Modal analysis and imperfection sensitivity of the post-buckling behaviour of cylindrical steel panels under in-plane bending

This paper presents and discusses elastic geometrically non-linear Generalised Beam Theory (GBT) results on simply supported cylindrical steel panels under in-plane bending stresses, extending the knowledge on curved panels under uniform compression recently reported by the authors. Due to its inherent modal nature, GBT enables the acquisition of in-depth knowledge on the behaviour of these complex structural elements, which cannot be obtained with standard shell finite element analysis. In particular, a modal analysis investigation is conducted to assess the imperfection sensitivity of curved panels characterised by distinct curvatures and by considering (i) four distinct loading conditions (including the pure bending case), (ii) two distinct critical-mode initial geometrical imperfection shapes (first two bifurcation modes), and (iii) three distinct amplitudes – whenever relevant, three “positive” and “negative” amplitudes are considered. The work begins by the GBT buckling analysis of the selected panels followed by an in-depth investigation on the corresponding post-buckling behaviour. These results provide the evolution, along the equilibrium paths, of relevant modal displacement profiles, modal participation diagrams and deformed configurations. For comparison and validation purposes, ABAQUS shell finite element results are also reported.