Damage effects of clamped square plates by near-field underwater explosion with complex boundary conditions
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摘要: 近场水下爆炸会产生复杂的载荷模式，而复杂的边界条件使结构在近场水下爆炸作用下的毁伤形态更加难以预测。因此，采用耦合的欧拉-拉格朗日算法探究了水下爆炸气泡在多边界耦合作用下（自由面、弹塑性板、泥沙边界）的演化过程及其对固支方板的毁伤效应。首先，开展了2.5 g TNT在不同尺寸（板边长为0.46、0.92和1.61倍最大气泡直径）固支方板底部10 cm起爆的水下爆炸试验，验证了有限元方法的准确性。然后，结合试验和有限元结果分析了不同边界条件下板的毁伤机理。最后，通过系列数值模拟发现：随着板尺寸和爆距的增大，气泡会出现溃散、下射流和上射流3种不同的演化方式；随着板尺寸的增大，爆距对板中心最终变形的影响减小；泥沙边界能减缓气泡收缩，使气泡从中部塌陷形成方向相反的对射流，降低固支方板的位移和应变，对于气泡提前溃散的工况，泥沙边界基本无影响。Abstract: Near-field underwater explosion produces complex loading patterns, and complex boundary conditions make the damage patterns of structures under near-field underwater explosion more difficult to predict. Thus, the investigation on the evolution of underwater explosion bubbles and the damage effects on the clamped square plates with the coupling of multi-boundary (free surface, elastoplastic plates and sediment boundary) was conducted using the coupled Eulerian-Lagrangian (CEL) method. Firstly, to verify the accuracy of the finite element method, underwater explosion tests were performed 10 cm under the bottom of the clamped square plates in different dimensions (the side lengths of the plates were 0.46, 0.92 and 1.61 times the maximum bubble diameter) using 2.5 g TNT. Then, the damage mechanism of the clamped square plates was analyzed by combining the test and finite element results. Finally, a series of numerical simulations reveal that with increasing plate dimension and stand-off distance, bubbles show three different evolution modes: collapse, downward jet, and upward jet. With increasing plate dimension, the effects of stand-off distance on the final deformation of the plate center decreases. The sediment boundary can alleviate the bubble shrinkage, make the bubble firstly collapse from the middle to form jets in the opposite direction, and reduce the displacement and strain of the clamped square plates. The sediment boundary has no effects when the bubbles collapse in advance.
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图 1 耦合欧拉-拉格朗日方法的求解过程
Figure 1. The solution procedure of the coupled Eulerian-Lagrangian method
图 4 不同网格尺寸下距药包中心不同距离处的冲击波峰值压力对比
Figure 4. Comparison of peak shock wave pressures at different distances from the charge center under different element sizes
图 5 TNT在20 cm×20 cm板底起爆引起的气泡演化
Figure 5. Evolution images of bubbles caused by the explosion of a TNT charge at the bottom of the 20 cm×20 cm plate
图 6 TNT在40 cm×40 cm板底起爆引起的气泡演化
Figure 6. Evolution images of bubbles caused by explosion of the TNT charge at the bottom of the 40 cm×40 cm plate
图 7 TNT在70 cm×70 cm板底起爆引起的气泡演化
Figure 7. Evolution images of bubbles caused by the explosion of a TNT charge at the bottom of the 70 cm×70 cm plate
图 16 固支方板的最终毁伤特征曲线
Figure 16. Final damage characteristic curves of clamped square plates
图 17 气泡的演化过程（μ=0.46, da=10 cm）
Figure 17. The evolution process of bubbles (μ=0.46, da=10 cm)
图 18 气泡的演化过程（μ=1.38, da=1 cm）
Figure 18. The evolution process of bubbles (μ=1.38, da=1 cm)
图 19 吃水深度对板动态响应的影响
Figure 19. Effects of draught depth on the dynamic responses of the plates
图 20 泥沙边界对气泡演化的影响（μ=0.46）
Figure 20. Effects of sediment boundaries on bubble evolution (μ=0.46)
图 21 泥沙边界对气泡演化的影响（μ=1.38）
Figure 21. Effects of sediment boundaries on bubble evolution (μ=1.38)
图 23 泥沙边界对板动态响应的影响
Figure 23. Effects of sediment boundaries on dynamic responses of plates
表 1 试验工况
Table 1. Test conditions
工况 药包质量/g 爆距/cm L/cm l/cm 厚度/mm 1 2.5 10 70 60 2 2 2.5 10 40 30 2 3 2.5 10 20 10 2 
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表 2 数值模拟工况设置
Table 2. Numerical simulation condition settings
工况 方板尺寸 μ 方板爆距/cm γ 1 20 cm×20 cm 0.46 10 0.46 2 15 0.69 3 20 0.92 4 25 1.15 5 30 1.38 6 40 cm×40 cm 0.92 10 0.46 7 15 0.69 8 20 0.92 9 25 1.15 10 30 1.38 11 50 cm×50 cm 1.15 10 0.46 12 15 0.69 13 20 0.92 14 25 1.15 15 30 1.38 16 60 cm×60 cm 1.38 10 0.46 17 15 0.69 18 20 0.92 19 25 1.15 20 30 1.38 21 70 cm×70 cm 1.61 10 0.46 22 15 0.69 23 20 0.92 24 25 1.15 25 30 1.38
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表 3 吃水深度工况设置
Table 3. Settings of draught depth
工况 方板尺寸 μ da/cm 1 20 cm×20 cm 0.46 0 2 1 3 3 4 5 5 10 6 60 cm×60 cm 1.38 0 7 1 8 3 9 5 10 10
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表 4 泥沙边界工况设置
Table 4. Sediment boundary condition settings
工况 方板尺寸 μ 药包距泥沙边界距离/cm λ 1 20 cm×20 cm 0.46 10 0.46 2 20 0.92 3 30 1.38 4 40 1.84 5 60 cm×60 cm 1.38 10 0.46 6 20 0.92 7 30 1.38 8 40 1.84
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