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:
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Organization (S): EDF-R & D/AMA, SINETICS
Handbook of Utilization
U4.5- booklet: Methods of resolution
U4.53.21 document
Operator DYNA_TRAN_MODAL

1 Goal

To calculate the transitory dynamic response of a system deadened or not in generalized co-ordinates.
Calculation is carried out by modal superposition or under-structuring.

Not-null initial conditions can be introduced making it possible amongst other things to use the results
of a former calculation.

The loading is given in the form of a linear combination of vectors generalized and of
functions of time describing the temporal evolution of these vectors.

Three explicit methods of integration: “EULER”, “DEVOGE”, “ADAPT” (method of integration with step
adaptive time), an integral method “ITMI” and a method of integration implicit: “NEWMARK”
are available. The explicit algorithms and “ITMI” support calculation with taking into account of
non-linearities located with the nodes of the shocks type and friction. Methods “EULER” and “ADAPT”
support the taking into account of non-linearities of the fluid blade type and antiseismic device type.

The structure of data result contains for various moments of calculation, the results
generalized and calculated forces of shock.

The conversion of the results generalized in physical space is possible by the operators
REST_BASE_PHYS [U4.63.21] or for a component by RECU_FONCTION [U4.32.03].

Product a concept of the tran_gene type.
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Count

matters

1 Goal ......................................................................................................................................................... 1
2 Syntax .................................................................................................................................................. 4
3 Operands ............................................................................................................................................. 8
3.1 Generalized matrices ...................................................................................................................... 8
3.2 Algorithms of integration ................................................................................................................. 8
3.2.1 Operand METHOD ............................................................................................................... 8
3.2.2 Key word INCREMENT .............................................................................................................. 11
3.3 Key word ETAT_INIT ....................................................................................................................... 12
3.3.1 Operands RESU_GENE/DEPL_INIT_GENE/VITE_INIT_GENE ............................. 12
3.3.2 Operand INST_INIT ......................................................................................................... 12
3.3.3 Operand CRITERION ............................................................................................................. 12
3.3.4 Operand PRECISION ......................................................................................................... 12
3.4 Description of the loading: key word EXCIT ................................................................................. 13
3.4.1 Operands VECT_GENE/NUME_MODE ............................................................................. 13
3.4.2 Operand FONC_MULT/COEF_MULT ............................................................................... 13
3.5 Particular case of the seismic analysis ............................................................................................ 13
3.5.1 Taking into account of the modes neglected by static correction: key words MODE_CORR,
CORR_STAT and D_FONC_ * .................................................................................................... 13
3.5.2 Taking into account of the multi-supports: key words MODE_STAT, MULTI_APPUI and ACCE, VITE,
DEPL ................................................................................................................................. 14
3.6 Taking into account of nonlocalized linearities of shock type, friction and fluid blade .................. 15
3.6.1 Not localized linearities of shock type and friction: key word CHOC ................................... 15
3.6.2 Not localized linearities of fluid blade type ....................................................................... 19
3.7 Key word VERI_CHOC ....................................................................................................................... 20
3.8 Key word ANTI_SISM ....................................................................................................................... 21
3.9 Key word FLAMBAGE ......................................................................................................................... 21
3.10
Key word RELA_EFFO_DEPL ................................................................................................... 22
3.10.1
Operand NODE ..................................................................................................... 22
3.10.2
Operand SOUS_STRUC ........................................................................................... 22
3.10.3
Operand NOM_CMP ................................................................................................. 22
3.10.4
Operand RELATION ............................................................................................... 22
3.11
Key word RELA_TRANSIS ....................................................................................................... 23
3.12
Key word RELA_EFFO_VITE ................................................................................................... 23
3.13
Response of mechanical systems very slightly deadened with couplings fluidélastiques23
3.14
Key word ARCHIVAGE .............................................................................................................. 25
3.14.1
Operand LIST_ARCH ............................................................................................. 25
3.14.2
Operand PAS_ARCH ............................................................................................... 26
3.15
Operand INFORMATION .................................................................................................................... 26
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3.16
Operand IMPRESSION ....................................................................................................... 27
3.16.1
Operands ALL/LEVEL .................................................................................. 27
3.16.2
Operands INST_INIT/INST_FIN ................................................................... 27
3.17
Operand TITRATES ................................................................................................................. 27
4 Production run ............................................................................................................................... 28
4.1 Checking on the matrices .......................................................................................................... 28
4.2 Checking and consulting on the choice of the step of time for diagrams EULER, DEVOGE and
NEWMARK:...................................................................................................................................... 28
4.3 Production run for method “ADAPT”:............................................................................ 28
4.4 Production run for method “ITMI” ................................................................................ 29
5 Examples of use .......................................................................................................................... 30
5.1 Calculation of the linear response of a system ................................................................................... 30
5.2 Calculation of the nonlinear response of a system ............................................................................ 31
5.2.1 Modeling of the side thrust ......................................................................................... 31

