Stochastic finite element for stability of columns considering the two-dimensional random field of elastic modulus

• Develop the Stochastic Finite element method (SFEM) using the weighted integral technique with a two-dimensional random field. • Analyze the stability of the column using SFEM considering the two-dimensional random field. • Moter Carlo Simulation two-dimensional random field to verify the proposed new SFEM approach. This paper aims to develop the stochastic finite element method (SFEM) based on the weighted integration and perturbation techniques for the random stability analysis of columns with a two-dimensional (2D) random field of Young's modulus. The statistical characteristics of the critical load, including mean, variance, and coefficient of variation ( COV ), are determined through a first-order Taylor series approximation of the critical load. Monte Carlo simulations, based on spectral representation and standard finite element analysis, were employed to validate the COV analysis results obtained from the SFEM. Furthermore, this study delves into the impact of the correlation lengths and the standard deviation of the 2D random field on the COV of the critical load. The results indicate a significant influence of the 2D random variation of the elastic modulus on the column's random response. The COV of the critical load tends to increase as the correlation lengths increase. At small correlation lengths, the critical load exhibits a narrow scatter around its mean value, while at more considerable correlation lengths, a wider scatter is observed. Notably, when the correlation length approaches infinity, the COV of the critical load asymptotically approaches the standard deviation of the random field. The correlation length along the column axis, the primary loading direction, has a more pronounced effect on the COV than the correlation length along the cross-sectional height. Additionally, a nearly linear relationship between the COV of the critical load and the standard deviation of the 2D random field is observed in this study.