Elastic representation as superelements

SDT-nlsim Contents Functions

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2.4 Elastic representation as superelements

The base documentation on superelement import is part of SDT, see SeImport .

2.4.1 NASTRAN cards used for sensors/non-linearities

The NASTRAN equivalent of superelement notions discussed in section ?? are

q_I interface DOF of are defined in NASTRAN using Bset cards. These are stored in SDT as a DofSet entry to the model.
b_res the independent vectors used to generate residual loads and lead to additional shapes using the residual vector procedures of NASTRAN
- point loads simply declared using the USET,U6 card
- relative loads simply can obtained by declaring a CDAMP element that generates a relative viscous load between its two nodes.
- [b] is defined by an DAREA real loading and possibly DPHASE definition. It should be noted that in SDT, it is strongly advised to define the phase using the input, since a complex input shape matrix has no sense in the time domain. The input is defined using a RLOAD2 B(f)e^{iφ(f)+θ−2π f τ} or RLOAD1 (C(f)+iD(f))e^{iθ −2π f τ}
T_C columns are associated to scalar DOFs called QSET. 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.
y=[c]{q} observation. Does not exist in NASTRAN documentation, but implemented exporting SPOINT for each observation component and an MPC for each row of the observation matrix. This is achieved by modifying the model using fe_sens('MeshSensAsMPC' prior to export.
rigid is known as RBE2 in NASTRAN.
rbe3 is known as RBE3 in NASTRAN.

Laws without internal states are similar to PGAP and import will be implemented in the future.

2.4.2 ABAQUS cards used for sensors/non-linearities

The Abaqus equivalent of superelement notions discussed in section ?? are

q_I interface DOF xxx
b_res the independent vectors used to generate residual loads are written as independent load cases using xxx SeWriteBres
```
*LOAD CASE, NAME=LC000001
*CLOAD, OP=MOD
1001, 1, 1
*END LOAD CASE
```
*FREQUENCY, RESIDUAL MODES : computation of attachment modes, coherent wit first order corrections.
*EQUATION : equivalent the SDT MPC definition with a direct constraint matrix declaration.
*KINEMATIC COUPLING : equivalent of SDT rigid connections where the spring is connected to a master node with 6 DOF which enforce motion of a number of slave DOFs.
*DISTRIBUTING COUPLING equivalent of SDT RBE3 : flexible connection where the spring is is connected to a slave node with 3 or DOF which depend from a set of master nodes.
*COUPLING : specific surface based definition, followed by either a *KINEMATIC card for rigid or *DISTRIBUTING card for RBE3 formulations.
*MPC : node based definition with type BEAM to constraint 6 DOF per node or type PIN to constraint the 3 translations only.
*CONNECTOR : connectors provide advanced structural kinematics, type BEAM without elasticity definition provides a rigid connection (linearized in SDT).

2.4.3 ANSYS cards used for sensors/non-linearities

For spring representations of volumes or surfaces, a first common approach is to use so called rigid elements. ANSYS supports

CE, CERIG, MPC184, RBE 2 : rigid connections where the spring is connected to a master node with 6 DOF which enforce motion of a number of slave DOFs.
TARGE 170+CONTA 173, TARGE 170+CONTA 174

2.4.4 Storing advanced SDT options in bulk format

For upcom parameters, export is done using design variables.

SDT-NLSIM provides an harmonic definition mechanism (see hdof). Storage in NASTRAN bulk format is as follows

$   1  $$   2  $$   3  $$   4  $$   5  $$   6  $$   7  $$   8  $$   9  $
$ All DOFs with sin(omega t) and cos(omega t) 
DTI     HDOF    1       ALL     123456  CS1     ENDREC
$ Gradual building of full list of DOFs 
DTI     HDOF    1       N1      THRU    N2      123     S1      N3
        THRU    N4      1       C1      N5      123456  S1      ENDREC

Node numbers are first specified using ALL all (independent) nodes, N1 THRU N2 a list of consecutive node numbers, N5 a single node number. Associated DOFs are then written using the CM field of RBE2 (Component numbers of the dependent degrees-of-freedom integers 1 through 6 with no embedded blanks). A third field then specifies the harmonics. cs1 is a short cut for both cos(1 ω t) and sin(1 ω t).

The specification of target frequencies follows the normal NASTRAN format using FREQ or FREQ1 cards. Provision for a single call generating responses at multiple amplitudes (hbm_solve AFMap .Freq and .Amp fields) is specified as a DTI HBMAmp entry with all target amplitudes given.

$   1  $$   2  $$   3  $$   4  $$   5  $$   6  $$   7  $$   8  $$   9  $
EIGRL,10,,,1
$FREQ,SID,F2,F2,F3
$FREQ1,SID,F1,DF,NDF
FREQ          10   0.318      1.     3.0     4.0
RLOAD1        10       1                       1

$   1  $$   2  $$   3  $$   4  $$   5  $$   6  $$   7  $$   8  $$   9  $
DTI     HBMAmp  1       1.0     2.0     3.0     ENDREC

To specify loads, a number of formats are defined.

$   1  $$   2  $$   3  $$   4  $$   5  $$   6  $$   7  $$   8  $$   9  $
DTI     Name    1       SID     101     FORM    Amp     UN1     UN2    
        Harmi   ACi     ASi     ENDREC

Name is an arbitrary string (at most 8 characters) but should be unique and differ from internal NASTRAN tables. By default it is proposed to use strings of the form P101 where 101 is the property number.
IREC (field 3 of the DTI) is only used when considering multiple entries with the same name and should be set to 1.
SID : first the string SID in field 4 then, in field 5, the property identifier (integer) which should correspond to the set identification number SID for which this amplitude dependence is defined.
Form (selected with the string on field 7) is the form name with the following formats defined
Form

Amp amplitudes {u(t)} = C₀+∑_{k∈ H} S_k sin(kω t) + C_k cos(kω t)

AmpT Amp table {u(t)} = C₀(ω)+∑_{k∈ H}S_k(ω) sin(kω t) + C_k(ω) cos(kω t)
Harmi number of retained harmonic. 1 for cos(1 ω t) and sin(1 ω t).
ACi, ASi amplitudes associated with the cosine and sine harmonic contributions. In the AmpT form integer numbers referring to table entries in the bulk.

Form
Amp	amplitudes	{u(t)} = C₀+∑_{k∈ H} S_k sin(kω t) + C_k cos(kω t)
AmpT	Amp table	{u(t)} = C₀(ω)+∑_{k∈ H}S_k(ω) sin(kω t) + C_k(ω) cos(kω t)