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 r_{0} = 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)**** **** **** **** **** ** |