Column buckling under stochastic three-dimensional material properties: A stochastic finite element analysis

This study develops a Stochastic Finite Element Analysis approach integrating a numerical integration method and a perturbation method to analyze the buckling response of columns subjected to three-dimensional (3D) stochastic material variations. The proposed method discretizes the 3D random field of Young's modulus into fundamental random variables. The method is further enhanced with perturbation techniques, supporting the estimation of important statistical descriptors, including the expected value, coefficient of variation (COV), and standard deviation of the critical buckling load. The accuracy of the Stochastic Finite Element Analysis is validated via Monte Carlo simulations (MCs) implemented with the conventional Finite Element Method (FEM), while spectral expansion techniques are employed to create random instances for the 3D stochastic field model. The results demonstrate that for small spatial correlation lengths, local material fluctuations are effectively averaged due to stochastic homogenization, leading to lower variability in the critical buckling load. Conversely, an expansion of the correlation length results in heightened variability in the critical load, reflecting the impact of stochastic variability of material properties. Among the spatial directions, the characteristic correlation distance along the column's longitudinal axis has the most significant influence on the uncertainty of the critical buckling load, as axial stiffness directly governs the global stability of the structure. Furthermore, the study reveals an approximately linear correlation between the COV of the critical buckling load and that of the elastic modulus, suggesting that material randomness can serve as a predictor of structural stability variability.