Probabilistic buckling analysis of functionally graded (Al/Al2O3) plates under axial compression using the Navier solution

This research endeavors to investigate the probabilistic buckling response of functionally graded (FG) plates, specifically composed of aluminum (Al) and alumina (Al₂O₃), under axial compressive loads. Rather than relying on deterministic solutions, we explore the inherent uncertainties that can impact the buckling behavior of such plates. This analysis utilizes a four-variable refined plate theory, enabling us to model the quadratic variance of transverse shear strains throughout the plate's depth, while adhering to the zero traction boundary conditions at the upper and lower surfaces. Crucially, we achieve this without the application of shear correction factors which are commonly needed in other approaches. This refined theory only necessitates the handling of four independent unknowns, unlike other shear deformation theories that often require five. This reduction in unknowns offers a computationally more efficient model for studying such complex behaviour. The current work employs the Navier solution within a probabilistic framework to account for the variability in material properties or geometric imperfections that are often present in such FG materials. Several numerical examples are then presented in order to assess the precision and performance of the suggested probabilistic approach applied to the buckling analysis of FG plates, and the uncertainty of the results. These investigations will demonstrate the significance of incorporating probabilistic considerations in structural analysis and provide valuable insights for practical engineering applications.