Isogeometric stability analysis of thin shells: From simple geometries to engineering models

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.