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

Arthur Lebée (1) , Karam Sab (1)

1 msa - Matériaux et Structures Architecturés

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.

Domaines: Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Mécanique des structures [physics.class-ph]; Physique [physics]; Mécanique [physics]; Mécanique des structures [physics.class-ph]

Arthur Lebée, Karam Sab. Homogenization of a space frame as a thick plate: Application of the Bending-Gradient theory to a beam lattice. Computers & Structures, 2013, pp.88-101. ⟨hal-00938967⟩