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2 Syntax

tranmo [tran_gene] = DYNA_TRAN_MODAL (


reuse
= tranmo,




MASS_GENE
=
my
,
[matr_asse_gene_R]



RIGI_GENE
=
laughed
,
[matr_asse_gene_R]


/AMOR_GENE = amndt
,
[matr_asse_gene_R]
/
AMOR_REDUIT
=

,
[l_R]
/
LIST_AMOR


=
l_amor
,
[listr8]



METHODE
=
/
“EULER”,
[DEFAUT]
/
“DEVOGE”,
/
“NEWMARK”,
/
“ADAPT”,
/
“ITMI”,



INCREMENT = _F (
INST_INIT =
to, [R]








INST_FIN = tf,
[R]








PAS
=
dt,
[R]








VERI_PAS =/
“OUI”,
[DEFAUT]
/
“NON”,





# Operands specific to an integration by step of adaptive times







VITE_MIN =/
“STANDARD”, [DEFECT]
/
“MAXI”,







COEF_MULT_PAS =/1.1,
[DEFAUT]
/
cmp
,
[R]







COEF_DIVI_PAS =/1.33333334, [DEFECT]
/
cdp
, [R]







PAS_LIMI_RELA =/1.E-6,
[DEFAUT]
/
per
, [R]







NB_POIN_PERIODE =
/50, [DEFAUT]
/
NR,
[I]







NMAX_ITER_PAS =/16,

[DEFAUT]
/
NR, [I]





# End of the operands specific to an integration by step of adaptive times






),



ETAT_INIT = _F (/RESU_GENE =
LMBO,
[tran_gene]









/
| DEPL_INIT_GENE = C, [vect_asse_gene]










| VITE_INIT_GENE = vo, [vect_asse_gene]








INST_INIT =
to, [R]








CRITERE =
/“RELATIVE”, [DEFECT]
/
“ABSOULU”,








PRECISION =/1.E-3,
[DEFAUT]
/
prec, [R]








),



EXCIT
= _F (
VECT_GENE
=
v,
[vect_asse_gene]







NUME_MODE
=
nmod,
[I]








/
FONC_MULT
=
F,
[function]









/
COEF_MULT
=
has,
[R]









/
ACCE
=
ac,
[function]










VITE
=
VI,
[function]










DEPL
=
dp,
[function]
# Operands and key words specific to the seismic analysis



[§3.5]








MULT_APPUI =/“NOT”,
[DEFAUT]
/
“OUI”,

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DIRECTION
= (dx, Dy, dz, drx, dry, drz), [l_R]







/NOEUD
= lno, [l_noeud]








/
GROUP_NO

=
lgrno,


[l_groupe_no]








CORR_STAT
=
/
“NON”
[DEFAUT]
/
“OUI”







D_FONC_DT

=
dfdt,
[function]








D_FONC_DT2
=
dfdt2,
[function]






)


