THE REISSNER–MINDLIN PLATE IS THE Γ-LIMIT OF COSSERAT ELASTICITY
Patrizio Neff, Kwon‐Il Hong, Jena Jeong · Mathematical Models and Methods in Applied Sciences · 2010
The linear Reissner–Mindlin membrane-bending plate model is the rigourous Γ-limit for zero thickness of a linear isotropic Cosserat bulk model with symmetric curvature. For this result we use the natural nonlinear scaling for the displacements u and the linear scaling for the infinitesimal microrotations Ā ∈ 𝔰𝔬(3). We also provide formal calculations for other combinations of scalings by retrieving other plate models previously proposed in the literature by formal asymptotic methods as corresponding Γ-limits. No boundary conditions on the microrotations are prescribed.