3.4.5.      Effective Independence

Selecting TAM DOF using the EI method is performed using the effind alter in Nastran. A candidate DOF set should be provided as a starting point. This candidate set typically includes all DOF that can be measured on the structure.  Because the EI algorithm does not reduce the mass matrix, the candidate DOF set can be much larger than for other algorithms (100,000+ DOF).

Because the effind alter does not reduce the mass matrix, it cannot calculate orthogonality based error norms at each step.  It does calculate and report the determinant of the FIM at each step.

The EI method is applied in Nastran by using the effind alter. Requirements for the use of this alter are as follows:

·         File Assignment Deck. The alter requires the FEM mode shapes as output from the write_modes alter. If the OUTPUT2 or OUTPUT4 options are chosen, the corresponding file must be assigned using an INPUTT2 or INPUTT4 assignment in the file assignment deck.

·         Executive Control Deck. The effind alter must be included before the CEND card.

·         Case Control Deck. No special input is required.

·         Bulk Data Deck. The bulk data deck must include the standard information for performing a normal modes analysis including USET,U1 cards to define the candi­date DOF. If pseudo- and cross-orthogonalities are desired and the DMIG option was chosen for the FEM mode shapes, these must be included in the bulk data. Otherwise the OMODES parameter must be set as follows:

OMODES < 0            Read the modal frequencies and shapes in OUTPUT2 for­mat from FORTRAN UNIT |OMODES|

OMODES > 0            Read the modal frequencies and shapes in OUTPUT4 for­mat from FORTRAN UNIT OMODES

The EI method is controlled by the following parameters:

NDOF                       Number of DOF to reduce matrices to (no default)

EFFILT                     Select DOF with EI values > EFFILT (default = 1.0)

N1                             1st FEM mode to use in EI calculation (default = 1)

N2                             Last FEM mode to use in EI calculation (default is all)

The number of DOF eliminated at each step in the EI process is controlled by the EFFILT parameter. By default this is set to 1.0, and only one DOF will be elimi­nated at each step. If it is set to a value less than 1.0, all DOF with their inverse effective independence greater than EFFILT times the maximum inverse effective independence will be elimi­nated at each step[21].

At the end of the EI procedure, the retained DOF are written to the .f06 file in MATGPR format and the .pch file in DMIG format. An eigensolution is performed using the reduced matrices and, if requested, the pseudo- and cross-orthogonalities are calculated. The solution then stops. Further processing of the reduced set can be performed by converting them to ASET cards and starting a new Nastran run.

The DOF eliminated at each step are written to the .f06 and .pch files.  The determinant of the FIM at each step is written to the .f06 file.  This determinant can be plotted vs. the number of DOF to evaluate the amount of information lost as each DOF is eliminated.  It cannot be directly mapped to an orthogonality error.

A sample EI run is illustrated in Figure 3-20. In this run the initial set is selected to be all translational DOF for every grid in the model that is not restrained. The goal is to choose the best 20 DOF, using a filter of 1.0 so that only one DOF is removed per iteration.

gpsc_ei.dat

 

ASSIGN INPUTT4='gpsc_fem.op4', UNIT=13

ASSIGN MASTER ='gpsc_ei.MASTER', DELETE

ASSIGN DBALL  ='gpsc_ei.DBALL',  DELETE

$

SOL 103 $

$

INCLUDE effind.v2001'

$

CEND

TITLE    =GENERAL PURPOSE SPACECRAFT (GPSC)

SUBTITLE =EFFECTIVE INDEPENDANCE

LABEL    =FIND BEST 20 DOF

$

SPC    = 10             $ Constrain booster interface points

METHOD = 70             $ Modes to 70 Hz

$

DISP(PLOT) = ALL        $ Recover displacements

$

BEGIN BULK

$

PARAM   WTMASS  .00259

PARAM   OMODES  13   

PARAM   NDOF    20   

PARAM   EFFILT  1.0

$

EIGRL   70      1.0     70.0

$

$  Spacecraft bulk data

$

INCLUDE 'gpsc.blk'

INCLUDE 'gpsc.prp'

$

$  Large candidate set (138 DOF) to start process

$

INCLUDE 'gpsc.uset'

$

ENDDATA

Figure 3-20. Sample input file for Effective Independence (EI).