A semi-analytical stochastic buckling quantification of porous functionally graded plates

Abstract

This paper introduces a semi-analytical approach integrated with Monte Carlo simulation for stochastic buckling analyses of porous functionally graded plates arising due to the inevitable source-uncertainties of geometrical configurations and material properties. Analytical derivations based on the classical plate theory in conjunction with three-variable refined shear deformation theory are carried out first leading to closed-form solutions for buckling loads and thereby, the closed-form equations are exploited to conduct the comprehensive stochastic quantification of buckling loads in a non-intrusive framework based on Monte Carlo simulation. The deterministic framework is validated with a separate finite element analysis before implementing it for stochastic analysis. The first-order and second-order perturbation theory integrated with the Taylor series expansion are utilized to derive closed-form expressions for the mean and variance of stochastic buckling loads which are compared with Monte Carlo simulation results. Sensitivity of stochastic buckling loads on individual and compound uncertainties are investigated to determine the relative importance of different uncertainty sources. Effects of plate thickness, volume fraction index, and degree of stochasticity variations on the probability distributions of the first three stochastic buckling loads are investigated for both uniaxial and biaxial load cases. The complete probabilistic descriptions presented in this paper assert that the overlapping areas in probability distribution plots corresponding to the consecutive buckling modes lead to the existence of non-unique critical buckling modes, which could potentially be crucial for analyses and designs of structural systems under an inevitable stochastic environment. This article convincingly demonstrates the importance of considering source-uncertainties in porous functionally graded structures including the critical loopholes for a buckling analysis in the presence of such uncertainties.