Generalized sensitivity and probabilistic analysis of buckling loads of structures

The imperfection sensitivity law by Koiter played a pivotal role in the early stage of research on initial post-buckling behaviors of structures, but seems somewhat overshadowed by numerical approaches in the computer age. In this paper, to make this law consistent with practical application, the law is extended to implement the influence of a number of imperfections, and the second-order (minor) imperfections are considered, in addition to the first-order (major) imperfections considered in the Koiter law. Explicit formulas are presented to be readily applicable to the numerical evaluation of imperfection sensitivity. A procedure to describe the probabilistic variation of critical loads is presented for the case where initial imperfections of structures are subject to a multivariate normal distribution; the formula for the probability density function of critical loads is derived by considering up to the second-order imperfections. The validity and usefulness of the present procedure are demonstrated through the application to truss structures.