颗粒随机分布复合材料热传导问题均匀化方法的理论分析

Homogenous Method of Heat Transfer Problem of Composite Materials with Random Grains

针对区域内颗粒随机分布复合材料的热传导问题给出了一种均匀化理论计算温度场.首先根据复合材料的特性以及通过用多尺度方法预测复合材料热传导参数的要求定义了一些基本的概率空间,然后结合材料的物理特性做合理的假设得到了在整个随机复合材料区域上的期望温度场与均匀化温度场之间的一种理论估计,从而说明了此均匀化温度场可以作为预测此类随机颗粒分布复合材料期望温度场的理论基础.

In this paper,a homogenous method to solve the heat transfer problem of the composite materials with random grains is presented.Firstly,based on the property of the composite material with random grains,some probability spaces for the composite material with random grain are introduced and some properties in these spaces are proved.Next,the error estimation between the expected temperature field and the homogenous temperature field is obtained under some suppositions,Finally,some conclusion and some remarks are drawn to illustrate the validity of this method for the composite materials with random grains.