/IMPL/DT/3
Engine Keyword Implicit automatic time step control with Riks method.
Format
/IMPL/DT/3
It_w L_arc L_dtn $\text{\Delta}{T}_{sca\_d}$ $\text{\Delta}{T}_{sca\_\mathrm{max}}$ C_type W_scal
Definition
Field  Contents  SI Unit Example 

lt_w  If the solution of a time
step converges within It_w iterations, the next
time step will be increased by a factor controlled by
$\text{\Delta}{T}_{sca\_\mathrm{max}}$
.


L_arc  Input arclength.


L_dtn  Maximum number of
iterations before resetting and decreasing the time step by a factor
of
$\text{\Delta}{T}_{sca\_d}$
.


$\text{\Delta}{T}_{sca\_d}$  Scale factor for
decreasing the time step when L_dtn is reached.


$\text{\Delta}{T}_{sca\_\mathrm{max}}$  Maximum scale factor for
increasing the time step.


C_type 


W_scal  Scale factor for
controlling the loading contribution in the constraint
equation. Default = 0.0 
Comments
 The Riks type
arclength method is suitable for nonlinear static analysis of unstable problems
like buckling, snapthrough. It solves at the same time for the displacement vector
and for a loading scale factor by adding a constraint equation.
This method can only be used for static analysis and the loading should be proportional in each restart run.
 A constant arc length can be defined by giving
$\text{\Delta}{T}_{sca\_d}=\text{\Delta}{T}_{sca\_\mathrm{max}}=1$
or directly defining L_arc.
Otherwise, an adaptive arc length based on the convergence rate will be used.
The adjustment is:
(1) $$L\_new=L\_old\cdot {\left(\frac{It\_w}{It\_old}\right)}^{0.5}$$Where, It_old is the number of convergence iterations of previous load increment.
 The time step adjustment uses the same factor than arc length but bound by $\text{\Delta}{T}_{sca\_d}$ and $\text{\Delta}{T}_{sca\_\mathrm{max}}$ . Each new time step is only the predictor value as Riks method will give the final time step at the end of each load increment. Therefore, a negative time step can be obtained for some loading increments.
 Riks method can only be used with Modified Newton (only in the sense of reforming the stiffness matrix) and line search methods, but a small number (L_A ≤ 3) is recommended for the reforming frequency of the stiffness matrix.
 A maximum cycle number (see /IMPL/NCYCLE/STOP) can be used to stop the run in case the solution never reaches the specified load.
 If /IMPL/DT/1, /IMPL/DT/2, or /IMPL/DT/3 are not present, the only time step controls are /IMPL/NCYCLE/STOP and /IMPL/DT/STOP. In the case of divergence, the time step will be reduced by half and repeated.
 For the postbuckling simulations involving contact, the Riks method may not work, especially if contact has not occurred at beginning or contact is lost during the simulation. In this case, it is better to use implicit dynamic analysis.
 If the Riks analysis includes irreversible deformation such as plasticity and a restart, using another Riks step is attempted while the magnitude of load on the structure is decreasing, the solver will find the elastic unloading solution. Therefore, restart should occur at a point in the analysis where the load magnitude is increasing, if plasticity is present.