Random initial imperfections of structures

This paper is a theoretical study on random initial imperfections of structures. The explicit form of probability density function of the load-bearing capacity (critical load) of structures is derived for random initial imperfections based on a decomposition of the space of imperfection vectors into two orthogonal subspaces: the subspace that asymptotically affects the load-bearing capacity and the other that does not. Tight bounds on the range of load-bearing capacity are presented for various types of simple critical points. By means of the asymptotic theory of statistics, we show the inefficiency of a conventional random method that approximates the minimum loadhearing capacity by the minimum load for a number of random initial imperfections. The theoretical and empirical probability distribution functions for simple truss structures are compared to show the validity and effectiveness of the present method.