Probabilistic eigenvalue buckling analysis solved through the ratio of polynomial response surface

An efficient procedure for the reliability analysis of frame structures with respect to the buckling limit state is proposed under the assumption that no imperfections are present and that the elastic parameters are uncertain and modeled as random variables. The approach allows a deeper investigation of structures which are not sensitive to imperfections. The procedure relies on a Response Surface Method adopting simple ratio of polynomials without cross-terms as performance function. Such a relationship approximates analytically the dependence between the buckling load and the basic variables furnishing a limit state equation which is very close to the exact one when a proper experimental design is adopted. In this way a Monte Carlo Simulation applied to the response surface leads to a good approximation with low computational effort. Several numerical examples show the accuracy and effectiveness of the method varying structural complexity, correlation between basic variables and their distribution.