Stochastic collocation method for thermal buckling and vibration analysis of functionally graded sandwich microplates

Thermal buckling and vibration behaviors of functionally graded (FG) sandwich microplates are investigated by using a unified higher-order shear deformation theory and stochastic collocation (SC) method. Uniform and linear distributions are considered for thermal effect and lognormal distributions are used to characterize the variability of the materials properties. The governing equations are derived by using Hamilton's principle and solved by Ritz's approach. To demonstrate the effectiveness and accuracy of the current model, the results from SC are compared with those from Monte Carlo Simulation. The effects of boundary conditions, temperature distribution, thickness-to-length ratio, material scale characteristics and power-law index on the fundamental frequencies and critical buckling temperature of the FG sandwich microplates are investigated. The FG sandwich microplates' stochastic analysis provides some new findings that may be utilized as references in the future.