TOPOLOGY OPTIMIZATION METHOD FOR INTEGRATED THERMAL PROTECTION STRUCTURE CONSIDERING TRANSIENT TEMPERATURE AND STRESS CONSTRAINTS
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摘要: 一体化热防护结构通常处于严酷的非稳态热环境, 热载荷作用的时间效应(即瞬态热效应)明显. 为了避免瞬态热分析的巨大计算消耗, 以往的一体化热防护结构优化设计研究通常将瞬态传热等效为相同热边界条件下的稳态传热, 将稳态传热分析的温度场作为设计热载荷. 然而, 已有的研究表明稳态传热无法准确等效瞬态传热的作用效果, 瞬态热效应对结构设计结果具有重要影响. 文章研究了考虑瞬态热效应的一体化热防护结构优化设计问题, 建立一种考虑瞬态温度和应力约束的一体化热防护结构拓扑优化方法. 该方法以SIMP (solid isotropic material with penalization) 法为基础, 构建两种针对一体化热防护结构的热弹性结构拓扑优化模型: (1)考虑材料体积分数、最大应力和底面最大温度约束, 以最小化结构应变能为目标的刚度设计模型; (2)考虑最大应力和底面最大温度约束, 以最小化材料体积分数为目标的轻量化设计模型. 通过求解瞬态热力耦合方程获得结构的热力耦合静力分析结果; 通过响应量在空间和时间域的凝聚积分函数表征结构响应在时域内的最大值, 并以此构建相应的约束和目标函数; 采用伴随法推导约束和目标函数的灵敏度表达式. 通过3个数值算例验证了本方法的有效性. 数值算例结果表明, 在瞬态传热条件下, 本方法能够准确反映瞬态热效应对一体化热防护结构设计结果的影响; 相比于基于稳态热分析的设计结果, 考虑瞬态热效应的设计结果具有更优的性能.Abstract: The integrated thermal protection structure is usually in a severe unstable thermal environment, and the time effect of thermal load, namely transient thermal effect, is obvious. In order to avoid huge calculation consumption of transient thermal analysis, previous optimization design studies of integrated thermal protection structures usually equivalent transient heat transfer to steady-state heat transfer under the same thermal boundary conditions, and take the temperature field of steady-state heat transfer analysis as the design thermal load. However, previous studies have shown that the steady-state heat transfer cannot accurately equivalent the effect of transient heat transfer, and the transient thermal effect has an important influence on the structural design results. In this paper, the optimization design problem of integrated thermal protection structure considering transient thermal effect is studied, and a topology optimization method of integrated thermal protection structure considering transient temperature and stress constraints is established. Based on the solid isotropic material with penalization (SIMP) method, two kinds of topology optimization models for integrated thermal protection structures are constructed: (1) the stiffness design model taking minimizing the structural strain energy as objective function, considering material volume fraction, maximum stress and maximum bottom-face temperature constraints; (2) the strength design model taking minimizing material volume fraction as objective function, considering maximum stress and maximum bottom-face temperature constraints. By solving the transient thermodynamic coupling equation, the thermodynamic coupling static analysis results of the structure are obtained. The maximum value of structural response in time domain is represented by the condensed integral function in space and time domains, which was taken as constraint and objective functions. The sensitivity expressions of objective function and constraint functions are derived by adjoint method. The effectiveness of the proposed method is verified by three numerical results. Numerical examples showed that the proposed method could accurately reflect the influence of transient thermal effects on the design results of integrated thermal protection structures under the condition of transient heat transfer. Compared with the design results based on steady-state thermal analysis, the design results considering transient thermal effects were significantly improved.
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图 1 受机−热载荷作用的一体化热防护结构
Figure 1. Integrated thermal protection structure under mechanical-thermal load
图 2 二维一体化承载−热防护结构优化模型
Figure 2. Optimization model of two-dimensional integrated thermal protection structure
图 3 稳态传热拓扑优化结果
Figure 3. Topology optimization results of steady-state heat transfer method
图 7 不同工作时间所得优化结果的性能分析
Figure 7. Analysis results of optimized structure obtained in different working times
图 8 轻量化设计结果及金属材料体积分数
Figure 8. Lightweight design results and metal material volume fraction
图 12 三维一体化承载−热防护结构优化模型
Figure 12. Optimization model of three-dimensional integrated thermal protection structure
图 16 本文方法优化结构的分析结果
Figure 16. Analysis of optimized structure obtained by proposed method
表 1 所用材料的属性列表
Table 1. Lists the properties of the materials used
Density/
(kg·m−1)Young’s
modulus/
GPaPoisson’s
ratioThermal
conductivity/
(W·m−1·°C−1)Heat
capacity/
(J·°C−1·kg−1)CTE/
K−1mat-1 4620 96 0.36 21.9 522 ${\text{9} }{\text{.4} } \times {\text{1} }{ {\text{0} }^{ {{-6} } } }$ mat-2 50 0.0001 0.36 0.15 942 0 
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表 2 优化结果瞬态热力耦合分析
Table 2. Transient thermodynamic coupling analysis of optimization results
Performance Method tf = 1800 s tf = 2400 s tf = 3600 s strain energy method 1 50.23 51.86 53.52 proposed method 45.17 46.95 48.57 σMax/MPa method 1 50.1 50.5 48.6 proposed method 46.0 46.0 46.0 TBFSMax/°C method 1 68.6 98.2 159.8 proposed method 59.8 84.4 137.9
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表 3 优化结果瞬态热力耦合分析
Table 3. Transient thermodynamic coupling analysis of optimization results
Performance Method tf = 1800 s tf = 2400 s tf = 3600 s volume fraction method 1 0.232 0.232 0.232 proposed method 0.179 0.216 0.251 σMax/MPa method 1 42.78 48.1 52.6 proposed method 46.0 46.0 46.0 TBFSMax/°C method 1 45.55 66.2 108.5 proposed method 56.64 76.0 102.7
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表 4 优化结果瞬态热力耦合分析
Table 4. Transient thermodynamic coupling analysis of optimization results
Strain energy σMax/MPa TBFSMax/°C method 1 26.45 50.50 55.1 proposed method 25.31 46.0 58.4
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