Shell Buckling With Polymorphic Uncertain Surface Imperfections and Sensitivity Analysis

In a probabilistic design approach for cylindrical shells, Gaussian random fields are used to simulate geometric imperfections. The shape of imperfections depends, among others, on the autocorrelation properties of the random field. Underlying uncertainties such as a small sample size or imprecise measurements make it practically impossible to define a crisp correlation function. For a more realistic description of the imprecise correlation structure, the classical probabilistic approach is extended to a fuzzy stochastic approach. More exactly, the polymorphic uncertainty approach is used taking into account natural variability and incompleteness. Consequently, geometric imperfections are represented as fuzzy probability based random fields. Therefore, the required correlation parameters are described as polymorphic uncertain parameters. The quantification of uncertainties is demonstrated on real data. Furthermore, the polynomial chaos surrogate model is used for the alpha-level optimization in the fuzzy analysis. The sensitivity indices as a by-product of the surrogate model show the influence of the input parameters on the statistical parameters of the critical buckling load factor. The main purpose of this paper is to show how the presented methods can support the design process of cylindrical shells.