3. Conclusion

To conclude, here is a summary of the various temporal integration possibilities offered by the operator:

• Explicit Euler (“EULER”) modified to ensure conditional stability,

• Newmark schema (“NEWMARK”) set to be implicit,

• Devogelaere-Fu diagram (“DEVOGE”) of order 4,

• Four explicit adaptive patterns:

• “ADAPT_ORDRE1 “based on the Euleur schema,

• “ADAPT_ORDRE2” based on the pattern of centered differences,

• two diagrams from the Runge-Kutta family: “RUNGE_KUTTA_32” and RUNGE_KUTTA_54 “

The schema by default is EULER but it is not always the most suitable step. The NEWMARK schema available in the Code_Aster is implicit and guarantees unconditional stability but can only be used for purely linear problems.

Figure DEVOGE is of order 4 and is therefore more accurate but it is expensive in terms of calculation time.

Adaptive schemes are more particularly indicated for problems with localized nonlinearities, where the « ideal » time step is not constant during the transient. It is therefore the modeling experience that makes it possible to choose the diagram best suited to the problem according to the ratio (calculation time) /precision.