Element Time Step

The default time step calculation used by Radioss is the element time step.

For one finite element, the element time step can be written as:(1)

Δ t_{E l e m e n t} = \frac{l_{c}}{c}

$Δ t_{E l e m e n t} = \frac{l_{c}}{c}$

Where,

$l_{c}$ $l_{c}$: The element’s characteristic length, whose calculation depends on the element type being used and is described in Finite Elements of the User Guide.
$c$ $c$: Speed of sound in the material, which can be expressed as $c = \sqrt{\frac{E}{ρ}}$ $c = \sqrt{\frac{E}{ρ}}$
$ρ$ $ρ$: Material density
$E$ $E$: Young's modulus

For every simulation cycle, each element’s characteristic length and sound speed are used to calculate the critical time step of every element in the model. The time step calculation occurs at the same time as the internal force calculation. To ensure stability, the simulation’s cycle time step is found by multiplying the minimum time step of all the elements by a scale factor (default is 0.9). The scale factor is needed to ensure that the simulation remains stable if there is a sudden change in the model stiffness.

The element time step method is applied for the entire model using:

/DT
$Δ T_{s c a}$ $Δ T_{s c a}$ $Δ T_{\min}$ $Δ T_{\min}$

Where,

$Δ T_{s c a}$ $Δ T_{s c a}$: Scale factor for the element time step
$Δ T_{\min}$ $Δ T_{\min}$: Minimum time step that activates specific actions listed in /DT