

Homogenization Analysis of Plane Structures with Three Dimensional Periodic Microstructures
Abstract
A rational homogenization method is presented for characterizing the in-plane material response for plane structures which have three dimensional periodic microstrcutures. This method is based upon the classical asymptotic expansion homogenization theory but with a novel multiscale displacement field expansion that is capable of reflecting the plane structure properties, i.e., the plane stress condition. Rigorous asymptotic expansion derivations yield the local unit cell problem. The in-plane material response is systematically computed via homogenization analysis of the local unit cell problem. The efficacy of the present method is verified by a numerical example.
Keywords
homogenization analysis; plane structure; three dimensional microstructures; periodicity; asymptotic expansionText