5. Summary of results

There is a slight difference between the solutions obtained by the two calculation codes. It is considered reasonable and the results are considered satisfactory. Even if in this test we wanted to approach Code_Aster modeling as much as possible to that of the Europlexus code, we are aware, in particular, of the difference in the calculation of the mass matrix. The mass matrix implemented in Europlexus follows the method proposed in [1], which is better suited for an explicit fast dynamics calculation software. Code_Aster uses a more standard approach, explained in [2]. The difference concerns in particular the calculation of inertias (components of the mass matrix corresponding to the degrees of freedom of rotation), which are not very important in the case of slow dynamics. On the other hand, in rapid dynamics, they are the ones that most influence the critical time step. For example, by neglecting them the mass matrix becomes singular and explicit integration becomes unconditionally unstable.

The various simulations proposed validate the use of modeling GRILLE_EXCENTRE for modal calculations, explicit dynamics and implicit dynamics.

The values obtained are in agreement with the analytical solutions, when these are available.