Statistics of normally distributed initial imperfections

This paper offers a theoretical study on the probabilistic nature of critical loads (buckling loads) of structures subject to normally distributed initial imperfections. Explicit form of probability density function of critical loads are derived for various types of critical points. Double bifurcation points of structures with regular-polygonal symmetry are dealt with by means of the group-theoretic bifurcation theory. The distribution of minimum values of the critical loads is investigated to present a statistical design index. The theoretical and empirical probability density functions for simple structures are compared to show the validity and effectiveness of this method. The method is quite efficient when it is directly applicable; otherwise, the explicit forms, at least, can greatly supplement the inefficiency of the conventional random method.