Effective Flexibility Calculation for Beams with Periodic In-Homogeneities

Abstract

Analysis of structures including periodically arrayed in-homogeneities, whether they are microscopic or macroscopic, can be simplified by using homogenized properties. If the unit structure is repeated in a longitudinal direction, the whole structure may be regarded as a beam with effective flexibility. This study proposes a kinematical periodicity constraint to be imposed on the FE model of the unit structure for beams, which improves the accuracy of the effective flexibility along with reduction of the model size. The method is applied to a beam-in-space containing repetitive un-symmetric holes, and it is demonstrated that the deformation behavior of the homogenized beam agrees well with that of the real structure.