Elastic Plates Motions with Transverse Variation of Microrotation

TL;DR

This paper introduces a new dynamic model for thin Cosserat elastic plates that incorporates transverse microrotation variation, extending classical plate theories to include microstructure effects.

Contribution

It develops a generalized dynamic theory for Cosserat plates considering transverse microrotation and microinertia, based on a polynomial approximation and variational principles.

Findings

Model captures transverse microrotation effects in elastic plates

Derives complete dynamic equations for Cosserat plates

Provides a basis for analyzing microstructured elastic materials

Abstract

The purpose of this paper is to present a new mathematical model for the dynamics of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner-Mindlin plate theory, takes into account the transverse variation of microrotation and corresponding microintertia of the the elastic 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 for the dynamics and strain-displacement relation we obtain the complete dynamic theory of Cosserat plate. Key words: Cosserat materials, elastic plates, transverse microrotation, variational principle, elastodynamics