Safety margin analysis of buckling for structures with unknown but bounded uncertainties

A safety margin of buckling for structures with unknown but bounded uncertainties is proposed in this paper. The perturbation matrixes, consisting of the elastic stiffness matrix and the geometric stiffness matrix, are introduced to derive the concept of safety margin. The concept of safety margin of buckling is first proposed to quantify the influence of uncertain parameters on structural buckling. Based on the spectrum norm and the singular value analysis, the mathematical basis of the safety margin is expounded. Furthermore, to obtain a more accurate estimation of safety margin, the correction factor for the safety margin is introduced through the interval extension of interval analysis. Two engineering examples, compared with traditional interval analysis method, are utilized to demonstrate the validity of the proposed safety margin, and numerical results indicate that the safety margin can provide a relatively accurate index to indicate the allowable perturbation range of the perturbation matrix of a structure under given loads.