Homogenization of a space frame as a thick plate: Application of the Bending-Gradient theory to a beam lattice

The Bending-Gradient theory for thick plates is the extension to heterogeneous plates of Reissner-Mindlin theory originally designed for homogeneous plates. In this paper the Bending-Gradient theory is extended to in-plane periodic structures made of connected beams (space frames) which can be considered macroscopically as a plate. Its application to a square beam lattice reveals that classical Reissner-Mindlin theory cannot properly model such microstructures. Comparisons with exact solutions show that only the Bending-Gradient theory captures second order effects in both deflection and local stress fields.