This study is devoted to the modeling and simulation of uncertainties in the constitutive elastic properties of material constituting a circular column under axial compression. To this aim, a probabilistic model dedicated to the construction of positive-definite random elasticity matrices was first used, involving two stochastic parameters: the mean value and a dispersion parameter. In order to compute the nonlinear effects between load and lateral deflection for the buckling problem of the column, a finite element framework combining a Newton-Raphson solver was developed. The finite element tool was validated by comparing the as-obtained critical buckling loads with those from Euler's formula at zero-fluctuation of the elasticity matrix. Three levels of fluctuations of material uncertainties were then propagated through the validated finite element tool using the probabilistic method as a stochastic solver. Results showed that uncertain material properties considerably influenced the buckling behavior of columns under axial loading. The coefficient of variation of a critical buckling load over 500 realizations were 15.477%, 26.713% and 41.555% when applying dispersion parameters of 0.3, 0.5 and 0.7, respectively. The 95% confidence intervals of column buckling response were finally given. The methodology of modeling presented in this paper is a potential candidate for accounting material uncertainties with some instabilities of structural elements under compression.
Keywords: Newton-Raphson; critical buckling load; finite element method; probabilistic model; random elasticity matrix; uncertainty quantification.