Homogenization of Periodically Heterogeneous Thin Beams

Abstract

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.

Keywords

Bernoulli-Navier model / Beam / Korn’s inequalities / Dimensional reduction / Homogenization

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