8. Conclusion

The operator DYNA_VIBRA/BASE_CALCUL =” PHYS “allows the choice between several methods of temporal integration. In their settings by default, Wilson and Newmark schemas are unconditionally stable implicit schemes. They therefore require an inversion of the linear system at each time step but in return offer a choice of time step which is restricted only by the delicacy with which it is desired to describe the temporal evolution of the modelled phenomena.

Schemes DIFF_CENTRE and ADAPT are explicit, which prevents them, in the case of a diagonal mass matrix, from an expensive matrix reversal. But the conditional stability of this type of scheme generally leads to the use of small time steps, conditioned by the smallest specific period of the system. It is therefore not guaranteed that explicit patterns will always be faster. It depends on the simulated phenomena. Although the physics of these phenomena requires fine temporal discretization, the time step used is naturally within the stability interval. Otherwise, numerical stability constraints cause inflation in the number of very costly time steps.

Figure ADAPT takes advantage of information on the frequency content of the response to adapt the time step. The discretization of time is therefore no longer imposed by the smallest specific period of the system but by its response. This can be an advantage when the frequency of the response changes over time, as in the case of impacts.