Generalized stochastic finite element method in elastic stability problems

The main issue of this paper is the stability analysis of elastic systems with random parameters using the Generalized Stochastic Finite Element Method. The Taylor expansion with random coefficients of nth order is used to express all random functions and to determine up to fourth order probabilistic moments of the critical force or critical pressure. The response function method assists to determine higher order partial derivatives of the structural response instead of the Direct Differentiation Method employed widely before. This approach is examined on the classical Euler problem, 2D and 3D steel frames as well as in addition to the cylindrical shell with some geometrical parameters defined as the Gaussian variables. The comparison of the GSFEM versus the Monte-Carlo simulation on the Euler problem proves the probabilistic convergence of this new technique.