| 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 |
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| 引用本文： | 李友云,向子权,郑健龙,崔俊芝.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[J].应用数学学报,2010,33(4). |
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| 作者姓名： | 李友云 向子权 郑健龙 崔俊芝 |
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| 作者单位： | 1. 长沙理工大学交通运输工程学院,长沙,410004
2. 中国科学院数学与系统科学研究院,北京,100190 |
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| 基金项目： | 国家自然科学基金，教育部归国人员启动基金 |
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| 摘 要： | 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.
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| 关 键 词： | 半随机分布复合材料 热传导均匀化参数 均匀化方法 期望温度场 均匀化温度场 |
Homogenous Method of Heat Transfer Problem of Composite Materials with Random Grains |
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| LI YOUYUN,XIANG ZIQUAN,ZHENG JIANLONG,CUI JUNZHI.Homogenous Method of Heat Transfer Problem of Composite Materials with Random Grains[J].Acta Mathematicae Applicatae Sinica,2010,33(4). |
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| Authors: | LI YOUYUN XIANG ZIQUAN ZHENG JIANLONG CUI JUNZHI |
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| Institution: | LI YOUYUN XIANG ZIQUAN ZHENG JIANLONG (School of traffic and transportation engineering,Changsha University of Science and Technology,Changsha 410004) CUI JUNZHI (Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing 100190) |
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| Abstract: | 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... |
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| Keywords: | random grains homogenous coefficent homogeneization method expected temperature field homogenous temperature field |
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