Indication of Problem

Currently there are no parametric studies of different geometries and boundary conditions that have been carried out to find buckling strength predictions for thin dome shells.

Illustration of Different Support Conditions                           
(European Shell Buckling Recommendations)                           


The European Standard on shell structures (EN1993-1-6) has no rules for the buckling of spherical dome shells, even though these are quite widely used. In its next version (2013), it must include such rules.  The European ECCS Recommendations (2008) has one chapter on the problem, but the rules are very approximate and do not follow the rules of the Eurocode, so they cannot be used.                 

Due to complexity of each individual shell structure there can be a different failure mode ranging from areas that are massively plastified with gross changes to geometry to unstable elastic imperfection sensitive buckling at very low stress levels.  This makes it very hard to use a prescribed method for each failure mode as it is very hard to tell which failure mode is going to occur.

R = radius of sphere (shell middle surface),
r = r(x) radius of shell middle surface, perpendicular
     to axis of rotation
r0 = radius of base circle of spherical cap,
t = thickness of shell,
φ  semi-angle of spherical cap     

For this analysis, the loading is to be uniform and perpendicular to the shell wall which is in keeping with the rules currently used in the European Shell Buckling Recommendations- Chapter 15.

                                                   Spherical cap subjected to external pressure                                                               Complete sphere subjected to internal vacuum or external pressure
(European Shell Buckling Recommendations)                                                            (European Shell Buckling Recommendations)

This project involves computational evaluations to explore the buckling behaviour and will certainly produce design rules of immediate value in design for implementation into the Eurocodes on tanks and shells, both committees for which are chaired by Prof. Rotter.

The computational work will be most easily done using the fast in-house FELASH software which can run on a PC. There will also be additional analysis using Abaqus, another finite element analysis computer programme. The results will almost certainly be publishable in an international journal.

                                       An example of a spherical cap buckling mode in birds-eye and 3D view                               Another example of a different spherical cap buckling mode
                  (Courtesy of Prof. Jakob Marcinowski, University of Zielona-Gora, Poland)                  (Courtesy of Prof. Jakob Marcinowski, University of Zielona-Gora, Poland)