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.

A Transversely Isotropic Magneto-Electro-Elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect

“…(15b-d), (24b-e) and (25b-d). The coupled high-order ordinary differential equations (ODEs) are not easy to solve by direct integration because the solutions containing modified Bessel functions are usually very complicated [27,32,33].…”

“…Considering the difficulties in determining additional material parameters and the physical interpretation of the microstructure, these modified theories have been successfully employed to develop non-classical beam and plate models [19,[25][26][27][28][29].…”

A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects

“…It should be mentioned that the last two terms in the virtual work expression in equation (2.25) account for the contribution of the normal stress on the top and bottom plate surfaces σ ± 33 (=±τ ± 3α,α from the equilibrium equations in equation (2.8a)), which is neglected in the Mindlin plate models that do not consider the surface energy effect (e.g. [22,34]).…”

Magnetic field effect on free vibration of smart rotary functionally graded nano/microplates: A comparative study on modified couple stress theory and nonlocal elasticity theory

“…Tsiatas (2009) represented a new Kirchhoff plate model based on MCST for a microplate with general boundary conditions. Zhou and Gao (2014) utilized MCST to represent a non-classical model for circular Mindlin plates. Reddy and Berry (2012) investigated microstructure-dependent axisymmetric bending of FGM circular plates based on MCST.…”