Nonlinear Analysis of Plates with Rotation Gradient–Dependent Potential Energy for Constrained Microrotation

Abstract

In this study, the weak-form finite-element model has been developed for bending of plates considering the rotation gradient–dependent potential energy along with the conventional strain energy in the case of moderate rotation for Cosserat solid. The microrotation of the material point is considered to be constrained with the macrorotation of the continua. First, the governing equations are obtained from the principle of virtual displacements considering the displacement field as general power (Taylor) series expansion about the displacement of the midplane of the plate, and then the formulations are specialized for the general third-order, first-order, and the classical plate theory. The nonlinear finite-element models have been developed for all the plate theories considered. Further, the analytical solution for a simply supported linear plate is presented. In the numerical examples, the stiffening and anisotropic effects in response to oriented microstructures in the continuum of a microplate are illustrated. The parametric effect of the material length scale on the various components of stress is also studied.