Static analysis of structures with uncertainties described by imprecise probabilities

The analysis of structures with random stiffness described by imprecise probability density function (PDF) is addressed. Uncertainties are modelled as random variables characterized by a PDF with interval basic parameters (mean-value, variance etc.). The aim of the analysis is to derive approximate bounds on the mean-value and variance of the response. The proposed method relies on the use of a ratio of polynomial response surface to approximate the dependency of the stochastic response on the random stiffness parameters. Then, the bounds of response statistics are evaluated by combining standard probabilistic analysis with the so-called improved interval analysis via extra unitary interval. The accuracy of the proposed procedure is demonstrated by appropriate comparisons with the bounds of response statistics obtained performing standard Monte Carlo Simulation in conjunction with a combinatorial procedure.