# Parameters: Static Solver

Command ElementModifies a static simulation parameter element.

## Format

<Param_Static
{
[ method = "MKEAM"
[ max_ke_tol       = "real" ]
[ max_dq_tol       = "real" ]
[ max_num_iter     = "integer" ]
| [ method               = { "FIM_S" | "FIM_D" }
[ max_imbalance    = "real" ]
[ max_error        = "real" ]
[ stability        = "real" ]
[ max_num_iter     = "integer" ]
[ compliance_delta = "real" ]
}
/>

## Attributes

method
Specifies the choice of the algorithm to be used for Static or Quasi-static simulation. For static equilibrium, there are two choices:
• "MKEAM"
• "FIM_S"
The "MKEAM" method is based on the minimization of maximum kinetic energy.
"FIM_S" is a modified implementation which supports all MotionSolve elements except Force_Contact.
For Quasi-static simulation, the "MKEAM" method is not applicable. However, there is an additional choice called "FIM_D". "FIM_D" is a time integration based approach to quasi-static solutions. It is not applicable for a pure static solution. In addition to the parameters specified in the Param_Static element, "FIM_D" also uses the parameters specified in the Param_Transient element to control the DAE integration. "FIM_D" defaults to "FIM_S" when a pure static solution is required.

In summary, both for static and quasi-static solutions, there are three solvers choices. See Comments for their strengths and weaknesses.

The default is "FIM_D".

For the Maximum Kinetic Energy Attrition Method ("MKEAM"), the relevant parameters are:

max_ke_tol
Applicable only if "MKEAM" was chosen. Specifies the maximum allowable residual kinetic energy of the system at the static equilibrium point. This should be a small number. The default value for max_ke_tol is 10E-5 energy units.
max_dq_tol
Applicable only if "MKEAM" was chosen.
This specifies the upper limit for the change in system states at the static equilibrium point. The iterations are deemed to have converged when the maximum relative change in the states is smaller than this value. The default value for max_dq_tol is 10-3.
max_num_iter
Applicable only if "MKEAM" was chosen. Specifies the maximum number of iterations that are allowed before simulation stops. If max_ke_tol and max_dq_tol are not satisfied at this point, the equilibrium iterations should be considered to have failed. The default value for max_num_iter is 50.

For the Force Imbalance method, the relevant parameters are:

max_error
Applicable only if one of "FIM_S" or "FIM_D" was chosen. This specifies the upper limit for the change in the residual of the system equations at the static equilibrium point. The iterations are deemed to have converged when the maximum residual in the equations of motion is smaller than this value. The default value for max_error is 10E-4.
max_imbalance
Applicable only if one of "FIM_S" or "FIM_D" was chosen. Specifies the maximum force imbalance in the equations of motion that is allowed at the solution point. This should be a small number. The default value for max_imbalance is 10E-4 force units.
max_num_iter
Maximum number of iterations that are allowed before the simulation terminates.
stability

Specifies the fraction of the mass matrix that is to be added to the Jacobian (see discussion on Newton-Raphson method in the Comments section) to ensure that it is not singular. The Jacobian matrix can become singular when the system has a neutral equilibrium solution and the initial guess is close to it. To avoid this, a fraction of the mass matrix (known to be non-singular) is added to the Jacobian to make it non-singular. The value of stability does not affect the accuracy of the solution, but it may slow the rate of convergence of the Newton-Raphson iterations. stability should be a small number. The default value for stability is 1-10.

Note: The square root of the value specified by stability is multiplied to the mass matrix and then added to the Jacobian to make it non-singular.
compliance_delta
Delta used during compliance matrix calculation (default = 0.001).

## Example

<Param_Static
method       = "MKEAM"
max_ke_tol   = "1.000E-05"
max_dq_tol   = "0.001"
max_num_iter = "50"
/>
<Param_Static
method       = "FIM_S"
max_residual = "1.000E-04"
max_fi_tol   = "1.000E-04"
max_num_iter = "50"
/>

1. For quasi-static simulation, only the force imbalance methods are supported.
2. For the Force Imbalance method, only a subset of the modeling elements are supported. The following are not supported:
• Body_Flexible
• Body_Point
• CVCV
• PTSF
• CVSF
• SFSF
• Constraint_Gear
• Constraint_UserConstr
• Force_Contact
• Force_Field
3. For a description of the two methods here, refer to the Parameters: Static Solver model element topic.