Author Contributions
Conceptualization, Q.L.; methodology, X.L.; software, X.L.; validation, X.L. and Z.-X.Z.; formal analysis, Q.L.; investigation, X.L. and Z.-X.Z.; resources, Q.L. and G.-H.Z.; data curation, X.L.; writing—original draft preparation, Z.W.; writing—review and editing, Q.L.; visualization, Z.W.; supervision, H.-B.H.; project administration, X.H.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Research flow chart of paper.
Figure 1.
Research flow chart of paper.
Figure 2.
Bubble-generation device.
Figure 2.
Bubble-generation device.
Figure 3.
Schematic diagram of the coupling between the bubble and the flat plate structure.
Figure 3.
Schematic diagram of the coupling between the bubble and the flat plate structure.
Figure 4.
Comparison between simulation results and experimental results: (a) 0.41 ms; (b) 0.50 ms; (c) 0.76 ms; (d) 1.00 ms; (e) 1.04 ms; (f) 1.08 ms; (g)1.12 ms; (h) 1.14 ms; (i) 1.16 ms; (j) 1.20 ms.
Figure 4.
Comparison between simulation results and experimental results: (a) 0.41 ms; (b) 0.50 ms; (c) 0.76 ms; (d) 1.00 ms; (e) 1.04 ms; (f) 1.08 ms; (g)1.12 ms; (h) 1.14 ms; (i) 1.16 ms; (j) 1.20 ms.
Figure 5.
Comparison of jet height time course curves.
Figure 5.
Comparison of jet height time course curves.
Figure 6.
Schematic of the XOZ plane of the simulation model.
Figure 6.
Schematic of the XOZ plane of the simulation model.
Figure 7.
Symmetric model of double-layered cylindrical shells.
Figure 7.
Symmetric model of double-layered cylindrical shells.
Figure 8.
Ring rib structure model.
Figure 8.
Ring rib structure model.
Figure 9.
T-beam structural dimensions.
Figure 9.
T-beam structural dimensions.
Figure 10.
Pressure cloud of the explosion shock wave at different moments in case 2: (a) 0.2 ms; (b) 0.4 ms; (c) 0.6 ms; (d) 2.5 ms.
Figure 10.
Pressure cloud of the explosion shock wave at different moments in case 2: (a) 0.2 ms; (b) 0.4 ms; (c) 0.6 ms; (d) 2.5 ms.
Figure 11.
Pressure cloud of the explosion shock wave at different moments in case 2: (a) 0.4 ms; (b) 0.5 ms; (c) 0.7 ms; (d) 1.5 ms; (e) 4.0 ms; (f) 9.0 ms.
Figure 11.
Pressure cloud of the explosion shock wave at different moments in case 2: (a) 0.4 ms; (b) 0.5 ms; (c) 0.7 ms; (d) 1.5 ms; (e) 4.0 ms; (f) 9.0 ms.
Figure 12.
Stress and strain cloud of ring rib structure: (a) stress cloud diagram; (b) strain cloud diagram.
Figure 12.
Stress and strain cloud of ring rib structure: (a) stress cloud diagram; (b) strain cloud diagram.
Figure 13.
Equivalent plastic strain time course curve.
Figure 13.
Equivalent plastic strain time course curve.
Figure 14.
Equivalent stress time course curve.
Figure 14.
Equivalent stress time course curve.
Figure 15.
Damage pattern of double-stiffened cylindrical pressure-resistant shells: (a) case 1; (b) case 2; (c) case 3; (d) case 4; (e) case 5.
Figure 15.
Damage pattern of double-stiffened cylindrical pressure-resistant shells: (a) case 1; (b) case 2; (c) case 3; (d) case 4; (e) case 5.
Figure 16.
Damage pattern of non-pressure-resistant shells with double-stiffened cylindrical shells: (a) case 1; (b) case 2; (c) case 3; (d) case 4; (e) case 5.
Figure 16.
Damage pattern of non-pressure-resistant shells with double-stiffened cylindrical shells: (a) case 1; (b) case 2; (c) case 3; (d) case 4; (e) case 5.
Figure 17.
Plastic strain cloud of pressure-resistant shell: (a) case 1; (b) case 2; (c) case 3.
Figure 17.
Plastic strain cloud of pressure-resistant shell: (a) case 1; (b) case 2; (c) case 3.
Figure 18.
Plastic strain cloud of non-pressure-resistant shell: (a) case 1; (b) case 2; (c) case 3.
Figure 18.
Plastic strain cloud of non-pressure-resistant shell: (a) case 1; (b) case 2; (c) case 3.
Figure 19.
Plastic deformation of the ring rib structure in different cases: (a) case 1; (b) case 2; (c) case 3.
Figure 19.
Plastic deformation of the ring rib structure in different cases: (a) case 1; (b) case 2; (c) case 3.
Figure 20.
Comparison of plastic strain at reference point under different cases.
Figure 20.
Comparison of plastic strain at reference point under different cases.
Figure 21.
Schematic diagram of the numerical model for double-layer plate.
Figure 21.
Schematic diagram of the numerical model for double-layer plate.
Figure 22.
Schematic diagram of a bubble jet interacting with a flat plate at typical moments: (a) 6 ms; (b) 7 ms; (c) 8 ms; (d) 9 ms; (e) 49 ms; (f) 99 ms; (g) 129 ms; (h) 162 ms.
Figure 22.
Schematic diagram of a bubble jet interacting with a flat plate at typical moments: (a) 6 ms; (b) 7 ms; (c) 8 ms; (d) 9 ms; (e) 49 ms; (f) 99 ms; (g) 129 ms; (h) 162 ms.
Figure 23.
Stress propagation cloud of the upper plate structure under jet impingement: (a) 6 ms; (b) 7 ms; (c) 8 ms; (d) 9 ms.
