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摘要:
为分析运载火箭整流罩锥壳夹层结构不确定性对结构热稳定性的影响并指导结构的轻量化设计，建立整流罩前锥段夹层圆锥壳模型，并建立温度场模型，据此对圆锥壳开展热稳定性分析，推导力热联合载荷作用下整流罩前锥段夹层结构失稳临界轴压。在此基础上，针对主要不确定性因素，开展灵敏度分析并建立区间不确定性优化模型，采用区间可能度方法将其转化为确定性问题，并采用遗传算法-区间分析算法（GA-CIAM）实现结构优化设计。计算结果表明：考虑气动力/热载荷及材料参数不确定性影响，对整流罩前锥段结构开展优化设计，在满足设计要求的前提下，有效实现结构轻量化。
Abstract:In order to analyze the influence of uncertainty on the thermal stability of the launch vehicle fairing cone shell sandwich structure and to guide the lightweight design of the structure, a model of the fairing front cone section sandwich shell is established and a temperature field model is built, based on which the thermal stability analysis of the cone shell is carried out and the critical axial pressure under the combined force-thermal load is derived. For the primary uncertainty factors, interval uncertainty optimization models and sensitivity analyses are also produced. The interval probability approach is then used to convert these models into deterministic optimization problems, which are then resolved using the genetic algorithm-collocation interval analysis method (GA-CIAM) method. The calculation results show that considering the influence of aerodynamic/thermal load and material parameter uncertainty, the optimization design of the front cone section of the fairing can effectively realize the structural lightweight on the premise of meeting the design requirements.
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图 1 前锥段夹层结构参数化模型
Figure 1. Parameterized model of sandwich structure of the front cone section
表 1 设计变量设计空间及初值
Table 1. Design space and initial value of design variables
参数 面板厚度${t_{\rm{s}}}/{\text{mm} }$ 芯子厚度${t_{\rm{c}}}/{\text{mm} }$ 设计空间 $\left[ {0.5 ,3} \right]$ $\left[ {2,50 } \right]$ 初始值 1.5 18 
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表 2 不确定性变量上下界
Table 2. upper and lower bounds of uncertainty variables
不确定性变量 变量上下界 需用轴压载荷$F$/MN [14.25,15.75] 净吸收热流${q_0}$/（kW·m−2) [19,21] 热流作用时间$t$/s [142.5,157.5] 玻璃板弹性模量${E_{\rm{s}}}$/MPa [68400,75600] 泡沫夹层弹性模量${E_{\rm{c}}}$/MPa [66.5,73.5] 玻璃板比热容${c_{\rm{s}}}$/（kJ·(kg·K)−1） [1.425,1.575] 泡沫夹层比热容${c_{\rm{c}}}$/（kJ·(kg·K)−1） [1.188,1.313] 玻璃板导热率${k_{\rm{s}}}$/（kW·(m·K)−1） [3.04×10−4,
3.36×10−4]泡沫夹层导热率${k_{\rm{c}}}$/（kW·(m·K)−1） [2.85×10−5,
3.15×10−5]
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表 3 优化结果对比
Table 3. Comparison of optimization results
优化 设计变量/mm 结构质量/kg 临界轴压/MN 内壁温度/℃ 外壁温度/℃ 优化前 [2/18] 414.206 [21.676,24.826] [20.002,20.003] [572.055,611.647] 优化后 [1.600/16.500] 352.674 [14.230,18.087] [20.002,20.019] [603.321,769.212]
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表 4 不同可能度水平下不确定性优化结果
Table 4. Uncertainty optimization results under different possibility levels
可能度
水平$\lambda $最优设计变量$\left[ { {t_{\rm{s} } },{t_{\rm{c} } } } \right]/{\text{mm} }$ 优化后目标
函数值$M/{\text{kg}}$0.2 [1.520/15.759] 335.288 0.5 [1.387/18.314] 344.726 0.8 [1.600/16.500] 352.674 1.0 [1.765/15.765] 364.333
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