Stochastic vibration and buckling analysis of functionally graded microplates with a unified higher-order shear deformation theory

Abstract

Based on equations of the elasticity, this paper proposes a unified higher-order shear deformation theory for stochastic vibration and buckling analysis of the functionally graded (FG) microplates. The governing equations of motions are derived from Hamilton’s principle. The solutions are approximated by bi-directional series in which hybrid shape functions are proposed, then the stiffness and mass matrix are explicitly derived. In order to investigate the stochastic responses of the FG microplates, the polynomial chaos expansion (PCE) is used. The multiple uncertain material properties are randomly changed via the lognormal distributions. Numerical results are presented for different configurations of the FG microplates such as the power-law index, material length scale parameter, length-to-thickness ratio and boundary conditions on their critical buckling loads and natural frequencies. The results from PCE are evaluated by comparing with those from Monte Carlo simulation to show the efficiency and accuracy of the present approach. Some new results for stochastic analysis of the FG microplates are presented and can be used for future references.