Application of the Homogenization Method to Beam Member with Periodic Structures

Abstract

A method to derive an equivalent beam model of a non-standard beam-like structure that possesses periodic microstructures is proposed based on the theory of homogenization. The fundamental equations of the Euler-Bernoulli beam is briefly reviewed, and a formal asymptotic expansion of the principle of virtual displacement is applied. The homogenized equation of a beam imbedding heterogeneity of structural constituent and the equation defining the characteristic deformation of the microstructure are derived. Then, the equivalent stiffness of the homogenized beam model is reasonably defined. A few examples of application of this proposed method are presented and the validity of this method is examined through an error estimation.