/MODE_STAT
=
psi, [mode_stat]
/
MODE_CORR
=
modcor, [mult_elas]
),
# End of the operands and key words specific to the seismic analysis

CHOC
=
_F (












[§3.6.1]







INTITULE =
int,
[l_Kn]







/NOEUD_1
=
no1,

[node]







/GROUP_NO_1
=
grno1,
[group_no]






/NOEUD_2
=
no2,

[node]







/GROUP_NO_2
=
grno2,
[group_no]








OBSTACLE
= obs,

[obstacle]






NORM_OBST
=
NOR,

[listr8]






ORIG_OBST
=
ori,

[listr8]






JEU
=
/
1.,
[DEFAUT]
/
play,
[R]







ANGL_VRIL
=
gamma,
[R]







DIST_1
=

dist1,
[R]






DIST_2
=

dist2,
[R]







SOUS_STRUC_1
= ss1, [K8]






SOUS_STRUC_2 = ss2, [K8]






REPERE
=
/
“GLOBAL”,
[DEFAUT]
/
nom_sst, [K8]







RIGI_NOR = kN,
[R]






AMOR_NOR =/
0.,
[DEFAUT]
/
Cn,

[R]






RIGI_TAN =/
0.,
[DEFAUT]
/
kt,

[R]






AMOR_TAN =/
0.,
[DEFAUT]
/
ct,

[R]






COULOMB
=
/
0.,
[DEFAUT]
/
driven,
[R]

# Operands and key words specific to the taking into account of a fluid blade

[§3.6.2]






LAME_FLUIDE
=/
“NON”,
[DEFAUT]
/
“OUI”,






ALPHA
=/
0.,
[DEFAUT]
/
alpha,
[R]






BETA
=
/
0.,
[DEFAUT]
/
beta, [R]






CHI
=
/
0.,
[DEFAUT]
/
chi,
[R]






DELTA
=/
0.,
[DEFAUT]
/
delta,
[R]






NMAX_ITER
=
/
20,
[DEFAUT]
/
niter,
[I]


RESI_RELA
=
/
1.E-3,
[DEFAUT]
/
residue, [R]


LAMBDA
=
/
10., [DEFAUT]
/
lambda, [R]
),
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# End of the operands and key words specific to the taking into account of a fluid blade


VERI_CHOC = _F (










[§3.7]







STOP_CRITERE
=/
“OUI”,
[DEFAUT]
/
“NON”,







SEUIL =
/0.5,
[DEFAUT]
/
S,
[R]





),


ANTI_SISM = _F (










[§3.8]







/NOEUD_1
=
no1,

[node]







/GROUP_NO_1
=
grno1,
[group_no]






/NOEUD_2
=
no2, [node]







/GROUP_NO_2
=
grno2,
[group_no]






RIGI_K1
=
/
0.,
[DEFAUT]
/
kN,

[R]






RIGI_K2
=
/
0.,
[DEFAUT]
/
kN,

[R]






SEUIL_FX =/
0.,
[DEFAUT]
/
Py,

[R]






C
=
/
0.,
[DEFAUT]
/
C,

[R]






PUIS_ALPHA
=
/
0.,
[DEFAUT]
/
alpha,

[R]






DX_MAX
=
/
1.,
[DEFAUT]
/
dx,

[R]







),


FLAMBAGE
= _F (










[§3.9]






/NOEUD_1
=
no1,

[node]






/GROUP_NO_1
=
grno1,
[group_no]





/NOEUD_2
=
no2,

[node]






/GROUP_NO_2
=
grno2,
[group_no]





OBSTACLE
=
obs,
[obstacle]





ORIG_OBST
=
ori,
[listr8]





NORM_OBST
=
NOR,
[listr8]





ANGL_VRIL
=
/
0, [DEFAUT]
/
gamma,
[R]





JEU
=
/
1.,
[DEFAUT]
/play,
[R]





DIST_1
=
dist1,
[R]





