 | 1.8 | 36 | 25 | |
2 | 2.0 | 3.0 | 1.8 | 1.8 | 36 | 25 | |
3 | 2.5 | 2.5 | 1.8 | 1.8 | 36 | 25 | 18.5 |
4 | 3.0 | 2.0 | 1.8 | 1.8 | 36 | 25 | |
5 | 3.5 | 1.5 | 1.8 | 1.8 | 36 | 25 |
工况 | ta/ mm | tb/ mm | te/ mm | tf/ mm | bc/ mm | hc/ mm | 总质量/ kg |
---|---|---|---|---|---|---|---|
1 | 2.5 | 2.5 | 2.5 | 2.0 | 36 | 20 | |
2 | 2.5 | 2.5 | 1.8 | 2.0 | 30 | 20 | |
3 | 2.5 | 2.5 | 1.6 | 1.7 | 30 | 25 | 18.5 |
4 | 2.5 | 2.5 | 1.8 | 1.8 | 36 | 25 | |
5 | 2.5 | 2.5 | 1.8 | 1.5 | 36 | 30 | |
6 | 2.5 | 2.5 | 1.3 | 1.5 | 30 | 30 |
Table 8 Size parameters of six different structures
工况 | ta/ mm | tb/ mm | te/ mm | tf/ mm | bc/ mm | hc/ mm | 总质量/ kg |
---|---|---|---|---|---|---|---|
1 | 2.5 | 2.5 | 2.5 | 2.0 | 36 | 20 | |
2 | 2.5 | 2.5 | 1.8 | 2.0 | 30 | 20 | |
3 | 2.5 | 2.5 | 1.6 | 1.7 | 30 | 25 | 18.5 |
4 | 2.5 | 2.5 | 1.8 | 1.8 | 36 | 25 | |
5 | 2.5 | 2.5 | 1.8 | 1.5 | 36 | 30 | |
6 | 2.5 | 2.5 | 1.3 | 1.5 | 30 | 30 |
类型 | ta/mm | tb/mm | bc/mm | hc/mm |
---|---|---|---|---|
初始值 | 2.5 | 2.5 | 30 | 30 |
下限 | 1.5 | 1.5 | 24 | 25 |
上限 | 3.5 | 3.5 | 36 | 35 |
Table 9 Variation range of design variables
类型 | ta/mm | tb/mm | bc/mm | hc/mm |
---|---|---|---|---|
初始值 | 2.5 | 2.5 | 30 | 30 |
下限 | 1.5 | 1.5 | 24 | 25 |
上限 | 3.5 | 3.5 | 36 | 35 |
序号 | ta/ mm | tb/ mm | bc/ mm | hc/ mm | FW/ kg | vZ/ (m·s-1) | FZ/ mm |
---|---|---|---|---|---|---|---|
1 | 3.05 | 2.87 | 25.78 | 34.90 | 25.44 | 0 | 11.40 |
2 | 1.61 | 2.65 | 35.73 | 29.17 | 17.93 | 0 | 13.02 |
3 | 2.03 | 3.25 | 28.75 | 33.62 | 22.62 | 0 | 9.84 |
4 | 1.78 | 1.81 | 34.65 | 33.94 | 17.45 | 98 | — |
5 | 2.21 | 3.02 | 32.88 | 32.27 | 21.05 | 0 | 10.37 |
6 | 2.64 | 3.42 | 32.24 | 25.51 | 21.40 | 0 | 10.54 |
7 | 2.96 | 1.52 | 24.58 | 25.07 | 19.79 | 103 | — |
8 | 2.11 | 2.07 | 30.99 | 25.84 | 17.68 | 0 | 14.98 |
9 | 2.36 | 1.73 | 27.20 | 27.96 | 19.16 | 0 | 15.64 |
10 | 2.76 | 2.40 | 28.06 | 30.16 | 21.61 | 0 | 12.26 |
11 | 3.30 | 2.73 | 29.37 | 29.02 | 22.70 | 0 | 10.37 |
12 | 3.31 | 2.51 | 26.73 | 32.18 | 23.98 | 0 | 10.99 |
13 | 3.39 | 3.27 | 31.22 | 27.05 | 23.16 | 0 | 9.18 |
14 | 1.95 | 3.35 | 27.40 | 26.03 | 20.96 | 0 | 10.36 |
15 | 1.74 | 3.16 | 31.65 | 32.59 | 20.88 | 0 | 10.51 |
16 | 2.27 | 2.80 | 26.01 | 29.76 | 21.93 | 0 | 11.92 |
17 | 3.50 | 2.45 | 30.33 | 31.47 | 23.02 | 0 | 10.77 |
18 | 3.09 | 1.88 | 34.96 | 30.69 | 19.74 | 0 | 13.31 |
19 | 1.55 | 2.93 | 24.26 | 31.57 | 21.85 | 0 | 10.93 |
20 | 1.63 | 1.60 | 29.67 | 26.56 | 16.26 | 146 | — |
21 | 2.89 | 2.57 | 33.89 | 29.61 | 20.73 | 0 | 11.71 |
22 | 1.89 | 1.94 | 26.28 | 34.24 | 22.82 | 0 | 13.24 |
23 | 1.84 | 2.37 | 33.68 | 26.52 | 17.59 | 0 | 14.24 |
24 | 3.19 | 1.64 | 28.22 | 33.36 | 21.60 | 0 | 14.49 |
25 | 2.49 | 2.29 | 32.57 | 28.54 | 19.12 | 0 | 13.26 |
26 | 2.52 | 3.44 | 30.73 | 32.95 | 23.01 | 0 | 8.96 |
27 | 2.82 | 2.06 | 33.23 | 28.26 | 21.56 | 0 | 12.00 |
28 | 2.74 | 2.96 | 24.83 | 27.73 | 23.00 | 0 | 12.07 |
29 | 2.15 | 1.84 | 25.23 | 30.96 | 20.08 | 0 | 14.38 |
30 | 3.16 | 2.21 | 34.46 | 30.40 | 20.57 | 0 | 11.62 |
31 | 2.62 | 2.13 | 35.34 | 34.44 | 20.15 | 0 | 12.22 |
32 | 2.40 | 3.11 | 29.24 | 27.42 | 21.19 | 0 | 10.78 |
Table 10 All sample points in the experimental design andtheir response results
序号 | ta/ mm | tb/ mm | bc/ mm | hc/ mm | FW/ kg | vZ/ (m·s-1) | FZ/ mm |
---|---|---|---|---|---|---|---|
1 | 3.05 | 2.87 | 25.78 | 34.90 | 25.44 | 0 | 11.40 |
2 | 1.61 | 2.65 | 35.73 | 29.17 | 17.93 | 0 | 13.02 |
3 | 2.03 | 3.25 | 28.75 | 33.62 | 22.62 | 0 | 9.84 |
4 | 1.78 | 1.81 | 34.65 | 33.94 | 17.45 | 98 | — |
5 | 2.21 | 3.02 | 32.88 | 32.27 | 21.05 | 0 | 10.37 |
6 | 2.64 | 3.42 | 32.24 | 25.51 | 21.40 | 0 | 10.54 |
7 | 2.96 | 1.52 | 24.58 | 25.07 | 19.79 | 103 | — |
8 | 2.11 | 2.07 | 30.99 | 25.84 | 17.68 | 0 | 14.98 |
9 | 2.36 | 1.73 | 27.20 | 27.96 | 19.16 | 0 | 15.64 |
10 | 2.76 | 2.40 | 28.06 | 30.16 | 21.61 | 0 | 12.26 |
11 | 3.30 | 2.73 | 29.37 | 29.02 | 22.70 | 0 | 10.37 |
12 | 3.31 | 2.51 | 26.73 | 32.18 | 23.98 | 0 | 10.99 |
13 | 3.39 | 3.27 | 31.22 | 27.05 | 23.16 | 0 | 9.18 |
14 | 1.95 | 3.35 | 27.40 | 26.03 | 20.96 | 0 | 10.36 |
15 | 1.74 | 3.16 | 31.65 | 32.59 | 20.88 | 0 | 10.51 |
16 | 2.27 | 2.80 | 26.01 | 29.76 | 21.93 | 0 | 11.92 |
17 | 3.50 | 2.45 | 30.33 | 31.47 | 23.02 | 0 | 10.77 |
18 | 3.09 | 1.88 | 34.96 | 30.69 | 19.74 | 0 | 13.31 |
19 | 1.55 | 2.93 | 24.26 | 31.57 | 21.85 | 0 | 10.93 |
20 | 1.63 | 1.60 | 29.67 | 26.56 | 16.26 | 146 | — |
21 | 2.89 | 2.57 | 33.89 | 29.61 | 20.73 | 0 | 11.71 |
22 | 1.89 | 1.94 | 26.28 | 34.24 | 22.82 | 0 | 13.24 |
23 | 1.84 | 2.37 | 33.68 | 26.52 | 17.59 | 0 | 14.24 |
24 | 3.19 | 1.64 | 28.22 | 33.36 | 21.60 | 0 | 14.49 |
25 | 2.49 | 2.29 | 32.57 | 28.54 | 19.12 | 0 | 13.26 |
26 | 2.52 | 3.44 | 30.73 | 32.95 | 23.01 | 0 | 8.96 |
27 | 2.82 | 2.06 | 33.23 | 28.26 | 21.56 | 0 | 12.00 |
28 | 2.74 | 2.96 | 24.83 | 27.73 | 23.00 | 0 | 12.07 |
29 | 2.15 | 1.84 | 25.23 | 30.96 | 20.08 | 0 | 14.38 |
30 | 3.16 | 2.21 | 34.46 | 30.40 | 20.57 | 0 | 11.62 |
31 | 2.62 | 2.13 | 35.34 | 34.44 | 20.15 | 0 | 12.22 |
32 | 2.40 | 3.11 | 29.24 | 27.42 | 21.19 | 0 | 10.78 |
序号 | ta/mm | tb/mm | bc/mm | hc/mm | FW/kg | FZ/mm |
---|---|---|---|---|---|---|
1 | 1.72 | 3.44 | 29.70 | 32.34 | 21.65 | 9.65 |
2 | 1.72 | 2.73 | 31.08 | 28.02 | 17.54 | 13.23 |
3 | 2.38 | 3.44 | 30.73 | 33.73 | 22.89 | 8.91 |
… | … | … | … | … | … | … |
287 | 1.74 | 2.77 | 30.89 | 27.46 | 17.68 | 13.08 |
288 | 1.72 | 2.77 | 30.71 | 27.46 | 17.69 | 13.06 |
289 | 1.75 | 2.65 | 31.01 | 28.11 | 17.24 | 13.57 |
… | … | … | … | … | … | … |
531 | 1.67 | 2.66 | 31.27 | 27.50 | 17.23 | 13.59 |
532 | 1.63 | 2.94 | 30.74 | 27.39 | 18.41 | 12.28 |
533 | 1.74 | 2.54 | 31.40 | 27.50 | 16.85 | 14.07 |
Table 11 Pareto partial solution set
序号 | ta/mm | tb/mm | bc/mm | hc/mm | FW/kg | FZ/mm |
---|---|---|---|---|---|---|
1 | 1.72 | 3.44 | 29.70 | 32.34 | 21.65 | 9.65 |
2 | 1.72 | 2.73 | 31.08 | 28.02 | 17.54 | 13.23 |
3 | 2.38 | 3.44 | 30.73 | 33.73 | 22.89 | 8.91 |
… | … | … | … | … | … | … |
287 | 1.74 | 2.77 | 30.89 | 27.46 | 17.68 | 13.08 |
288 | 1.72 | 2.77 | 30.71 | 27.46 | 17.69 | 13.06 |
289 | 1.75 | 2.65 | 31.01 | 28.11 | 17.24 | 13.57 |
… | … | … | … | … | … | … |
531 | 1.67 | 2.66 | 31.27 | 27.50 | 17.23 | 13.59 |
532 | 1.63 | 2.94 | 30.74 | 27.39 | 18.41 | 12.28 |
533 | 1.74 | 2.54 | 31.40 | 27.50 | 16.85 | 14.07 |
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