SUMMARYThe paper deals with the collapse safety of slender elastic structures subjected to local buckling interaction. Using Koiter's asymptotic approach, the mechanical problem is reduced to the search for all the local minima of an indefinite quadratic form over the unit simplex. An efficient recursive branch-and-cut algorithm is proposed for solving this non-convex QP problem, allowing a numerical procedure providing statistical information about the collapse load for a given distribution of random imperfections to be set up.