Generalized stochastic finite element method in elastic stability problems

Authors:
M. M. Kamiński;P. wita
Affiliations:
Department of Steel Structures, Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Łód, Al. Politechniki 6, 90-924 Łód, Poland;Department of Steel Structures, Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Łód, Al. Politechniki 6, 90-924 Łód, Poland
Venue:
Computers and Structures
Year:
2011

Citing 2
Cited 2

Generalized perturbation-based stochastic finite element method in elastostatics

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Potential problems with random parameters by the generalized perturbation-based stochastic finite element method

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On the application of intervening variables for stochastic finite element analysis

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Stochastic stability analysis of steel tubes with random initial imperfections

Finite Elements in Analysis and Design

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Abstract

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.