An efficient size-dependent computational approach for functionally graded isotropic and sandwich microplates based on modified couple stress theory and moving Kriging-based meshfree method

Abstract

We present a non-classical model for bending, free vibration and buckling analyses of functionally graded (FG) isotropic and sandwich microplates based on the modified couple stress theory (MCST) and the refined higher order shear deformation theory. Unlike the classical higher order shear deformation theory, the present model retains four variables and contains a single material length scale parameter which can be considered as the size-dependent effect. Effective material properties of FG isotropic and sandwich microplates are calculated by a rule of mixture. The discrete system equations are derived from the Galerkin weak form and are then solved using the moving Kriging meshfree method. Due to satisfying the Kronecker delta function property of moving Kriging integration (MKI) shape function, essential boundary conditions are directly enforced by the same way as the standard finite element method. In addition, a simple rotation-free technique originated from isogeometric analysis is used to eliminate the slopes in clamped plates. The effects of material length scale parameter, volume fraction, geometrical parameters and boundary conditions are investigated to conduct the effectiveness of the present approach.