DIST_2
=
dist2,
[R]





REPERE
=

/“TOTAL”, [DEFECT]
/
nom_sst
,
[K8]





RIGI_NOR = kN, [R]





FNOR_CRIT
=
flim, [R]





FNOR_POST_FL
=
fseuil,
[R]





RIGI_NOR_POST_FL
=
k2,
[R]





),


RELA_EFFO_DEPL = _F (









[§3.10]







NOEUD
= Noah, [node]







SOUS_STRUC
=
S,
[K8]







NOM_CMP
=
nomcmp, [K8]







RELATION
= F,
[function]









),


RELA_TRANSIS = _F (









[§3.11]







NOEUD
= Noah, [node]







SOUS_STRUC
=
S,
[K8]







NOM_CMP
=
nomcmp, [K8]







RELATION
= F,
[function]









),
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RELA_EFFO_VITE = _F (









[§3.12]







NOEUD
= Noah,

[node]







SOUS_STRUC
=
S,
[K8]








NOM_CMP=
nomcmp, [K8]







RELATION
= F,
[function]









),

# Key Words only associated with method “ITMI”



[§3.13]


BASE_ELAS_FLUI =
mix, [melasflu]


NUME_VITE_FLUI =
Nvitf, [I]


ETAT_STAT
=
/
“NON”,
[DEFAUT]
/
“OUI”,


PREC_DUREE =/1.E-2,
[DEFAUT]
/
prec,
[R]


CHOC_FLUI
=
/
“NON”,
[DEFAUT]
/
“OUI”,


NB_MODE = Nmode,
[I]


NB_MODE_FLUI
=
Nmodef, [I]


TS_REG_ETAB = tsimu,
[R]
# End of the key words only associated with method “ITMI”


ARCHIVAGE
=
_F (/LIST_ARCH
=
l_arch, [l_I]
[§3.14]








/PAS_ARCH = ipa,



[I]







),


INFO =/1,
[DEFAUT]







/2,


IMPRESSION
=
_F (





/ALL = “YES”, [DEFECT]
/
NIVEAU
=
|
“DEPL_LOC”,
|
“VITE_LOC”,
|
“FORC_LOC”,
|
“TAUX_CHOC”,





INST_INIT
=
Ti,
[R]





INST_FIN
=

tf,
[R]







),


TITER
=
titrate,
[l_Kn]
)
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3 Operands

3.1 Matrices
generalized

In the case of a calculation by modal recombination, the generalized matrices must be established by
operator PROJ_MATR_BASE [U4.63.12] or by macro-command MACRO_PROJ_BASE [U4.63.11],
starting from the same modal base.
In the case of a calculation by dynamic under-structuring, the generalized matrices must be
established by operator ASSE_MATR_GENE [U4.65.04], starting from same generalized classification.

MASS_GENE = my

Stamp of mass of the generalized system.
Concept of the matr_asse_gene_R. type.

RIGI_GENE = laughed

Stamp rigidity of the generalized system.
Concept of the matr_asse_gene_R. type.

/AMOR_GENE = amndt

Stamp damping of the generalized system.
Concept of the matr_asse_gene_R. type.
This option is not available with method “DEVOGE”.


/AMOR_REDUIT = lam

List reduced depreciation (percentage of damping criticizes) corresponding to
each mode of the system in the form of list of realities.

This option is not available in dynamic under-structuring because depreciation
reduced must be defined for each substructure separately (operator
MACR_ELEM_DYNA [U4.65.01]).

Note:

If the number of reduced depreciation given is lower than the number of vectors of
base used in the modal base, depreciation of the additional vectors
are taken equal to the last damping of the list.


/LIST_AMOR = l_amor

List the depreciation reduced in the form of concept listr8.

