11. Summary of results

Reference

TRIA7

QUAD9

TRIA7

QUAD9

The critical load is well detected. The first two results corresponding to loads \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}1.015\) and \(1.063\) are correct, the maximum error is 3.5% for mesh TRIA7 and 2.2% for mesh QUAD9. The QUAD9 mesh gives better results.

If we continue the calculations with the shell elements, mesh QUAD9 continues to give better results. In the zone where the movements in DZ are the most important, the error made on the load reaches 9% on the quadrangles and goes up to 30% on the triangles. The errors increase in this region due to the slopes of the curves.

The transverse shear correction coefficient A_ CIS was set to 0.833, corresponding to thick shells. The value (\(9000\mathrm{=}{10}^{6}\mathrm{\times }H\mathrm{/}L\)) that should have been taken into account does not allow the calculations to be carried out. It introduces poor conditioning of stiffness matrices by increasing their disparities.

The code beam solution, whether it is modeling POU_D_T_GD or POU_D_TGM, provides very good results compared to the reference analytical solution. However, the calculation times are different, modeling POU_D_T_GD, which is geometrically accurate, leads to almost 40% less calculation time compared to modeling POU_D_TGM. In fact, the “PETIT_REAC” deformation used for the multi-fiber model is only an approximation of large displacements and especially of large rotations, it requires small loading increments. On the other hand, we must remember that we are able to treat behaviors other than elastic with POU_D_TGM.

Regardless of the TRIA3 or QUAD4 mesh, the DKT and DKTG models detect the critical load well. The DKT (QUAD4 and TRIA3) and DKTG (TRIA3) models no longer converge beyond \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}1.2\). On the other hand, for modeling DKTG (QUAD4) the calculations go beyond that, to reach \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}3.73969\). The error committed on trips is a maximum of 3% and 5% for \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}1.063\) and 10% for \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}2.451\).