7. Summary of results

The results are generally satisfactory. The discrepancies that occur at the points tested, in particular point \(D\), seem to be due to experimental uncertainty, undoubtedly reinforced by uncertainty as to the graphical sampling.

On the other hand, the solutions proposed by Batoz in « deep shells » theory are well verified by the four models, with relative errors of less than 5% for the long cylinder.

It appears that:

• models TRIA3 and QUAD4 are substantially equivalent for this problem,

• the relative errors are much lower for the long cylinder (models C and D) than for the short cylinder (models A and B): at point \(F\), the error is reduced by a factor of 10 compared to the Batoz reference solution,

• the refinement of the mesh does not decisively minimize the relative differences, both with the TRIA3 and with the QUAD4.

It is therefore observed that the results deteriorate when the ratio of length to diameter decreases, in fact geometric effects become important with this type of modeling. It would be desirable to be able to perform a finite element calculation of shells in an orthotropic environment, in order to better take into account curvature, with plates constituting a limiting case.