12. Summary of results#
Models COQUE_3D, POU_D_T_GD, and POU_D_TGM
Convergence difficulties are noted which disappear by multiplying the thickness by 3 or 4.
It is necessary to increase the value of COEF_RIGI_DRZ which assigns a stiffness around the normal of the shell elements which by default has the value of \({10}^{\mathrm{-}5}\) (the smallest flexural stiffness around the directions in the plane of the shell) in order to be able to increase the value of the angle of rotation that can be achieved. Values of this coefficient up to \({10}^{\mathrm{-}3}\) remain legal.
During Newton’s iterations, membrane deformations appear and cancel out at convergence.
The convergence speeds of the NEWTON algorithms are comparable for the POU_D_T_GD and COQUE_3D models.
The convergence speed of the NEWTON algorithm in the case of POU_D_TGM modeling is much lower than the other two because this modeling requires in this case to make very small loading increments to properly describe the geometric transformation and to remain in the hypothesis of small deformations. The time cost \(\text{CPU}\) is affected since the calculation is nearly 10 times longer than that of modeling POU_D_T_GD. Of course, the multi-fiber element has the advantage of being able to treat several types of behavior and not only elastic behavior like element POU_D_T_GD. If the required precision is not in the order of 1%, we can afford to use fewer time steps.
Moreover, for a problem such as this one, where the inertia of the section plays a major role, it is important to take care to discretize the section with sufficient fibers when using POU_D_TGM, in order to obtain the inertia as close as possible to the theoretical value (this is why we meshed with nearly 40 fibers in the thickness).
Models DKT and DKTG
Modeling DKTpermet achieves a large rotation angle \(300°\), which is more important than that obtained with modeling DKTG \(86°\).
Compared to the analytical solution, the maximum displacement difference is 2% for models DKTet DKTG