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。
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.
出处
《计算数学》
CSCD
北大核心
2009年第3期275-286,共12页
Mathematica Numerica Sinica
基金
国家自然科学基金(10593053)
湖南省教育厅青年项目(06B003)
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(Rfj080203)
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
composites with random grains
expected displacement fields
homogenous method
homogenous displacement fields
