Structural reliability analysis based on probabilistic response modelling using the Maximum Entropy Method

Abstract

This paper investigates the efficiency of different approaches for structural reliability analysis with implicit limit state functions. The focus is on techniques that provide the probabilistic description of response quantities obtained by non-linear Finite Element Analysis (FEA) that are then used in the reliability assessment. Using this approach, statistical moments of the response and probabilities associated with specific failure events can be calculated, both of which are of interest in most probabilistic mechanics applications. In this paper, an efficient method for response variability and reliability analysis based on FEA is proposed. The approach combines the Maximum Entropy Fitting Method (MEM) for probabilistic modelling of the response and the First Order Reliability Method (FORM) for reliability evaluation. The results obtained by the MEM are compared with the ones obtained by an approach also available for probabilistic characterization of the response that consists in fitting a 3-parameter lognormal distribution to three fractiles of the response calculated by inverse FORM. The reliability analysis is performed using FORM with explicit limit state functions derived from the different probabilistic models of the response. These results are also compared with the ones obtained using FORM directly linked to the FEA and the Response Surface Method (RSM). The proposed approach is first applied to a simple elastic problem of a portal frame and then applied to the analysis of a ship stiffened plate subjected to longitudinal compression and lateral pressure.