Limit analysis of stochastic structures in the framework of the Probability Density Evolution Method. (1st April 2018)

• Record Type: Journal Article
• Authors: Kalogeris, Ioannis; Papadopoulos, Vissarion
• Is Part Of: Engineering structures. Volume 160(2018)
• Page Start: 304
• Page End: 313
• Publication Date: 2018-04-01
• Subjects: Stochastic analysis -- Probability Density Evolution Method -- Limit analysis -- Buckling -- Displacement control -- Random imperfections; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2018.01.020
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: A reformulation of PDEM is proposed for the limit analysis of stochastic systems. A solution for the resulting pde's is obtained via the method of characteristics. A methodology for the estimation of stochastic load-displacement curves is proposed. The applicability of the proposed methodology for buckling analysis is demonstrated. The merits of the proposed methods include high accuracy and low computational cost. Abstract: In the present paper a Probability Density Evolution formulation is proposed for the limit analysis of stochastic systems, which can accurately and efficiently evaluate the effect the system's random parameters have on its nonlinear and limit response. The proposed formulation of the classic Probability Density Evolution Method reduces the corresponding Generalized Density Evolution equations, which are partial differential equations, to a system of ordinary differential equations, that can be efficiently solved with the method of characteristics. With this reformulation, the cumulative distribution function of the critical load of the structure can be accurately and efficiently evaluated. The estimation of stochastic limit buckling loads of imperfection sensitive structures is a natural extension of this method. In addition, a methodology is put forward for the estimation of the probabilistic characteristics of the full load-displacement curve for a stochastic nonlinear system in the context of Newton-Raphson incremental-iterative schemes. The main advantage of the proposed approaches is that they allow for a quantification of the effect of uncertainties on the structural capacity, with only a small number of deterministic analyses compared to Monte Carlo simulation. The applicability and validity of the proposed methodology for limit and nonlinear structural analysis is verified through extensive numerical investigations.