Nodal Time Step

The nodal time step calculates the time step based on the nodal mass and nodal stiffness in the model.

The nodal time step is calculated after the computation of all the internal forces at each node using:(1)

Δ t_{n o d a l} = \sqrt{\frac{2 m}{k}}

Where,

$m$: Nodal mass
$k$: Equivalent nodal stiffness

The equivalent nodal stiffness is calculated using one half of the eigenvalue from each attached element stiffness matrix. If the node is also involved in contact, the contact stiffness is also included in the equivalent nodal stiffness calculation. The stiffness is calculated during internal force computation. To ensure stability, the simulation's cycle time step is found by multiplying the minimum time step of all the nodes by a scale factor (default is 0.9).

For a high quality finite element mesh, the element time step and nodal time step conditions are nearly identical. Most typical finite element meshes include some elements with poor element quality and for these situations the nodal time step calculation is usually higher than the element time step calculation.

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

/DT/NODA
$Δ T_{s c a}$ $Δ T_{\min}$

Where,

$Δ T_{s c a}$: Scale factor for the element time step
$Δ T_{\min}$: Not used and is entered as zero