Command Element

Description

Modifies 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:

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).

Comments

For quasi-static simulation, only the force imbalance methods are supported.

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"

/>

Command Element

Description

Modifies a static or quasi-static simulation parameter element.

Declaration

def EQUILIBRIUM(TYPE="", ERROR=0.0, IMBALANCE=0.0, KINETIC_ENERGY_ERROR=0.0, MAXIT=0, PATTERN="", STABILITY=0.0, METHOD=""):

Attributes

TYPE

Type of the simulation to be carried out.  Choose from STATIC or DYNAMIC equilibrium.

ERROR

Modifies 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 ERROR is 1e-4.

IMBALANCE

Applicable if Force Imbalance method was chosen.  Modifies 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 IMBALANCE is 1e-4 force units.

KINETIC_ENERGY_ERROR

Applicable if MKEAM method was chosen.  Modifies the maximum allowable residual kinetic energy of the system at the static equilibrium point.  This should be a small number.  The default value for KINETIC_ENERGY_ERROR is 1e-5 energy units.

MAXIT

Modifies the maximum number of iterations that are allowed before simulation stops. If ERROR and KINETIC_ENERGY_ERROR are not satisfied at this point, the equilibrium iterations should be considered as having failed.  The default value for MAXIT is 75.

PATTERN

Modifies the frequency of evaluation of the Jacobian matrix during corrector iterations.

Specify PATTERN only when the default setting does not work well.  Frequent Jacobian iterations can slow down the simulations dramatically.

When not specified, the integrator automatically determines when a new Jacobian is needed by examining the rate of convergence.

STABILITY

Modifies the fraction of the mass matrix that is to be added to the Jacobian 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 in order 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 1e-10.

METHOD

Modifies the choice of the algorithm to be used for Static or Quasi-static simulation. Choose from following:

MKEAM is not applicable for quasi-static analysis.

Comments

See Param_Static

Example

The examples below show how the EQUILIBRIUM parameters can be modified:

EQUILIBRIUM(ERROR=0.001, MAXIT=50, KINETIC_ENERGY_ERROR=1e-5, METHOD="MKEAM"))

EQUILIBRIUM(ERROR=0.0001, IMBALANCE=0.0001, MAXIT=50, METHOD="FIM_S")