Second-order statistics of the elastic buckling of functionally graded rectangular plates

The material properties of functionally graded materials (FGMs) possess inherent randomness due to their complicated fabrication process, in which the total control of various design parameters is often impossible. The present work investigates the effect of this randomness on the elastic buckling of FGM rectangular plates which are resting on an elastic foundation and subjected to uniform in-plane edge compressions. The interaction between the plate and foundation is included in the formulation with a two-parameter Pasternak model. The elastic material properties (including the Young’s modulus and Poisson’s ratio of each constituent material) and the foundation stiffness parameters are modeled as independent random variables. First-order shear deformation plate theory and a mean-centered first-order perturbation procedure are used to examine the stochastic characteristics of the buckling load. Typical results are presented for plates with aluminum/zirconia two-phase functionally graded material to show the influence of variation in material constants and foundation stiffness parameters, volume fraction index, edge in-plane forces, side-to-thickness ratio, and plate aspect ratio on the second-order statistics of buckling loads.