Elastic Plate Deformation with Transverse Variation of Microrotation

TL;DR

This paper introduces a new mathematical model for thin Cosserat elastic plates that incorporates transverse microrotation variation, extending classical plate theories with polynomial approximations and a variational approach.

Contribution

It develops a generalized Cosserat plate theory considering transverse microrotation variation, providing a complete and unique solution framework.

Findings

Model accounts for transverse microrotation variation.

Polynomial approximations ensure consistency with physical laws.

Proved solution uniqueness for boundary value problems.

Abstract

The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse variation of microrotation of the plates. The model assumes polynomial approximations over the plate thickness of asymmetric stress, couple stress, displacement, and microrotation, which are consistent with the elastic equilibrium, boundary conditions and the constitutive relationships. Based on the generalized Hellinger-Prange -Reissner variational principle and strain-displacement relation we obtain the complete theory of Cosserat plate. We also proved the solution uniqueness for the plate boundary value problem.