NONLINEAR BUCKLING OF A COLUMN WITH INITIAL IMPERFECTION VIA STOCHASTIC AND NONSTOCHASTIC CONVEX MODELS

Buckling of initial imperfection sensitive structure - column on a non-linear elastic foundation - is investigated. A criterion based on the concept of ''modal buckling load'' is proposed to determine which modes should be included in the analysis when the weighted residuals method is utilized to calculate the limit load - maximum load the structure can support - for a given initial deflection. For stochastic analysis, a random field model is suggested for the uncertain initial imperfection, and Monte Carlo simulations are performed to obtain the probability density of the buckling load and the reliability of the column. Finally, a non-stochastic convex model of uncertainty is employed to describe a situation when only limited information is available on uncertain initial deflection, and the minimum buckling load is obtained for this model. The results from both the stochastic and the non-stochastic approaches are derived and critically contrasted.