Figure 23.
Stress propagation cloud of the upper plate structure under jet impingement: (a) 6 ms; (b) 7 ms; (c) 8 ms; (d) 9 ms.
Figure 24.
Velocity time range curves of Z-direction at the center point of the plate under different cases.
Figure 24.
Velocity time range curves of Z-direction at the center point of the plate under different cases.
Figure 25.
Time history curve of equivalent stress at the center point of the plate.
Figure 25.
Time history curve of equivalent stress at the center point of the plate.
Figure 26.
Time history curve of deflection at the reference point.
Figure 26.
Time history curve of deflection at the reference point.
Figure 27.
Time history curve of bubble radius variation.
Figure 27.
Time history curve of bubble radius variation.
Figure 28.
Schematic diagram of the numerical model for double-layer shell.
Figure 28.
Schematic diagram of the numerical model for double-layer shell.
Figure 29.
Motion of bubbles near the rupture in the cylindrical shell: (a) 3 ms; (b) 7 ms; (c) 12 ms; (d) 17 ms; (e) 27 ms; (f) 269 ms; (g) 379 ms; (h) 449 ms; (i) 519 ms; (j) 577 ms.
Figure 29.
Motion of bubbles near the rupture in the cylindrical shell: (a) 3 ms; (b) 7 ms; (c) 12 ms; (d) 17 ms; (e) 27 ms; (f) 269 ms; (g) 379 ms; (h) 449 ms; (i) 519 ms; (j) 577 ms.
Figure 30.
Contour plot of equivalent stress in the pressure-resistant shell at a typical moment: (a) 8 ms; (b) 9 ms; (c) 10 ms; (d) 11 ms.
Figure 30.
Contour plot of equivalent stress in the pressure-resistant shell at a typical moment: (a) 8 ms; (b) 9 ms; (c) 10 ms; (d) 11 ms.
Figure 31.
Contour plot of plastic strain in the pressure-resistant shell at a typical moment: (a) 8 ms; (b) 9 ms; (c) 11 ms; (d) 12 ms.
Figure 31.
Contour plot of plastic strain in the pressure-resistant shell at a typical moment: (a) 8 ms; (b) 9 ms; (c) 11 ms; (d) 12 ms.
Figure 32.
Time history curve of the deflection at the center point of the pressure-resistant shell.
Figure 32.
Time history curve of the deflection at the center point of the pressure-resistant shell.
Figure 33.
Time history curve of the Z-direction velocity at the center point of the pressure-resistant shell.
Figure 33.
Time history curve of the Z-direction velocity at the center point of the pressure-resistant shell.
Figure 34.
History of acceleration at midpoint over time.
Figure 34.
History of acceleration at midpoint over time.
Table 1.
TNT material parameters [
26].
Table 1.
TNT material parameters [
26].
Case | Material Parameters | Numerical Value |
---|
1 | A (Pa) | 3.7 × 1011 |
2 | B (Pa) | 3.2 × 109 |
3 | ρ (kg/m3) | 1630 |
4 | Explosive velocity (m/s) | 6930 |
5 | R1 | 4.15 |
6 | R2 | 0.95 |
7 | ω | 0.35 |
8 | e (J/kg) | 4.29 × 106 |
Table 2.
Material parameters of Q235 steel [
27].
Table 2.
Material parameters of Q235 steel [
27].
ρ (kg/m3) | E (MPa) | ε | σ0 (MPa) | Failure Strain |
---|
7800 | 2.10 × 105 | 0.3 | 235 | 0.23 |
Table 3.
Material parameters of air [
29].
Table 3.
Material parameters of air [
29].
Material | C0–C3, C6 | C4 | C5 | ) |
---|
air | 0 | 0.4 | 0.4 | 2.53 × 105 |
Table 4.
Parameters of the Equation of the state for water [
30].
Table 4.
Parameters of the Equation of the state for water [
30].
ρ (kg/m3) | C (m/s) | S1 | S2 | S3 |
---|
1000 | 1480 | 2.56 | 1.986 | 1.2268 |
Table 5.
Case settings.
| Case 1 | Case 2 | Case 3 | Case 4 | Case 5 |
---|
Equivalent/kg | 30 | 30 | 30 | 30 | 30 |
Distance/m | 0.2 | 0.5 | 1 | 2 | 3 |
Table 6.
Summary of damage patterns for double-layer cylindrical shells.
Table 6.
Summary of damage patterns for double-layer cylindrical shells.
Cases | Non-Pressure-Resistant Shell | Pressure-Resistant Shell |
---|
Case 1 | exhibits elongated petal-shaped ruptures with overall concave deformation | undergoes localized concave deformation |
Case 2 | exhibits elongated tear-shaped ruptures, accompanied by overall concave deformation | experiences localized concave deformation at its center |
Case 3 | displays symmetric tear-shaped ruptures, accompanied by overall concave deformation | undergoes localized concave deformation, with overall minor deformation |
Case 4 | undergoes overall concave deformation | experiences overall concave deformation |
Case 5 | experiences overall concave deformation | undergoes overall slight concave deformation |
Table 7.
Case settings.
| Case 1 | Case 2 | Case 3 |
---|
Charge weight/kg | 40 | 60 | 100 |
Distance/m | 3 | 3 | 3 |
Table 8.
Case settings.
| Case 1 | Case 2 | Case 3 |
---|
Equivalent/kg | 2 | 4 | 6 |
Distance/m | 0.6 | 0.6 | 0.6 |
Table 9.
Case settings.
| Case 1 | Case 2 | Case 3 | Case 4 |
---|
Equivalent/kg | 30 | 30 | 30 | 30 |
Distance/m | 1 | 1.5 | 2 | 2.5 |