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| 一种颗粒随机分布复合材料弹性位移场均匀化方法的理论分析 | |
| 引用本文： | 李友云,崔俊芝,郑健龙.一种颗粒随机分布复合材料弹性位移场均匀化方法的理论分析[J].计算数学,2009,31(3):275-286. |
| 作者姓名： | 李友云 崔俊芝 郑健龙 |
| 作者单位： | 1. 道路结构与材料交通行业重点实验室,长沙,410004 2. LSEC,中国科学院,数学与系统科学研究院,计算数学研究所,北京,100190 3. 长沙理工大学交通运输工程学院,长沙,410077 |
| 基金项目： | 国家自然科学基金，湖南省教育厅青年项目，长沙理工大学道路结构与材料交通行业重点实验室开放基金资助项目 |
| 摘 要： | 针对计算随机颗粒分布复合材料弹性位移/力学场时,采用样本求力学性能期望值需要花费大量时间和内存的问题,给出了一种计算颗粒随机分布复合材料弹性位移场的均匀化方法,并且获得了均匀化位移场与期望位移场之间的一种理论误差.首先由复合材料的特性定义了均匀化理论的随机场和概率空间,然后结合单胞内颗粒随机分布复合材料的特性做了一些合理假设得到了在整个颗粒随机分布复合材料组成区域上的期望位移场与均匀化位移场之间的一种理论估计,最后对此法所具有的优点、适应范围,缺点、以及需要改进的地方做了进一步讨论. |
| 关 键 词： | 颗粒随机分布复合材料 期望位移场 均匀化方法 均匀化位移场 |
| 收稿时间： | 2008-04-27 |
HOMOGENOUS METHOD ANALYSIS FOR ELASTICITY DISPLACEMENT FIELDS OF COMPOSITES WITH RANDOM GRAINS |
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| Li Youyun,Cui Junzhi,Zheng Jianlong.HOMOGENOUS METHOD ANALYSIS FOR ELASTICITY DISPLACEMENT FIELDS OF COMPOSITES WITH RANDOM GRAINS[J].Mathematica Numerica Sinica,2009,31(3):275-286. | |
| Authors: | Li Youyun Cui Junzhi Zheng Jianlong |
| Institution: | 1. Key Laboratory of Road Stracture & Material of Ministry of Communications, Changsha 410004, China; 2. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China; 3. School of Highway Engineering, Changsha University of Science and Technology, Changsha 410077, China |
| Abstract: | In this paper, a homogenous method to solve the elasticity mechanics problem of the composites with random grains is presented to overcome the shortcoming of too much time and memory. At the same time, the error between the homogenous displacement fields and the expected displacement fields is also obtained. Firstly, based on the property of the composites with random grains, some probability spaces for the composites with random grain are introduced. Next, the error between the expected displacement fields and the homogenous displacement fields is obtained under some suppositions. Finally, some conclusion and some remarks are given to illustrate the validity of this method for the composites with random grains. |
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