Stochastic Stability Analysis of Columns with Randomly Elastic Joint Ends and Two-Dimensional Random Material Properties Using Monte Carlo Simulation

This paper develops a Monte Carlo simulation (MCs) to analyze the stochastic stability of a pin-ended column with elastic rotational springs at both ends. The randomness of input factors is considered, including the rotational stiffness of elastic couplings at both ends of the column as random variables following a normal distribution and the elastic modulus of the column as a two-dimensional (2D), stationary, homogeneous Gaussian random field. The spectral representation method is applied to represent the 2D random field and generate realizations of the elastic modulus. The influence of random factors such as the standard deviation of the 2D random field, the standard deviation of normal random variables, and correlation distance in each direction on the coefficient of variation (COV) of the critical load is analyzed in detail in this study. The results indicate a strong correlation between the COV of the critical load and both the standard deviation of the 2D random field and the correlation distance. The COV increases significantly with increasing standard deviation, particularly for larger correlation lengths. However, the influence of the variability of rotational stiffness is relatively minor, especially at larger correlation distances.