Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 585624, 19 pages
http://dx.doi.org/10.1155/2011/585624
Research Article

Finite Element Analysis with Iterated Multiscale Analysis for Mechanical Parameters of Composite Materials with Multiscale Random Grains

Youyun Li,1,2 Yuqing Pan,1 Jianlong Zheng,1 Chiqing Zhou,1 and Desheng Wang3

1School of Traffic and Transportation Engineering, Changsha University of Science and Technology, Hunan 410004, China
2State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
3Division of Mathematical Sciences, School of Physical and Mathematical Science (SPMS), Nanyang Technological University, 21 Nanyang Link, Singapore 637371

Received 11 August 2010; Revised 22 December 2010; Accepted 17 March 2011

Academic Editor: Moran Wang

Copyright © 2011 Youyun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based on the iterated statistically multiscale analysis (SMSA), we present the convergence of the equivalent mechanical parameters (effective moduli), obtain the error result, and prove the symmetric, positive and definite property of the equivalent mechanical parameters tensor computed by the finite element method. The numerical results show the proved results and illustrate that the SMSA-FE algorithm is a rational method for predicting the equivalent mechanical parameters of the composite material with multiscale random grains. In conclusion, we discuss the future work for the inhomogeneous composite material with multiscale random grains.