On Random Imperfections for Structures of Regular-Polygonal Symmetry

Abstract

A theoretical study is made on the effect of random initial imperfections on the load-bearing capacities of structures of regular-polygonal symmetry. The group-theoretic method is employed to implement the symmetry in the formulation. In view of the concept of critical initial imperfection, the explicit form of probability density function of the load-bearing capacity of structures is derived for random initial imperfections. In particular, tight bounds on the range of load-bearing capacity are presented for various types of simple and double critical points. The theoretical and empirical probability distribution functions are compared for simple truss structures to show the validity and effectiveness of the present method.