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

基于自洽平均微观力学W-T(Wakashima-Tsukamoto)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,以热应力作为输出,基于本征正交分解POD(Proper Orthogonal Decomposition)对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。结果表明,陶瓷材料的热导率和热膨胀系数不确定性对结构的热响应有很大的影响;将POD方法用于热应力时间历程预测能显著提高Kriging代理模型的精度和效率;提出的概率分析方法能够同时考虑多种随机因素对功能梯度材料热响应的影响,并验证了该方法的准确性和有效性,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。

A probabilistic thermo-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 structural analysis 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 thermal stress as outputs.The results show that the uncertainty of the thermal expansion coefficient and the thermal conductivity of the ceramic material have a significant effect on the thermal response of the structure;The use of the POD reduced order method for thermal stress prediction over time can significantly optimize the Kriging surrogate models;Meanwhile the proposed probabilistic analysis method can consider the effects of multiple random factors on the thermal response of functional gradient materials, and verifies the accuracy and validity of the method, which provides a reference for the design and sensitivity analysis improvement of functional gradient materials.