The Reissner-Mindlin plate is the Y-limit of Cosserat elasticity
The Reissner-Mindlin plate is the Y-limit of Cosserat elasticity
- Mathematical Models and Methods in Applied Sciences, 20(09), p.1553-1590, 2010 .
The linear Reissner-Mindlin membrane-bending plate model is the rigourous ?-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 A ? 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 ?-limits. No boundary conditions on the microrotations are prescribed.
COSSERAT ELASTICITY
The linear Reissner-Mindlin membrane-bending plate model is the rigourous ?-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 A ? 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 ?-limits. No boundary conditions on the microrotations are prescribed.
COSSERAT ELASTICITY