FAQ 002356 EN

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Two solution methods are available for the nonlinear time history analysis in the RF-/DYNAM Pro module. What is the difference between them?


In the RF-DYNAM Pro-Nonlinear Time History Analysis add-on module, two different methods are available for nonlinear dynamic analyzes: the explicit Central Difference Method and the implicit Newmark analysis of the mean acceleration.

Nonlinear Implicit Newmark Analysis

The nonlinear Newmark analysis is an implicit method that solves unknown values at time i+1 in relation to the values of time i and i+1. This method is numerically stable, regardless of the selected time step length. This is one reason why this method is usually preferred for dynamic loads that act over a longer period of time.

Explicit analysis

The explicit analysis is unique because it solves values independently of the unknown values at the time i+1. However, this is one reason why the explicit analysis is only stable if the selected time step is smaller than a certain, critical time step. The calculation time of a single time step is very short, but countless, very fine time steps may be necessary to obtain a result at all.

Therefore, the explicit solver is to be preferred if you have to select very fine time steps anyway in order to obtain a usable (converging) result. This is the case, for example, with very short-term and abruptly variable loads, such as impact or explosion loads.


In summary, both methods are "only" numerically stable in the nonlinear range, while the implicit Newmark analysis is still more stable than the Central Difference Method in most cases.

However, it should be noted that a sufficiently small time step must also be observed for the Newmark analysis in order to achieve exact results. Which time step should be selected in a dynamic calculation is explained in detail in FAQ 2655.

More detailed information, especially about the critical time step in the explicit analysis, can be found in the RF-DYNAM Pro manual.


Dynamics Nonlinear Time step Time history analysis Explicitly Newmark



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  • Updated 5 April 2021

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