Stability analysis of edge corrugated shells

The practical construction of reinforced concrete shells highlights two points, both of theoretical and practical interest: 1. in the neighbourhood of the edge, the membrane state is not representative of the actual stress and strain, and the effect of bending moments must be taken into account; 
 2. thin shells involve buckling and sudden snap-through instability, which designers commonly address by adopting simplified methods, based on the use of empirical knock-down factors. 
 This research stems from an original building in Rome, the Palazzetto Flaminio dome, designed by A. Vitellozzi and P. L. Nervi for the Rome Olympic Games in 1960. This structure covers a considerable span, about 60 m; the cross section is thin (about 15 cm), and 36 inclined pillars support it. To avoid the first problem, Nervi envisioned a structure with constant thickness, but its shape is slightly changed near the edge, so the shell is corrugated where an increase of stiffness is needed. The ongoing research deals with the instability problems and how this shape change can affect global mechanical behaviour. Firstly, a geometric model of several corrugated surfaces suitable for civil engineering and architecture applications has been proposed. Secondly, the effect of corrugation at the edge increases the static performances: by making use of numerical analyses and theoretical comparison, a noteworthy decrease in the membrane stresses and in the bending moment has been ascertained, adopting a wavy shape. Finally, the research investigated the buckling and post-buckling behaviour of the proposed corrugated shapes. The numerical analyses demonstrated the effect of increasing the safe load against elastic instability issues. Nevertheless, this result by itself is not completely representative, because imperfections significantly influence the equilibrium path and, most importantly, are unavoidable. Therefore, analyses for the imperfect structure were performed, introducing each time customised imperfections (e.g., local displacements or different reference states of the structure). The outcome shows that a clever shape significantly improves mechanical performance. Given the recent advancement in concrete printing and the incentive for shape optimisation due to the fairly small thickness (in comparison with the span), instability must be carefully considered. Consequently, the pursuit of new shapes should be oriented towards the ones that provide intrinsically a significant improvement against edge-bending effects and sudden instability issues. The outcome of this research will provide foundations for structural analyses of corrugated surfaces, besides providing a new gaze for a different approach to structural optimisation.