6.4 Superelement import
6.4.1 Generic representations in SDT
For interfacing with external finite element software the well documented superelement formalism is used. This formalism is largely used by Multibody Dynamic Software (Simpack, Adams, Excite, ...) and thus widely documented.
A superelement representation of the model is of the form
In general, the reduction is performed so that the DOFs retained {qR} are related to the original DOFs of a larger model by a Rayleigh Ritz reduction basis T using
This representation is fairly standard. The data structure representation within SDT is described in section 7.6. SDT/FEMLink supports import from various FEM codes and more details are given in section 6.4.2 for NASTRAN and section ?? for Abaqus.
For Craig-Bampton type reduction (enforced displacement on a set of interface DOF I and fixed interface modes on other DOF C), the reduction basis has the form
which verifies the constraints on basis columns that TII=I and TIC=0.
For the free mode variant (McNeal) (see sdtweb('fe_reduc','free')), the form is
with no TI columns.
The observation formalism of SDT which is applicable to both test/analysis sensors (see sdtweb('sensor')) and strain observations used for non-linearities .
Standard notions that have an equivalent in other code are
-
qI interface DOF are directly comparable in SDT and other software when using a DofSet entry that contains an identity enforced motion matrix on a set of DOF idof, typically known as MASTER degree of freedom. That can be initialized with a call of the form model=fe_case(model, 'DofSet', 'In',struct('DOF',idof, 'def', speye(length(idof)))).
- TC columns may correspond to generalized or internal DOFs. External software will often require that a DOF number be associated to these interfaces.
- bres the independent vectors used to generate residual loads are found as columns of a DofLoad entry. For point loads on a set of DOF adof the entry would be struct('DOF',adof, 'def',speye(length(adof))).
- [c] observation matrices do not exist in other environments. The strategy usually retained for export is to add additional nodes of a set ObsNode to correspond to the observations of interest and define the observation equation using a multiple point constraint. This is achieved by modifying the model using fe_sens('MeshSensAsMPC).
- rigid assuming that the 3D motion of all nodes in the set depend rigidly on the center node motion. Can be used to define motion of sensor nodes. This tends to over-stiffen the area of connected nodes.
- rbe3 assuming that the center node moves as the mean motion of the set of nodes is often considered to observe motion of nodes. The case dependent observations of SDT are more general, but may correspond to rbe3.
Implementations of these are discussed for Abaqus section 6.4.5, NASTRAN section 6.4.2, ANSYS section 6.4.6.
6.4.2 NASTRAN Craig-Bampton example
For a demo, see d_cms('Tuto'). The superelement generation by NASTRAN is saved to an .op2 file that is automatically transformed to the SDT superelement format by FEMLink. A sample file is given in ubeamse.dat.
ASSIGN OUTPUT2='./ubeam_se.op2',UNIT=30
$
ID DFR
SOL 101
GEOMCHECK NONE
TIME 100
$
CEND
TITLE=Generic computation of mode shapes
METHOD=1
DISP(PLOT) = ALL
SPCFORCES(PLOT)=ALL
MPCFORCES(PLOT)=ALL
$ Now extract stresses on base
SET 101=1 THRU 16
STRESS(SORT)=101
$
MPC=1
SPC=1
$ RESVEC(NOINRL)= YES
EXTSEOUT(ASMBULK,EXTBULK,EXTID=100,DMIGOP2=30)
PARAM,POST,-2
PARAM,BAILOUT,-1
$
BEGIN BULK
$EIGRL,SID,V1,V2,ND,MSGLV,MAXSET,SHFSCL,NORM
EIGRL,1,,,20
$ DOF and nodes to support modal DOF
QSET1,0,1000001,THRU,1000050
SPOINT,1000001,THRU,1000050
$ Master DOF 4 base corners
BSET1,123,1,5,8,12
$
$ Residual on 3 DOF of input node 104
USET,U6,104,123
$
$ Residual associated with CAMP1 vector
CDAMP1 161 2 114 1 244 1
PDAMP* 2 1.
