随机复合材料统计多尺度边界元算法研究

热传输行为是空天飞行器热防护系统服役过程中的重要问题,研究随机复合材料的热传输机理,可为热防护系统材料与结构的一体化设计提供理论依据。针对随机复合材料的热传导问题,发展一种统计多尺度边界元算法,首先建立等效材料参数的统计多尺度分析模型,然后给出统计意义下等效参数的多尺度边界元预测算法,并通过与理论结果的对比来验证算法的有效性,最后研究微结构分布状态对陶瓷多孔材料等效导热系数的影响。结果表明:采用统计多尺度模型及多尺度边界元算法预测随机复合材料的热传导性能是有效的。

Research on Statistical Multiscale Boundary Element Algorithm for Random Composite Materials

Random Uncertainty is the inherent attribute of natural and engineering materials; the heat conduction behavior is one of the most important questions in servicing process of thermal protection system, and the research on the heat conduction problem of random materials can provide theoretical basis for integrative design of material and structure in thermal protection system. A novel statistical multiscale analysis method based on two-scale asymptotic expansions is proposed to predict heat conduction performances of random porous materials. The statistical multiscale formulations and statistical multiscale boundary element algorithm are brought forward. Besides, the validity of the proposed method by comparison with theoretical results was verified. Finally, the effect of microstructures on the macroscopic thermal properties for the porous ceramic materials is investigated. Numerical results prove the accuracy and efficiency of our method for multiscale simulation of heat conduction problem in random porous materials.