Enhanced mathematical model for Cosserat plate bending

The purpose of this paper is to present a bending plate model, which assumes physically and mathematically motivated approximations over the plate thickness for asymmetric stress, couple stress, displacement, and microrotation. The approximations are consistent with the three-dimensional Cosserat elasticity equilibrium equations, boundary conditions and the constitutive relationships. Based on the generalized Hellinger–Prange–Reissner variational principle for Cosserat materials and the proposed strain–displacement relation, we formulate the Cosserat bending plate variational principle. This principle allows us to obtain the equilibrium equations, constitutive relations and optimal value for the minimization of the elastic energy with respect to the splitting parameter in the approximation of the σ33σ33 stress component. The obtained solution is proved to be unique. The preliminary computations for a plate bending produce a relative error of the order 1% in comparison with the exact three-dimensional solution. The results are compatible with the precision of the well-known Reissner model used for bending of simple elastic plates. The low relative error is stable with respect to the standard range of the plate thickness.

► We present new stress and kinematic approximations over the plate thickness.
► We formulate the Cosserat bending plate variational principle using the splitting parameter.
► The plate model produces less than 1% relative error in comparison with exact 3-D solutions.
► The low relative error is stable with respect to the standard range of the plate thickness.