$
include 'ubeam_include.bdf'
ENDDATA
The resulting basis has the following form
The op2 file contains nodes and superelement definition. It is advised to read the bulk file to obtain a model containing elements and material properties.
- The interface DOF are defined in NASTRAN usingBset cards. These are stored in SDT as a DofSet entry to the model.
- QSET correspond to modal/generalized DOFs. These require the definition of a QSET card (to declare existing DOFs), SPOINT grids (to have node numbers to support these QSET DOFs). Note also that the SPOINT numbers should be distinct from other NodeId. The number of modes defined in the EIRGL card should be lower than the the number of SPOINT and the QSET card.
- Fixed interface modes φc are computed by specifying the EIRGL card.
- Residual loads bres are defined as follows and lead to additional shapes using the residual vector procedures of NASTRAN
-
point loads simply declared using the USET,U6 card
- relative loads simply obtained by declaring a CDAMP element that generates a relative viscous load between its two nodes.
6.4.3 Free mode using NASTRAN
When using a free mode computation, NASTRAN provides mechanisms to compute residual vectors, you should just insert the RESVEC=YES card. An example is given in the ubeamfr.dat file. The resulting basis has the following form
The main mechanisms to generate residual vectors are
-
Free interface modes φc are computed by specifying the EIRGL card.
- Residual loads bres are defined as follows and lead to additional shapes using the residual vector procedures of NASTRAN
-
point loads simply declared using the USET,U6,NodeId,DofList card. Alternatively RVDOF (MSC but possibly not NX-NASTRAN) can given a list of up to four NodeId,Dof per card.
- relative loads simply obtained by declaring a CDAMP element that generates a relative viscous load between its two nodes.
6.4.4 Abaqus Craig-Bampton example
Superelement generation in Abaqus is divided in three steps.
-
*STEP, PERTURBATION//*STATIC used to define residual vectors. Note that export of residual loads associated with non-linearities is not yet implemented in SDT.
- *FREQUENCY, EIGEN=LANC to compute internal modes with possibly a Craig-Bampton interface declared by a *BOUNDARY card.
- *SUBSTRUCTURE GENERATE to generate and export the superelement, use *RETAINED NODAL DOF associated to fixed DOF in the frequency step for a Craig Bampton reduction.
See SeGenResidual.inp
6.4.5 Abaqus McNeal example
xxx
6.4.6 ANSYS Craig-Bampton example
The cards typically used for superelement generation in ANSYS are
-
antype,substr specify FE substructure generation in after /SOLU
- cmsopt,fix,Nshapes,,,,,tcms card generates .sub. Use ans2sdt('subSE','file.sub') to import matrices from .sub, restitution from .tcms and mesh from .cdb files using the same file root.
- resvec,on to use residual vectors in the basis
- seopt,name,MatType,1 with MatType=2 for mass and stiffness, and 3 for stiffness, mass, viscous damping, name must be defined with card /FILENAME before the analysis.
- m,NodeId,all master DOF definition repeat card for the various interface nodes. You will have to replace all with UX,,UY,UZ,ROTX,ROTY,ROTZ if the DOF is used by an element that supports multi-physics.
/FILENAME,ubeam_se ! name must be the one used in SeOpt command
/PREP7
!...
! Use command F to apply loads that will define the residual vector
/SOLU
antype,substr ! substructure analysis
CmsOpt,Fix,20,,,,,TCMS
RESVEC, ON
SeOpt,ubeamse_ans,3,1,0,, ! 3(all matrices,2 for m and k), 1 to print
! Define list of master DOF, you cannot use ALL if the elements support multi-physics
M,1,UX,,,UY,UZ,ROTX,ROTY,ROTZ
M,5,UX,,,UY,UZ,ROTX,ROTY,ROTZ
M,8,UX,,,UY,UZ,ROTX,ROTY,ROTZ
M,12,UX,,,UY,UZ,ROTX,ROTY,ROTZ
SAVE ! save .db file
SOLVE ! generate the matrices
FINISH
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