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# When Do I Need a Dynamic Analysis?

SimScale provides both static and dynamic structural analysis capabilities. This article answers when is it necessary to perform a dynamic analysis.

## Solution

A dynamic structural analysis differs from a static structural analysis in the fact that the former takes into account the inertial forces created by the rigid body motions and the deformation speed and acceleration, instead of only taking into account the elastic forces due to deformations. This difference can be illustrated by looking at the assembled equations of the Finite Elements Model:

$$[K] \vec{u} = \vec{F} \tag{1}$$

$$[M] \ddot{\vec{u}} + [C] \dot{\vec{u}} + [K] \vec{u} = \vec{F} \tag{2}$$

The additional terms in equation $$(2)$$ are mass times acceleration $$([M] \ddot{\vec{u}})$$ and damping times velocity $$([C] \dot{\vec{u}})$$. These are are the dynamic forces terms that differentiate dynamic from static simulations. Also, it is worth noting that the mass times acceleration term is often referred to as ‘inertial forces’. Besides, the damping term is optional.

If your application model involves loads that are changing rapidly, significant accelerating or decelerating motions will be developed, thus inertial forces will be present and a dynamic analysis is required to capture their effects. On the contrary, for slowly moving cases there is little acceleration, thus a non linear static analysis will suffice.

As an example, here are two typical situations in which engineers apply dynamic analyses on the SimScale platform: