A New Analytical Prediction for Energy Responses of Hemi-Cylindrical Shells to Explosive Blast Load
Abstract
:1. Introduction
2. Systems of Motion
2.1. Frequency Analysis
2.2. Relationship between Energy and Position
2.3. Energy Analysis of the Damping Load
2.4. Pressure Load
2.5. Numerical Verification
3. Numerical Simulations
3.1. Simulation Model
3.2. Natural Frequencies and Corresponding Mode Shapes
3.3. Global Energy
3.4. Displacement
3.5. The Velocity of the Air Part
4. Parametric Analyses
4.1. Displacement Analysis
4.2. Total Energy vs. Thickness
4.3. Decrease Ratio vs. Thickness
4.4. The Analysis of Elastic Modulus
4.5. Material Parameters
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Density of Mesh (m) | 2.0 | 1.0 | 0.8 | 0.5 | 0.3 | 0.2 | 0.1 |
Total Energy (104 J) | 4.52 | 4.21 | 3.93 | 3.90 | 3.89 | 3.89 | 3.88 |
Max Displacement (mm) | 82 | 73 | 70 | 69 | 68 | 67 | 67 |
0.010 | 0/4 with x = 0 R = 5 L = 30 | 6.2 | 3.87 | 1/4 with x = 0 R = 5 L = 30 | 12 | 3.74 | 2/4 with x = 0 R = 5 L = 30 | 12.5 | 3.93 | 2/4 with x = 0 R = 7.5 L = 30 | 9.9 | 3.89 |
0.015 | 4.1 | 2.53 | 8.1 | 2.46 | 8.25 | 2.59 | 6.6 | 2.59 | ||||
0.020 | 3.2 | 2.03 | 6.2 | 2.04 | 6.31 | 2.16 | 4.9 | 1.94 | ||||
0.025 | 2.5 | 1.44 | 4.8 | 1.72 | 4.94 | 1.89 | 4.0 | 1.55 | ||||
0.030 | 2.0 | 0.87 | 3.9 | 0.77 | 4.03 | 0.83 | 3.3 | 1.26 | ||||
0.040 | 1.5 | 0.69 | 2.9 | 0.65 | 2.94 | 0.69 | 2.3 | 0.86 | ||||
0.060 | 1.0 | 0.38 | 2.0 | 0.39 | 1.96 | 0.38 | 1.5 | 0.33 | ||||
0.100 | 0.6 | 0.24 | 1.2 | 0.24 | 1.25 | 0.24 | 1.0 | 0.23 | ||||
0.200 | 0.3 | 0.12 | 0.6 | 0.13 | 0.59 | 0.12 | ||||||
0.500 | 0.1 | 0.02 | 0.2 | 0.03 | 0.19 | 0.03 |
0.010 | 0/4 with ×2.5 R = 5 | 5.2 | 1.6 | 5.12 | 0.38 | 1/4 with ×2.5 R = 5 | 9.8 | 3.6 | 4.46 | 0.32 | 2/4 with ×0.0 R = 7.5 | 9.9 | 3.89 |
0.015 | 3.2 | 1.4 | 3.35 | 0.26 | 5.9 | 3.4 | 3.57 | 0.28 | 6.6 | 2.59 | |||
0.020 | 2.0 | 1.5 | 2.95 | 0.32 | 4.1 | 3.0 | 3.01 | 0.25 | 4.9 | 1.94 | |||
0.025 | 1.6 | 1.2 | 1.74 | 0.24 | 3.1 | 2.5 | 1.81 | 0.24 | 4.0 | 1.55 | |||
0.030 | 0.8 | 1.5 | 1.30 | 0.37 | 2.4 | 2.4 | 1.86 | 0.27 | 3.3 | 1.26 | |||
0.040 | 0.8 | 0.9 | 1.24 | 0.15 | 1.6 | 1.9 | 1.41 | 0.17 | 2.3 | 0.86 | |||
0.060 | 0.6 | 0.6 | 1.07 | 0.13 | 1.3 | 1.1 | 1.18 | 0.13 | 1.5 | 0.33 | |||
0.100 | 0.3 | 0.5 | 1.11 | 0.17 | 0.6 | 0.9 | 1.07 | 0.16 | 1.0 | 0.23 |
910 | Case 1 0.23 Z = 0/4 × 0.0 | 1.89 | 3.29 | Case 2 0.13 Z = 0/4 × 0.0 | 1.91 | 3.28 | Case 3 0.07 Z = 2/4 × 2.5 | 3.37 | 3.25 | 5.28 | 0.30 |
470 | 3.46 | 3.45 | 3.52 | 3.45 | 2.11 | 5.09 | 3.53 | 0.61 | |||
210 | 6.16 | 3.82 | 5.91 | 3.86 | 10.8 | 6.41 | 3.73 | 0.55 | |||
170 | 6.76 | 4.01 | 7.26 | 3.95 | 12.7 | 7.19 | 3.10 | 0.46 | |||
140 | 7.81 | 4.29 | 8.25 | 4.53 | 12.2 | 7.34 | 4.40 | 0.52 | |||
70 | 10.2 | 4.55 | 11.7 | 4.62 | 13.0 | 7.82 | 5.65 | 0.37 | |||
40 | 11.8 | 4.29 | 11.7 | 4.42 | 11.5 | 9.13 | 6.78 | 0.31 | |||
10 | 14.3 | 4.31 | 13.8 | 4.37 | 8.64 | 14.6 | 19.7 | 0.05 |
(ton/m3) | 10 | 7.8 | 4.0 | 2.0 | 1.0 | 0.6 | 0.3 |
(104 J) | 1.94 | 2.13 | 2.31 | 2.31 | 2.18 | 1.95 | 1.80 |
4.62 | 3.84 | 2.18 | 1.16 | 1.73 | 2.33 | 3.53 |
(ton/m3) | 10 | 7.8 | 4.0 | 2.0 | 1.0 |
(104 J) | 5.62 | 6.08 | 7.52 | 7.86 | 8.21 |
4.63 | 3.76 | 3.12 | 1.48 | 2.75 | |
/ | / | 0.12 | 0.03 | 0.06 |
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Liu, P.; Xu, N.; Pan, Z.-H. A New Analytical Prediction for Energy Responses of Hemi-Cylindrical Shells to Explosive Blast Load. Buildings 2019, 9, 168. https://doi.org/10.3390/buildings9070168
Liu P, Xu N, Pan Z-H. A New Analytical Prediction for Energy Responses of Hemi-Cylindrical Shells to Explosive Blast Load. Buildings. 2019; 9(7):168. https://doi.org/10.3390/buildings9070168
Chicago/Turabian StyleLiu, Ping, Ning Xu, and Zhi-Hong Pan. 2019. "A New Analytical Prediction for Energy Responses of Hemi-Cylindrical Shells to Explosive Blast Load" Buildings 9, no. 7: 168. https://doi.org/10.3390/buildings9070168