A Nonclassical Model for Circular Mindlin Plates Based on a Modified Couple Stress Theory

Abstract

A nonclassical model for circular Mindlin plates subjected to axisymmetric loading is developed using a modified couple stress theory. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation based on Hamilton's principle. The new model contains a material length scale parameter and can capture the size effect, unlike existing circular Mindlin plate models based on classical elasticity. In addition, both the stretching and bending of the plate are considered in the formulation. The current plate model reduces to the classical elasticity-based Mindlin plate model when the material length scale parameter is set to be zero. Additionally, the new circular Mindlin plate model recovers the circular Kirchhoff plate model as a special case. To illustrate the new model, the static bending problem of a clamped solid circular Mindlin plate subjected to an axisymmetrically distributed normal pressure is analytically solved by directly applying the new model and using the Fourier–Bessel series. The numerical results show that the deflection and rotation angle predicted by the new model are smaller than those predicted by the classical Mindlin plate model. It is further seen that the differences between the two sets of predicted values are significantly large when the plate thickness is small, but they are diminishing with the increase of the plate thickness.