Uncertain Buckling Load and Reliability of Columns with Uncertain Properties

Continuous and finite element methods are utilized to determine the buckling load of columns with material and geometrical uncertainties considering deterministic, stochastic and interval models for the bending rigidity of columns. When the bending rigidity field is assumed to be deterministic, the ordinary finite element method slightly overestimates the buckling load, and with a very few number of elements high rate of convergence to the exact results is observed. If the bending rigidity field is modelled using random fields, stochastic finite element method is utilized. The discretization is performed using weighted intergrals. Then, the buckling load becomes a random variable. The sensitivity of the lower order moments of the buckling load with respect to the mesh size, the correlation length and coefficient of variation of the random field are examined. The reliability of columns designed considering safety factors are estimated by means of extensive Monte Carlo simulations. For the case, when the bending rigidity field is taken to be bound from above an below, an integral equation formulation and optimization methods are used to determine conservative bounds for the buckling load. for structural design, the lower bound is of crucial interest. The buckling load of fixed-free, simple-supported, pinned-fixed, fixed-fixed columns and a sample frame are calculated.