FAQ 002376 IT

12. luglio 2018

# Which explicit method is used in the RF-DYNAM Pro - Nonlinear Time History add-on module?

#### Risposta

The RF-DYNAM Pro - Nonlinear Time History offers, in addition to the implicit NEWMARK method of mean acceleration, also an explicit method. In the manual of this add-on module, it is mentioned that this is a solver which uses the central difference method.

It should be noted that not the "original" version of the central difference method is used here, but a modified form. The modified form is characterized by the fact that it is simply not a central difference when applying the speed difference. The following two equations show the applied speed and acceleration differences.

Speed: (no central difference)
${\dot{\mathrm x}}_{\mathrm n+\frac12}=\frac{{\mathrm x}_{\mathrm n+1}-{\mathrm x}_\mathrm n}{{\mathrm{Δt}}_{\mathrm n+{\displaystyle\frac12}}}$

Acceleration: (central difference)
${\ddot{\mathrm x}}_\mathrm n=\frac{{\dot{\mathrm x}}_{\mathrm n+{\displaystyle\frac12}}-{\dot{\mathrm x}}_{\mathrm n-\frac12}}{{\mathrm{Δt}}_\mathrm n}$

This approach leads to a faster convergence since it responds "faster" to changes in loading or structure (nonlinearities).

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