3.2 Algorithms
of integration

3.2.1 Operand
METHODE

METHODE
=

Choice of the numerical method of resolution.
In the case of a traditional calculation by modal recombination, the user has three
methods of the explicit type, an integral method and method of an implicit type.
In the case of a calculation by dynamic under-structuring [R4.06.04], method of calculation
transient on modal basis calculated by under-structuring supports all the diagrams
of integration evoked except the integral method. On the other hand, method of calculation transitory on
the “bases” of the substructures supports only the diagram of Euler and the diagram with step of time
adaptive.
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3.2.1.1 METHOD = “EULER”: diagram clarifies command 1

This diagram supports calculation with taking into account of the whole of localized non-linearities
available.

3.2.1.2 METHOD = “DEVOGE”: diagram clarifies command 4

The diagram of DEVOGELAERE supports calculation with taking into account of the whole of not
localized linearities available.

3.2.1.3 METHOD = “NEWMARK”: implicit scheme

This diagram allows only the integration of linear problems.

3.2.1.4 METHOD = “ADAPT”: diagram clarifies command 2

This diagram supports calculation with taking into account of the whole of localized non-linearities
available. This method uses the diagram of the centered differences, the algorithm of adaptation of
no time is based on the calculation of a “apparent frequency”:

1
X
& - x&
F
T
T-1
APt =

2
X - X
T
T-1

One specifies Ci after the operands specific to the method of integration per step of adaptive times.
They are the operands following of the key word factor INCREMENT:

NB_POIN_PERIODE = NR

A number of points per apparent period. It is this parameter which fixes the precision of calculation. It must
to be at least equal to 20; its default value (50) guarantees a satisfactory precision (command
from 1%) in the majority of the cases.

VITE_MIN
=

Method of calculation the speed of reference used to evaluate the apparent frequency.
When the denominator of the frequency connects (X - X
N
n-1) becomes weak, this one can
to become very high, which leads to an unjustified refinement of the step of time. To cure it,
the algorithm uses the following criterion:

X - X
N
n-1
1
(X & - X
N
& N
& - 1)
V
F
=
T
min
AP N

2

V
T

min

Vmin can be calculated in two ways different according to the value from VITE_MIN:

V tn
“NORM” = min (N)
()
V
T
=
for all the degrees of freedom.
100
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Can be used:

·
if the system has several degrees of freedom,
·
if the order of magnitude of displacement is not too different according to degrees' from
freedom.

Max (V I (tp))
I
<
0 T <t
p
N
“MAXI” = Vmin (tn) =
for the degrees of freedom I.
100

Can be used:

·
if the system has a small number of degrees of freedom (from 1 to 3),
·
for a system with several degrees of freedom, if the order of magnitude of
displacement is very different according to degrees of freedom's (for example involved
of ddl of Lagrange in under-structuring),
·
if the order of magnitude speed does not vary too much in the course of time.

NMAX_ITER_PAS = NR

A maximum number of reductions of the step of time per step of calculation. It is by defect equal to 16, it
who limits the coefficient of reduction of the step to 0 7516
10 2
.
=
- by iteration (when the step of time
is too high, one takes again calculation with a weaker step: T = 0 7
. 5t
N
N).

NMAX_ITER_PAS can be:

·
increased to allow the step time to fall in a more brutal way,
·
decreased if the step of time seems excessively refined, for example in presence
discontinuities (solid friction, discontinuous excitation,…).

COEF_MULT_PAS = cmp

Coefficient of increase in the step when the error is sufficiently weak:

0 7
. 5
T <
T
= cmp T
N
.
Nf
n+1
N
APn

Its default value (cmp = 1.1) guarantees stability and precision, but it can in general be
increased (with more up to 1.3) to accelerate integration.

COEF_DIVI_PAS = cdp

Coefficient of refinement of the step of time (>1) when the error is higher than 1, that the number
maximum iterations (N_MAX_ITER_PAS) is not reached and that the step of minimal time is not
not reached:
1.
T <
, NR
< NR
and T > plr.t
N
Nf
iter
iter _max
N
initial
AP N
T

T
N
=
N
cdp

The default value is 1.33333334, that is to say a reduction of a factor 0.75.
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PAS_LIMI_RELA = plr

Coefficient applied to the step of initial time to define the limit of refinement and thus the step of
minimal time:

The default value is 1.33333334, that is to say a reduction of a factor 0.75.

