A size-dependent moving Kriging meshfree model for deformation and free vibration analysis of functionally graded carbon nanotube-reinforced composite nanoplates

Abstract

In this paper, a size-dependent meshfree model using the higher-order shear deformation plate theory in conjunction with the nonlocal Eringen elasticity theory for bending and free vibration analyses of functionally graded carbon nanotube-reinforced composite (FG CNTRC) nanoplates is presented. Configurations of carbon nanotubes (CNTs) are carried out for the uniform and functionally graded distributions via the plate thickness. Effective material properties are computed by the extended rule of mixture. The differential equation form of nonlocal elasticity theory is utilized to take account of size-dependent effects. Based on the principle of virtual work, discretized governing equations for nanoplates are obtained. Thereafter, the displacement and natural frequency of the FG CNTRC nanoplates are determined by a moving Kriging meshfree method. Essential boundary conditions are directly enforced at nodes the same with the finite element method because the moving Kriging shape function satisfies the Kronecker delta function property. Numerical results prove that the present model is simple, stable and well accurate prediction for nanostructures. Moreover, the stiffness-softening mechanisms are found when using the nonlocal elasticity theory leading to a rise of deflection and a decrease of natural frequency of FG CNTRC nanoplates.