7.5.           FAST_ITER_RKE Alter

 

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$  Rigid Format 103 - Normal modes analysis

$  MSC/NASTRAN Version 2001 or NX Nastran Version 1.0

$

$

$     ******************************************************

$     *****            COPYRIGHT  (C)  2003            *****

$     *****          BY ATA ENGINEERING INC.           *****

$     *****             ALL RIGHTS RESERVED            *****

$     ******************************************************

$

$     09-03- ATA/Paul Blelloch

$

$     07-18-06 ATA/George Antoun

$        o Now writes initial user-defined ASET to punch file

$

$  Description:

$

$  This alter performs an Iterative Residual Kinetic Energy scheme to optimally

$  select A-set DOF.  It starts from a small A-set defined by the user and

$  iteratively adds DOF until it reaches a user specified number.  At

$  each iteration it adds one or more DOF based on the Residual Kinetic Energy

$  associated with a set of FEM modes provided by the user.

$

$  The residual kinetic energy is defined as follows

$

$  RKE = (MFF*(PHIFX-PHIF)).*(PHIFX-PHIF)

$

$  where

$  PHIFX - Mode shapes expanded from A-set using Guyan shapes

$  PHIF  - FEM mode shapes

$

$  The number of DOF added at each step of the iterative process is

$  controlled by the parameter RKFILT.  The default value of 1.0 will

$  add one DOF at each step.  Setting RKFILT to a value less than

$  1.0 may result in a larger number of DOF eliminated at each iterative

$  step.  All DOF with a residual kinetic energy  greater than RKFILT times

$  the largest value are added at each step.

$

$  This alter uses a number of numerical "tricks" to acceleration the calculation

$  of residual kinetic energy.  The primary trick is that the O-set stiffness

$  matrix is never decomposed, and the constraint shapes are never explicitly

$  constructed.  Instead flexibility shapes are calculated from the F-set

$  stiffness matrix and used to execute the required operations.

$

$  The alter will optionally calculate two error norms at each step in the

$  iteration.  The error norm is based on the following orthogonality

$  error matrix:

$

$  EORT = [I] - PHIX'*MXX*PHIX

$

$  The first norm (NORT) is the RSS of all the terms in this matrix.  The

$  second norm (MORT) is the maximum absolute value of all terms in

$  this matrix.  The error norms used the same modes used to calculate

$  residual kinetic energy (modes N1 to N2).

$

$  This alter uses the following set convention:

$

$  X - Current set of retained DOF (equivalent to A-set)

$  Y - Current set of omitted DOF (equivalent to O-set)

$  Z - Set of retained DOF added at this iteration (subset of X)

$

$  Special instructions to use this alter:

$-----------------------------------------------------------------------

$  FILE MANAGEMENT SECTION (FMS)

$

$  A set of FEM mode shapes must be provided in OUTPUT2, OUTPUT4 or DMIG

$  format.

$

$  If the OUTPUT2 or OUTPUT4 options are chosen these should be assigned

$

$  ASSIGN INPUTT4=fem_modes.op4 UNIT=11

$

$  or

$

$  ASSIGN INPUTT2=fem_modes.op2 UNIT=11

$

$  Note that a formatted OUTPUT4 file can be used as follows

$

$  ASSIGN INPUTT4=fem_modes.op4 UNIT=11 FORMATTED

$

$  The format and unit number are controlled by PARAM,OMODES.  See the

$  write_modes alter for more details

$

$-----------------------------------------------------------------------

$  EXECUTIVE CONTROL DECK

$

$    SOL 103

$    Include this alter immediately before the CEND statement

$

$-----------------------------------------------------------------------

$  CASE CONTROL DECK

$

$    No special input is required.

$

$-----------------------------------------------------------------------

$  BULK DATA DECK

$

$    ASET cards must be included to define the initial DOF

$

$    USET,U1 cards can optionally be included to define a candidate set.  Only

$    DOF from this candidate set will be added to the A-set

$

$    Optional parameters:

$

$    PARAM,ENORM,CHAR   'YES' : Calculate error norm

$                       'NO'  : Do not calculate error norm (default)

$                

$    PARAM,NDOF,I       : Number of DOF in final set (default = 1000)

$

$    PARAM,RKFILT,RS    : Filter to remove DOF at each step (default = 1.0)

$

$    PARAM,OMODES,I     <0 : Read FEM modes from OUTPUT2 file UNIT = |OMODES|

$                        0 : Read FEM modes from DMIG cards

$                       >0 : Read FEM modes from OUTPUT4 file UNIT = OMODES

$

$    PARAM,N1,I         : 1st FEM mode to use in RKE calculation (default = 1)

$

$    PARAM,N2,I         : Last FEM mode to use in RKE calculation (default = all)

$

$-----------------------------------------------------------------------

$  EXAMPLE NASTRAN DECKS

$

$

$    ASSIGN  OUTPUT4='gpsc_fem.op4', UNIT=13

$    ASSIGN  MASTER='gpsc_irke.MASTER'

$    ASSIGN  DBALL ='gpsc_irke.DBALL'

$    $

$    SOL     103

$    INCLUDE fast_iter_rke.v2001

$    CEND

$    $

$    TITLE    = GENERAL PURPOSE SPACECRAFT

$    SUBTITLE = SELECT DOF

$    LABEL    = ITERATIVE RESIDUAL KINETIC ENERGY

$    $

$    SPC = 1

$    METHOD = 50                 $ Modes to 50 Hz

$    $

$    BEGIN BULK

$    $

$    PARAM,NDOF,50               $ Select best 50 DOF

$    PARAM,RKFILT,0.9            $ ADD DOF with > 90% of max RKE

$    PARAM,OMODES,13             $ Read FEM modes from Unit 13

$    PARAM,ENORM,YES             $ Calculate error norm at each step

$    $

$    EIGR,50,AHOU,1.0,50.0

$    $

$    INLCUDE 'gpsc.blk'

$    $

$    INCLUDE 'gpsc_init.aset'

$    $

$    INCLUDE 'gpsc_candidate.uset'

$    $

$    ENDDATA

$

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