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