Journal of Applied Mathematics
Volume 2012 (2012), Article ID 526846, 15 pages
Research Article

A Simple Circular Cell Method for Multilevel Finite Element Analysis

1Bauhaus-University Weimar, Marien-Str. 15, 99423 Weimar, Germany
2Department of Civil, Environmental and Architectural Engineering, Korea University, 5 Ga 1, Anamdong, Seongbuk-gu, Seoul 136-701, Republic of Korea
3Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
4Civil Engineering School and Grupo de Ciencias de la Tierra y el Ambiente, Universidad de Cuenca, Av. 12 de Abril s/n., Cuenca, Ecuador

Received 24 October 2011; Accepted 23 February 2012

Academic Editor: Zhilong L. Huang

Copyright © 2012 Hossein Talebi 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.


A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.