Stochastic Finite-Element Analysis for Elastic Buckling of Stiffened Panels

The variability of the random buckling loads of beams and plates with stochastically varying material and geometric properties is studied in this paper using the concept of the variability response function. The elastic modulus, moment of inertia, and thickness are assumed to be described by homogeneous stochastic fields. The variance of the buckling load is expressed as the integral of the auto- and cross-spectral density functions characterizing the stochastic fields multiplied by the deterministic variability response functions. Using this expression spectral-distribution-free upper bounds of the buckling load variability are established. Further, the buckling load variability for prescribed forms of the spectral density functions is calculated. Using a local average approach, the commercial finite-element package ABAQUS is incorporated into the analysis of these random buckling loads. The technique is applied to study variability of the critical buckling load of a stiffened steel plate used in experiments to model a barge deck.