Stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters

The research work presents the study on non-deterministic problems in the presence of the multiple imprecise-random-field uncertainties by extending the spectral stochastic finite element framework. The standard random field is expanded to characterize the behaviour of physical model with imprecise randomness more appropriately for real engineering problems based on available sources of uncertainty. The Young's modulus and body force of structures are considered as imprecise random fields with bounded statistical moments. Mathematical expressions and solution procedure are developed to produce the uncertain-but-bounded statistical characteristics of responses, namely interval mean value, interval standard deviation and bounding distribution functions. The bounding probability density and cumulative distribution of the imprecise random response are then effectively visualized by means of Polynomial Chaos Expansion. The feasibility and effectiveness of the presented method are illustrated by three numerical examples.