Rapid prediction and optimization method for protective effectiveness of flexibly supported plate structure under underwater explosive
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摘要: 为实现柔性支撑板架结构在水下爆炸下防护效能的快速评估和设计优化，基于高置信度仿真，建立了水下爆炸作用下柔性支撑板架防护效能的评估方法并开展试验验证。采用验证后的高置信度仿真方法生成样本工况数据，并通过径向基神经网络模型构建能快速评估柔性支撑板架结构防护效能的代理模型。结合多岛遗传算法对建立的代理模型进行防护结构高防护效能和轻量化的多目标优化并获取最优结构参数。建立的快速预报与优化方法可以为相关的结构设计优化提供重要的技术支撑。Abstract: In order to make a rapid assessment and design optimization of the protective performance of flexibly supported plate structure subjected to underwater explosion, a high-confidence simulation method is first established for the protective performance of flexibly supported plate structure subjected to underwater explosion. Then, underwater explosion tests were conducted on the flexibly supported plate structure to validate the computational accuracy of the developed high-confidence simulation method by comparing the deformation between the simulation results and the experimental results. The thickness of the blast-facing panel, the thickness of the flexible supports, and the thickness of the stiffened web are identified as the three key characteristic parameters that affect the protective performance of the flexibly supported plate. Utilizing optimized Latin-hypercube sampling method, 15 sample conditions are extracted from the sample space. The validated high-confidence simulation method is then used to generate protective performance data for these 15 sample conditions, which is subsequently employed to construct a proxy model for rapid assessment of the protective performance of the flexibly supported plates by using a radial basis function (RBF) neural network. The accuracy of the proxy model is assessed by using 5 randomly selected conditions, and the results show that the prediction error is within 7%, indicating a high level of prediction accuracy. The multi-island genetic algorithm (MIGA) is applied to the proxy model to perform multi-objective optimization and obtain a pareto set of solutions. The condition with the maximum specific ultimate energy absorption per unit mass is selected as the optimal structural parameters for the flexibly supported plate, achieving the goals on enhancing the ultimate protective performance and reducing the total structural mass. The rapid prediction and optimization method developed in this study provides significant technical support for the design and optimization of flexibly supported plate, and ensures both effective protection and weight savings.
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图 2 迎爆面面板后弧形支撑板与T形筋分布
Figure 2. Distribution of the flexible support plate and T-shaped reinforcement behind the explosion facing panel
图 7 柔性支撑板架结构试验模型的仿真计算
Figure 7. Simulation calculation of test model for flexibly supported plate structure
表 1 钢材的J-C本构参数和失效参数设置[10]
Table 1. J-C constitutive and failure parameter settings for steel material[10]
A/MPa B/MPa n m C 破坏位移/μm 706 648 0.58 0 0.01 1 D1 D2 D3 D4 D5 ${\dot \varepsilon _{ {0}}} $/s−1 0.272 −0.073 −0.65 −0.003 0 1 
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表 2 柔性支撑板架结构各主要部分的极限吸能
Table 2. The ultimate energy absorption of the main parts of the flexibly supported plate structure on the ship’s side
柔性支撑板架结构主要部分 极限吸能/MJ 吸能占总能量比例/% 柔性支撑板架结构 112.21 100 迎爆面面板 52.85 47.1 水平弧形板 22.17 19.8 水平弧形板肘板 1.05 0.9 迎爆面T形筋腹板 10.40 9.3 迎爆面T形筋面板 2.75 2.5 背爆面面板 2.84 2.5
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表 3 Q355B钢的J-C本构参数与失效参数设置[12]
Table 3. J-C constitutive and failure parameter settings for Q355B steel[12]
A/MPa B/MPa n m C 破坏位移/μm 360 300 0.547 0 0.046 1 D1 D2 D3 D4 D5 $ {\dot \varepsilon _{ {0}}} $/s−1 −0.091 1.532 −0.091 0 0 1
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表 4 试验结果与高精度仿真结果比较
Table 4. Comparison between experimental results and high-precision simulation results
最大挠度 横向变形长度 垂向变形长度 仿真/m 实验/m 误差/% 仿真/m 实验/m 误差/% 仿真/m 实验/m 误差/% 0.241 0.233 3.4 1.358 1.342 1.2 2.565 2.546 0.7
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表 5 网格尺寸对于计算结果的影响
Table 5. The influence of grid size on calculation results
网格尺寸/mm 网格数量 结构总吸能/kJ 最大挠度 仿真/m 实验/m 误差/% 20 80094 1130 0.241 0.233 3.4 30 54459 1179 0.245 0.233 5.2 40 37334 1206 0.246 0.233 5.5
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表 6 样本点及计算结果
Table 6. Sample points and calculation results
抽样工况 tb/mm th/mm tfb/mm Et/MJ mt/t 1-1 26.57 9.71 4.00 199.2 79.6 1-2 23.71 6.29 12.00 151.2 72.7 1-3 24.86 5.71 4.57 189.9 72.3 1-4 22.57 8.57 5.14 162.2 69.5 1-5 27.71 4.57 6.86 207.5 78.9 1-6 26.00 8.00 8.57 180.3 78.4 1-7 24.29 12.00 6.29 164.1 77.0 1-8 23.14 5.14 8.00 163.4 68.9 1-9 29.43 6.86 9.71 208.1 85.9 1-10 30.00 7.43 5.71 226.8 86.3 1-11 28.29 10.86 7.43 198.5 85.8 1-12 27.14 4.00 10.86 189.1 78.4 1-13 28.86 10.29 11.43 189.5 88.1 1-14 25.43 11.43 10.29 160.2 80.6 1-15 22.00 9.14 9.14 140.0 70.1
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表 7 RBF代理模型在检验工况上的精度检测
Table 7. Accuracy detection of RBF proxy model in testing conditions
检验工况 tb/mm th/mm tfb/mm Et,d/MJ Et,f/MJ re/% 2-1 22 6 4 167.0 157.1 6.3 2-2 24 8 6 172.6 174.6 −1.2 2-3 26 12 12 157.6 163.2 −3.4 2-4 28 8 4 184.7 178.4 −3.5 2-5 30 4 8 224.3 213.7 −4.9
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表 8 优化得到的Pareto前沿解集
Table 8. Optimized Pareto frontier solution set
Pareto解集工况 tb/mm th/mm tfb/mm Et,d/MJ mt/t γ/(MJ·t−1) 3-1 27.76 4.01 5.32 214.7 78.00 2.75 3-2 24.66 4.33 4.51 191.0 70.63 2.70 3-3 28.45 5.31 4.04 220.9 79.58 2.78 3-4 26.62 5.57 4.06 207.2 76.19 2.72 3-5 25.50 5.96 4.99 193.3 74.19 2.61
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