A Non-Classical Model for Circular Mindlin Plates Incorporating Microstructure and Surface Energy Effects

A new non-classical model for circular Mindlin plates is developed using a modified couple stress theory, a surface elasticity theory and Hamilton's principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation, and the microstructure and surface energy effects are treated in a unified manner. The new plate model contains a material length scale parameter to account for the microstructure effect and three surface elasticity constants to describe the surface energy effect. The current non-classical model includes the plate models considering the microstructure influence only and the surface energy effect alone as special cases, and it recovers the classical elasticity-based circular Mindlin plate model when both the microstructure and surface energy effects are suppressed. To illustrate the new model, the static bending problem of a clamped circular Mindlin plate under a uniform normal load is analytically solved by directly applying the general formulas derived.