In this section, several representative analysis scenarios and their corresponding settings are described.

ebc 1 value 0. dof [UX UY UZ RX RY RZ] nodeset nodes_left value 0. dof [ UY UZ RX RY RZ] nodeset nodes_right value -1. dof [UX ] nodeset nodes_right end end (max_displacement=3.) (duration=0.5) case 1 analysis dynamic_nonlinear stage 2 sfactor (duration) end stage 2 ebc 1 sfactor (max_displacement/duration) step_size_init (0.1*duration) tol_dynamic 1e-2 residue_function_type rayleigh_damping rayleigh_alpha 123.6 rayleigh_beta 0.00008074 end adirr case 1 shell_intersection_angle 10 end

In this example, a panel is compressed in the x-direction by 3mm within 0.5s. If the analysis duration is different from the value of 1 (in time units, usually seconds), a separate stage has to be defined, stage 2 in the present example. The duration of the analysis is given with the MDL command

stage 2 sfactor`f`

The amplitude of any specified boundary conditions in the
stage must be inversely-scaled by the analysis duration, this is
done with the `sfactor`

option. On the other hand,
the sizes for the minimum, maximum, and initial step are given in
absolute values. Hence, `step_size_init`

should
always be defined.

The dynamic tolerance (`tol_dynamic`

) option
has a significant influence on both accuracy and numerical effort. A
large dynamic tolerance leads to relatively large time step sizes,
requiring many Newton iterations per increment. Using a dynamic
tolerance that yields smaller time step sizes which require only one
or two Newton iterations is not only more accurate but often more
effective. In some cases, a modified Newton method may further
reduce the computational effort. Conversely, when the dynamic
tolerance is set to an overly conservative value, the resulting time
step size may become extremely small in the presence of
high-frequency vibrations and fast movements.

When geometric instabilities are present, Rayleigh damping
should be selected (by setting the
`residue_function_type`

option to
`rayleigh_damping`

and by setting the values for
`rayleigh_alpha`

and `rayleigh_beta`

)
to ensure an effective solution process.

For highly nonlinear problems, the full Newton method
(default) is often more expedient than the modified Newton method.
For mildly nonlinear problems and for problems where the time step
size is predominantly limited by the time integration error, a
modified Newton method may be more effective. The default maximum
number of Newton iterations (```
max_newton_iterations
50
```

) should be sufficient in many cases. Lower values may
cause many small time increments or even failure to converge, while
higher values may lead to increased computation time. In case of
very slow but reliable convergence, higher values (100-200) may be
necessary.

(max_displacement=3.) (duration=0.05) case 1 analysis dynamic_nonlinear stage 2 sfactor (duration) end stage 2 ebc 1 sfactor (max_displacement/duration) step_size_init (0.1*duration) tol_dynamic 1e-4 end

In this example, the options for Rayleigh damping are omitted since all dissipation should come from the visco-elastic material. The dynamic tolerance is crucial for the accuracy of the time integration: If the time step sizes are too large, the numerical damping which is caused by the time integration error may be larger than the material damping.

case 1 analysis dynamic_nonlinear ebc 1 tol_dynamic 1e-3 residue_function_type artificial_damping dissipated_energy_fraction 1e-3 end

The dynamic solver can also be applied to load-controlled quasi-static analysis. In this case, the analysis duration is irrelevant, and a separate stage does not need to be defined. Also in this case, the dynamic tolerance controls the time step size and is important to computational efficiency and accuracy.

Energy is dissipated with artificial damping; the
`residue_function_type artificial_damping`

option
also tells the solver to neglect inertia forces. The amount of
damping is controlled with the
`dissipated_energy_fraction`

parameter. High values
accelerate the analysis, increasing the increment sizes, but may
influence the results on the other hand. Therefore, a compromise
between analysis time and accuracy has to be found. While the
parameter value is independent of the physical units, the necessary
amount of damping depends on the problem. Thus, the default of 1e-4
may not be appropriate. It is recommended to vary this parameter in
powers of 10 (e.g. make an analysis for 1e-7, 1e-6, 1e-5, 1e-4,
1e-3) and observe its effect.

(one_day=84600) (duration=365*one_day) case 1 analysis dynamic_nonlinear stage 2 sfactor (duration) end stage 2 dof_init 1 ebc 1 sfunction '1' multistep_integration_order 4 newton_method delayed_modified step_size_min (one_day) step_size_init (one_day) step_size_max (one_day) tol_dynamic 1e6 end

In this example, an initial temperature field is given
(`dof_init`

), and a constant temperature is applied
at the boundary (`ebc 1 sfunction '1'`

). If the
problem is well behaved, it can be solved with a higher-order BDF
that is more accurate but not unconditionally stable, and a modified
Newton method can be used.

The analysis duration is one year (365 days), and the time step size is fixed to one day (84600 seconds). A very large dynamic tolerance is used to inactivate the solver's error estimator.