A spectral stochastic formulation for nonlinear framed structures. (January 2019)

• Record Type: Journal Article
• Authors: Papadopoulos, Vissarion; Kalogeris, Ioannis; Giovanis, Dimitris G.
• Is Part Of: Probabilistic engineering mechanics. Volume 55(2019)
• Page Start: 90
• Page End: 101
• Publication Date: 2019-01
• Subjects: Spectral stochastic finite element method -- Load control -- Displacement control -- Geometric nonlinearity -- Co-rotational beam element; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2018.11.002
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: The present paper proposes a stochastic formulation which enables the effective coupling of spectral stochastic finite elements with geometrically nonlinear analysis of framed structures. This is achieved by projecting the stochastic part of the incremental displacements, formulated in the framework of a Newton–Raphson solution scheme, to a polynomial chaos expansion basis. The nonlinear solution is consequently achieved by introducing these expansion coefficients in the iterative solution algorithm as unknowns to be evaluated. With this approach, an augmented system of nonlinear equations is produced and the values of the coefficients are obtained through convergence of the iterative algorithm. In a similar to the deterministic problems manner, the nonlinear load or displacement control algorithms are extended to their stochastic counterparts and a discussion on the appropriate choice of such algorithms depending on the problem at hand is presented. This work focuses on stochastic beam finite element systems in which uncertainty is considered in the system properties. The efficiency of the proposed methodology is demonstrated in benchmark problems with strong geometrically nonlinear behavior. In order to verify the validity of the proposed approach the results obtained are compared to those of Monte Carlo simulations and fair accuracy can be reported. Highlights: A methodology is proposed for the stochastic analysis of nonlinear framed structures The co-rotational beam formulation is coupled with the spectral stochastic fem Stochastic formulations of the load and displacement control algorithms are presented The accuracy of the method is demonstrated through a series of benchmark problems The computational merits of the proposed approach are showcased