The buckling properties of thin-walled structures are sensitive to different sources of imperfections, among which the geometric imperfections are of paramount importance. This work contributes to the methodology of shell buckling analysis with respect to the following aspects: first, we propose an isogeometric analysis framework for the buckling analysis of shell structures which naturally eliminates the geometric discretization errors; second, we introduce a parameter-free Nitsche-type formulation for thin shells at large deformations that weakly enforces coupling constraints along trimmed boundaries. In combination with the finite cell method, the proposed conceptual modeling and analysis framework is able to handle engineering-related shell structures; and third, we introduce a NURBS modeling of measured geometric imperfection fields, which is much closer to the true imperfection shape compared to the classically used faceted FE models. We demonstrate with a number of benchmark problems and engineering models that our proposed framework is able to fully compete with established and highly sophisticated finite element formulations but at a significant higher level of accuracy and reliability of the analysis results.

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Shell structures are used as primary structures of space launch vehicles. These structures are thin-walled and are thus prone to buckling when loaded in compression. Because of the imperfection sensitivity of these structures, small deviations of the real shell from the theoretically perfect shell may result in a tremendous decrease in load carrying capacity. For this reason, geometrical imperfections need to be taken into account. When designing unstiffened composite shells, the laminate stacking sequence influences both, the buckling load of the geometrically perfect shell and the imperfection sensitivity of the shell. Consequently, to derive laminate stacking sequences that maximize the buckling load of real shell structures, geometrical imperfections need to be taken into account already in an early design phase. In this paper, two laminate stacking sequences that were derived to maximize the buckling load of the geometrically perfect and imperfect shell structure are studied using stochastic methods. To this end, combination of non-rotational symmetric imperfections derived from measured data and variations of the ply orientation are studied in a stochastic analysis on basis of Monte Carlo simulations. The results of this study will be used to evaluate the influence of the stacking sequence as one of the essential properties dominating the structural response of geometrically imperfect laminate composite shell structures.@en