Convex/Probabilistic Models of Uncertainties in Geometric Imperfections of Stiffened Composite Panels

Thin walled stiffened composite panels, which are among the most utilized structural elements in engineering, possess the unfortunate property of being highly sensitive to geometrical imperfections. Existing analysis codes can predict the buckling load of a structure with specified initial imperfections. However, it is impossible to determine the amplitude and shape of imperfections of nonexistent composite panels that are only being designed. This is due to a variety of uncertainties that are involved in fabrication of panels. Due to the very nature of the manufacturing processes, it is hard to imagine that a given process could ever produce two identical panels. Currently, however, rather than analyzing the manufacturing processes that lead to imperfections , panels are typically designed using probabilistic models to account for the uncertainties in imperfections. This paper presents an efficient approach that employs a convex model of the uncertainties in the imperfections. This approach can replace the computationally expensive probabilistic approach typically used in the study of imperfection sensitive structures. Several example problems are solved to show the accuracy of the predictions of the convex model. A Monte Carlo simulation has also been performed to validate the results obtained by the convex model and show the effort and cost reductions obtained by the use of such models.