10. Summary of results

• Even if the results obtained are honorable, the models DKQ, DSQ,,, DKT,,,, DST, TUYAU and TUYAU_6M do not allow the out-of-plane modes of the ring to be estimated. Only the model COQUE_3D with a mesh in QUAD9 and the elements COQUE_SOLIDE provide a good frequency estimate of these modes

• The models DSQ and COQUE_3D in QUAD9 give an error of around 0.3% for the ovalization and trifoliate modes. For the COQUE_3D models in TRIA7, TUYAU and TUYAU_6M, this error is around 0.7% and is greater than 1% for the DKQ, DKT and DST.

• The better results of DSQ compared to DKQ confirm that the effect of transverse shear is not negligible in shells of significant thickness.

• On a developable geometry such as that of the cylinder studied here, quadrangular finite elements provide better results than triangular finite elements. The DST, tested on a cob mesh and on a symmetric star mesh, are much worse than the DSQ. The same remark is also valid for COQUE_3D in TRIA7 compared to COQUE_3D in QUAD9.

• The performances of COQUE_3D are good quantitatively and in terms of calculation time. The richness of the interpolation, the taking into account the curvature of the cylinder in the elements and the metric correction made in the thickness of the shell seem to explain these good results.

• Element COQUE_SOLIDE gives excellent results despite a plate approach (and therefore an approximation using plane facets). Unlike DKQ and DST, off-plane modes are represented correctly.