Modified Monte Carlo method for buckling analysis of nonlinear imperfect structures

In this paper, we propose a modified Monte Carlo method for analysis of buckling of an imperfect beams on softening nonlinear elastic foundation. Such structures exhibit considerable imperfection sensitivity, i.e. reduction in the maximum load that the structure is able to support in contrast to classical buckling load of the perfect structure. The initial imperfections are treated as random functions of axial coordinate. In order to reduce the needed number of simulations, the Monte Carlo method is coupled with maximum likelihood methodology and the Kolmogorov–Smirnov test.