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| 功能梯度材料结构热力耦合概率分析方法 |
| Probabilistic analysis method of thermos-mechanical coupling of functional gradient materials structure |
| 投稿时间：2021-01-20 修订日期：2021-06-01 |
| DOI： |
| 中文关键词: 功能梯度材料 热响应 不确定性 概率分析 代理模型 降阶模型 |
| 英文关键词:Functional gradient Thermal response Uncertainty Probabilistic analysis Surrogate model Reduced order model |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 功能梯度材料是一种先进的复合材料，其材料成分随空间位置连续变化，在热障涂层、高超飞行器热结构与热防护系统等领域有着重要的应用。由于制造过程中存在着大量的误差和不确定性，使得材料的物理参数、几何参数以及载荷等均具有不确定性，从而导致功能梯度材料结构的热响应具有很强的随机性，这给工程设计和可靠性评估带来了很大的挑战。因此，本文基于自洽平均微观力学(Wakashima-Tsukamoto，W-T)模型和拉丁超立方抽样，建立一种功能梯度平板热力耦合概率分析方法。以材料物理属性和空间分布的不确定性随机参数作为概率分析的输入，以温度和热应力作为输出，基于本征正交分解(Proper Orthogonal Decomposition, POD)对温度和热应力的随机时间历程进行变量减缩，进而构建Kriging代理模型。算例结果表明：陶瓷材料的空间分布幂指数和热导率不确定性对结构的热响应有很大的影响；Kriging代理模型能够准确地预测具有不确定性功能梯度材料的温度；将POD方法用于热应力时间历程预测能显著优化Kriging代理模型的精度，为功能梯度材料及其结构的设计和灵敏度分析提供了参考。 |
| 英文摘要: |
| Functionally graded materials (FGMs) are advanced composites with material compositions varying continuously as a function of spatial position, which are widely used for thermal barrier coatings, thermal structures and thermal protection system for hypersonic vehicles. It is always a great challenge for engineering design and reliability assessment for FGMs since there are numerous uncertainties in the manufacturing and service process, which result in a strong randomness in the thermal response of the high-temperature structure. Therefore, a probabilistic thermos-mechanical coupling analysis tool based on the self-consistent mean micromechanical (Wakashima-Tsukamoto, W-T) model and Latin hypercube sampling is proposed in this paper. The Kriging surrogate model for thermal analysis and the Proper Orthogonal Decomposition (POD) reduced-order Kriging model for prediction of structural analysis results are constructed by using uncertain random parameters to describe the physical properties and spatial distribution of the material as inputs to the probabilistic analysis and the temperature and thermal stress as outputs. The results show that the uncertainty of the power exponent of spatial distribution and the thermal conductivity of the ceramic material have a significant effect on the thermal response of the structure; The Kriging surrogate model can accurately predict the temperature of materials. Meanwhile the use of the POD reduced order method for thermal stress prediction over the time history can significantly optimize the accuracy of Kriging surrogate models. It provides a reference for functional gradient material design and sensitivity analysis improvement. |
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