The MWEI algorithm is implemented in TAMKIT using the mass_weighted_effind alter. There are two ways to run this procedure. For fairly small models (<10,000 DOF) it may be possible to start the procedure with no preliminary reduction and allow the algorithm to pick from all DOF in the model. However, for most practical problems it is not possible to do this since the preliminary reductions will require too much memory and disk space[22]. Instead, a candidate DOF set should be provided. This candidate set can be identified using any other method including EI, but should be limited to no more than 5,000 – 10,000 DOF.
The mass_weighted_effind alter will optionally calculate the pseudo-orthogonality matrix listed in Equation 2.4-1 and report two norms on the difference between this matrix and the identity matrix. The first norm (NORT) is the Frobenius norm, which is defined as the square root of the sum of the squares (RSS) of the elements of a matrix. The second norm (MORT) is the maximum absolute value of any element in the matrix. These error norms can be plotted against number of DOF to develop an understanding of TAM accuracy as a function of number of retained DOF.
Requirements for the use of the mass_weighted_effind 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 mass_weighted_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 ASET 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 MWEI method is controlled by the following parameters:
ENORM = ‘NO’ Do not calculate error norms at each step (default)
ENORM = ‘YES’ Calculate error norms at each step
EFFILT Select DOF with MWEI values > EFFILT (default = 1.0)
NDOF Number of retained DOF to stop algorithm (default=1000)
N1 1st FEM mode to use in MWEI calculation (default = 1)
N2 Last FEM mode to use in MWEI calculation (default is all)
The number of DOF eliminated at each step in the MWEI 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 mass weighted effective independence greater than EFFILT times the maximum inverse effective independence will be eliminated at each step[23].
At the end of the MWEI procedure, the retained DOF are written to .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.
A sample MWEI run is illustrated in Figure 3-21. 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_mwei.MASTER', DELETE
ASSIGN DBALL ='gpsc_mwei.DBALL', DELETE
$
SOL 103 $
$
INCLUDE ‘mass_weighted_effind.v2001'
$
CEND
TITLE =GENERAL PURPOSE SPACECRAFT (GPSC)
SUBTITLE =MASS WEIGHTED 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_cdof.aset'
$
ENDDATA
Figure 3-21. Sample input file for Mass Weighted Effective Independence (MWEI).