Influence of the curved geometrical shape on the thin shell buckling phenomenon behaviour

The present paper deals with instabilities of long homogeneous and isotropic thin shells, characterized by geometrical non-linearities and imperfections, with reference to a bent helicoidally geometrical shape of particular interest for the helicoidal steam generators tube bundle. Apparently no data exist in the literature to describe the non-linear buckling behaviour of curved thin shells under external pressure, thus, the theoretical analyses based on the classical linear elastic theory, as expected, might be inadequate to evaluate the collapse load especially if the curvature is rather large. To the purpose of determining the buckling pressure load the effects of a pre-existing level of geometrical and technological imperfection, unavoidably caused by various manufacturing processes were also considered. A numerical analysis, based on detailed three-dimensional finite element (FE) code, was performed on curved thin shell subject to combined pressure and in-plane bending in order to take into account the non-linear geometrical and material properties as well as to assess and quantify their detrimental effects on the buckling phenomenon behaviour. Moreover, at Pisa University a rather intense experimental research activity is being carried out on the buckling of thin-walled tube specimens in the dimensional range suitable for the above mentioned applications. Collapse experiments have demonstrated that the detriment of the mechanical properties resulted in a reduction in the collapse pressure load of about 15% and the obtained results have highlighted also the dependence of the buckling behaviour on the stress-initial defects/imperfection width (mainly on the diameter-to-thickness or tube/bending diameters ratios) relationship