Stochastic Post-buckling of Frames Using Koiter's Method

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first_order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first_order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.