A MAXIMUM ENTROPY APPROACH FOR UNCERTAINTY QUANTIFICATION OF INITIAL GEOMETRIC IMPERFECTIONS OF THIN-WALLED CYLINDRICAL SHELLS WITH LIMITED DATA

Initial imperfections with uncertainty characteristics are well-known recongnized as the main reason why the actual critical load values of thin-shell structures do not match the theoretical solutions and exhibit dispersion characteristics. In order to model the initial imperfections of actual thin-shell structures more appropriately, seveal sources of uncertainty quantification should be handled carefully, such as the quantification of the inherent randomness in the form and magnitude of the imperfection distribution, and the quantification of the uncertainty in the statistics due to small sample size and inaccurate measurements in practice. In this paper, a novel modeling approach for initial geometric imperfections of thin-walled shells is proposed based on the principle of maximum entropy and the Karhunen-Loeve expansion method of random fields. Firstly, the maximum entropy approach is used to estimate the probability density function of the Karhunen-Loeve random variables, which is aimed to model the gemometric imperfections as random fields without the assumpation of Gaussian and homogeneity. Secondly, the quantification of the epistemic uncertainty caused by the availability of only a small size of data on geometric imperfections of thin-walled shells is achieved by extending the classical equationally constrained maximum entropy model to an interval constrained maximum entropy model. Finally, the proposed method is used for imperfection modeling and critical load prediction for A-Shell of the international imperfection databank. It is shown that the proposed random field modeling approach based on the interval constrained maximum entropy principle not only has the ability to quantify the epistemic uncertainty due to small size of data, but also effectively characterizes the higher order moment information of the measured data. Furthermore, it is shown that the Gaussian random field model and the random field model based on the equation constrained maximum entropy principle are the two special cases of the proposed modeling approach in this paper.