T
= plr T
min
. initial

3.2.2 Word
key
INCREMENT

3.2.2.1 Operands
INST_INIT/INST_FIN

INST_INIT = to

·
Methods “EULER”, “DEVOGE”, “NEWMARK”, “ADAPT”:

Moment of beginning of transitory calculation. In the event of recovery, one uses key word ETAT_INIT
cf [§3.3]: under this key word, the initial moment is recovered with operand INST_INIT or taken
equal to the last moment of filed preceding calculation. Operand INST_INIT must thus be
used only if there is no resumption of a preceding calculation.

·
Method “ITMI”:

Indicate the moment of beginning of simulation. When calculation in a step of time of the phase
transient is required, simulation begins with INS_INIT + “calculating time from
transient “

INST_FIN = tf

Moment of simulation.

3.2.2.2 Operands
NOT/VERI_PAS

PAS = dt

·
Methods “EULER”, “DEVOGE”, “NEWMARK”:

No the time of transitory calculation.

·
Method “ADAPT”:

Indicate at the same time the step of initial time and the step of maximum times used by the algorithm.
This parameter must be sufficiently weak:

- to allow the calculation of the static phases (which always uses the step of time
maximum),
-
to start the algorithm correctly.

It must however be sufficiently high not to penalize the whole of calculation.

·
Method “ITMI”:

Indicate the step of time appointed for the first step of calculation (after possible passage of
transient). Thereafter, the algorithm automatically manages the step of calculation according to
rigidity of the structure and the zones of transition flight/shock.

VERI_PAS = reference mark

Checking of the step of calculating time relative to the step of time limits given in function
the highest frequency of the modes of the modal base considered or bases of
substructures (cf [§4.2]).
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3.3 Word
key
ETAT_INIT

Key word factor which allows a continuation of a transitory calculation, while taking as initial state:

·
that is to say a result resulting from a calculation by modal synthesis preceding EXCIT (RESU_GENE);
·
maybe displacements and speeds expressed in the form of generalized assembled vectors
EXCIT (DEPL_INIT_GENE and VITE_INIT_GENE)

Note:

· This functionality is not available for a calculation by transitory under-structuring
without double projection nor for method ITMI.
· At the time of a continuation, the state of adherence or shock is not backed up.
· Displacements and speeds generalized must be establish by the operator
PROJ_VECT_BASE [U4.63.13] starting from the modal base used for the matrices of
rigidity generalized or by operator RECU_GENE [U4.71.03] steady to a calculation
precedent.

3.3.1 Operands
RESU_GENE/DEPL_INIT_GENE/VITE_INIT_GENE

/RESU_GENE = tran

Concept of the tran_gene type resulting from a preceding calculation with DYNA_TRAN_MODAL.

/I
DEPL_INIT_GENE = C

Concept of the vect_asse_gene type, generalized displacements initial.


I VITE_INIT_GENE = vo

Concept of the vect_asse_gene type, initial generalized speeds.

3.3.2 Operand
INST_INIT

INST_INIT = to

Moment of preceding calculation to in the case of extract and take as initial state a recovery. In
the absence of this operand, the moment of recovery is taken equal to the last moment of preceding calculation
filed.

3.3.3 Operand
CRITERE

CRITERE

Indicate with which precision the search of the moment must be done:

“RELATIF”: interval of search [(1-prec) .instant, (1+prec) .instant]
“ABSOLU”: interval of search [moment-prec, instant+prec]

The criterion is “RELATIF” by defect.

