Effects of Uncertain Material Properties on Structural Stability

Abstract

The effects of uncertain material properties on the elastic stability of structural members and frames are analyzed using a stochastic finite-element method. The uncertain material properties are modeled as continuous random fields by a series expansion involving orthogonal functions. The expanded random fields are incorporated into the finite-element formulation leading to an eigenvalue problem involving random parameters. A mean-centered second-order perturbation technique is used to find the probabilistic characteristics of the buckling load. Illustrations involving a simply supported beam, a simply supported beam on an elastic foundation, and a frame are presented. These illustrations demonstrate the impact on instability of characteristics of the random fields, including correlation length and coefficients of variation of random flexural rigidity and/or random elastic foundation modulus, finite-element mesh selection, and the interrelation between statistical and finite-element modeling. A comparison of the perturbation solutions with the results from Monte Carlo simulation serves to validate the solutions and identify some of their limitations.