Buckling analysis of periodic elastic trusses by homogenization

This paper addresses the determination of buckling loads and mode shapes for periodic reticulated linear elastic structures. The study focuses on a family of ladder beams – 1D periodic structures with a frame unit cell – in the context of plane displacements. The method relies on the asymptotic homogenization of periodic discrete media. The discrete equilibrium equations are linearized around a prestressed configuration, and homogenized under a scale-separation assumption between the unit-cell size and the characteristic length of the mode amplitude variations. The original contributions are: (i) the ability to consider different stiffness ratios between the elements of the structure, (ii) the derivation of effective beam models whose parameters depend on the prestress, (iii) the consideration of both symmetric or asymmetric loadings, and (iv) formulations with mono- or multi-cell periodicity, enabling the identification of both short- and long-wavelength buckling modes. Experiments conducted on 3D-printed ladder beams confirmed the buckling modes and loads predicted by the analytical models. These models are also validated against finite element calculations. • Asymptotic homogenization adapted to buckling analysis of reticulated structures. • Derivation of buckling modes and shapes from linear analytical reduced models. • Consideration of stiffness contrasts, loading asymmetry, multi-cell periodicities. • Theoretical results for ladder beams validated numerically and experimentally.