Stochastic Buckling Analysis of Functionally Graded Porous Beams Reinforced with Graphene Platelets

This paper uses a stochastic finite element approach based on perturbation theory to explore the impact of uncertain material properties on the buckling characteristics of functionally graded porous (FGP) beams reinforced with graphene platelets (GPL). The first-order perturbation technique (FOPT) has been employed to accurately quantify diverse sources of uncertainties. A stochastic finite element formulation, ensuring C0 continuity, has been developed to calculate the stochastic buckling behaviour of FG-GPLRC porous beams. Convergence and validation analyses have been performed to validate the formulation's precision, comparing results with those obtained through a conventional Monte Carlo simulation. The Halpin-Tsai micromechanics model and Voigt's mixture rule have assessed the effective material properties at a homogenised level. Ultimately, the study delves into how material uncertainties influence the buckling responses of FG-GPLRC porous beams, particularly focusing on low variability (randomness) in key material design parameters like porosity content, nanofiller quantity, Young's modulus of the metal matrix, and nanofiller properties. The findings underscore that uncertainties in material properties significantly influence the buckling behaviours exhibited by FG-GPLRC porous beams.