一种三维线弹性随机数值均化方法

doi:10.3969/j.issn.1001-2400.2016.04.017

西安电子科技大学学报 ›› 2016, Vol. 43 ›› Issue (4): 92-99.doi: 10.3969/j.issn.1001-2400.2016.04.017

一种三维线弹性随机数值均化方法

王南;马娟;张玉林

(西安电子科技大学机电工程学院，陕西西安 710071)

收稿日期:2015-04-20 出版日期:2016-08-20 发布日期:2016-10-12
作者简介:王南(1990-)，男，西安电子科技大学硕士研究生，E-mail：wangnan@stu.xidian.edu.cn．
基金资助:
国家自然科学基金青年基金资助项目(11102143)；西安电子科技大学留学回国人员择优资助项目(6450041101)

Random computational homogenization for three-dimensional linear elasticity

WANG Nan;MA Juan;ZHANG Yulin

(School of Mechano-electronic Engineering, Xidian Univ., Xi'an 710071, China)

Received:2015-04-20 Online:2016-08-20 Published:2016-10-12

摘要/Abstract

摘要：

对小变形下具有随机微观结构非均质材料的数值均化问题进行了研究．当考虑材料微观结构形态、各组分性质的随机性及相关性时，基于多尺度有限元方法和蒙特卡罗法，建立了非均质材料的随机均化模型．求出了不同边界条件下的随机有效量及其数字特征值以及有效量之间所具有的相关性．考察了随机微观结构参数对随机有效量以及表征体积单元中应力分布的影响．结果表明，在分析非均质材料的宏观有效力学性质时，考虑材料微观结构中客观存在的随机性和相关性非常重要．

Abstract:

The computational homogenization of heterogeneous materials under infinitesimal deformation is addressed in the context of elasticity when the uncertainty in microstructure is fully considered. Based on the multi-scale finite element method and Monte-carlo method, the random homogenization model of heterogeneous materials is established when the randomness of microstructural morphology and of material properties of constituents as well as the correlation of material properties are accounted for simultaneously. The random effective quantities and their numerical characteristics as well as their correlations under different boundary conditions are then found. And the impacts of microstructural parameters on random effective quantities are also investigated and illustrated. Finally, the random stress distributions within a representative volume element under different boundary conditions are revealed as well. Obviously, it is necessary that the randomness and correlation existing in the microstructure should be fully considered during the solution of the effective mechanical properties of heterogeneous materials.

Key words: homogenization, randomness and correlation, three-dimensional linear elasticity, finite element method, Monte-Carlo method

王南;马娟;张玉林. 一种三维线弹性随机数值均化方法[J]. 西安电子科技大学学报, 2016, 43(4): 92-99.

WANG Nan;MA Juan;ZHANG Yulin. Random computational homogenization for three-dimensional linear elasticity[J]. Journal of Xidian University, 2016, 43(4): 92-99.

参考文献

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一种三维线弹性随机数值均化方法

Random computational homogenization for three-dimensional linear elasticity

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