3.3.4 Operand
PRECISION

PRECISION
=/1.E-03
[DEFAUT]
/
prec [R8]

Indicate with which precision the search of the moment must be done.
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3.4
Description of the loading: key word EXCIT

EXCIT

Key word defining the loading. This key word must be repeated time as many as there are vectors
loading generalized fi. The total loading is the sum of these vectors loading.

3.4.1 Operands
VECT_GENE/NUME_MODE

The loading is taken into account in the form of vector projected on the modal basis
EXCIT =_F (VECT_GENE) or in the form of modal component EXCIT =_F (NUME_MODE) or both
at the same time.


/VECT_GENE = v

Generalized vector allowing to describe the space distribution of the loading.
Concept of the vect_asse_gene type.
The generalized vectors must be establish by operator PROJ_VECT_BASE [U4.63.13] with
to leave the modal base used for the generalized matrices. In the case of a calculation by
dynamic under-structuring, the generalized vectors must be establish by the operator
ASSE_VECT_GENE [U4.65.05] starting from the generalized classification used for
generalized matrices.


/NUME_MODE = nmod

Number of the mode of excitation of the structure.

3.4.2 Operand
FONC_MULT/COEF_MULT

/FONC_MULT = F

Function of time (function) allowing to describe the temporal evolution of the vector
loading.


/COEF_MULT = has

Multiplying coefficient of the generalized vector (constant actual value compared to time).

3.5
Particular case of the seismic analysis

3.5.1 Taking into account of the modes neglected by static correction: key words
MODE_CORR, CORR_STAT and D_FONC_ *

During the seismic analysis of an excited mono structure, it is possible to take into account, has
posteriori, the static effect of the neglected modes. In this case, at the time of the return on the physical base, them
calculated relative displacements (respectively relative speeds and accelerations) are corrected
by a pseudo-mode.
One will find the details of this type of correction in [R4.05.01].

Key words MODE_CORR and EXCIT (CORR_STAT, D_FONC_DT and D_FONC_DT2) specific to
static correction a posteriori must be simultaneously present.

MODE_CORR = modcor

Concept of the mult_elas type produces by the macro-command MACRO_ELAS_MULT [U4.51.02] which
corresponds to the linear static response of the structure to a unit loading of type forces
imposed (constant acceleration) in the direction of the seism considered.
It is noted that there is as many loading case of direction of seism.
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EXCIT
=_F (CORR_STAT)

If MODE_CORR is present, CORR_STAT = “OUI” makes it possible to take into account the contribution
modal correction a posteriori for each occurrence of key word EXCIT.

EXCIT =_F (D_FONC_DT and D_FONC_DT2)

D_FONC_DT and D_FONC_DT2 are respectively the derivative first and derived seconds of
time of the definite accélérogramme, in each seismic direction considered, by the operand
FONC_MULT. They balance the contribution of the modal correction a posteriori for each
occurrence of key word EXCIT in order to obtain the corrections speed respectively and
of acceleration on the physical basis.

Note:

· The taking into account of the static correction excludes that from the multi-supports.
· The concept mult_elas must be based on a coherent classification of the equations
(even profile and even option of renumerotation) with that of the system solved in
operator DYNA_TRAN_MODAL.
· To the ième occurrence of key word EXCIT the ième elastic solution of MODCOR corresponds.

3.5.2 Taking into account of the multi-supports: key words MODE_STAT, MULTI_APPUI and
ACCE, QUICKLY, DEPL

In the case of a multimedia structure, in order to restore the sizes calculated in the reference mark
absolute or to take into account nonlocated linearities, it is necessary to calculate the answer generalized in
taking into account the component of drive.
For more details, one will refer to the reference [R4.05.01].

Key words MODE_STAT and EXCIT (MULT_APPUI; ACCE, VITE, and DEPL; DIRECTION and NOEUD or
GROUP_NO) specific to the taking into account of the multimedia character must be simultaneously
present.

MODE_STAT = psi

Concept of the mode_stat type produces by the command MODE_STATIQUE [U4.52.14] which
corresponds to (3 or 6) the .nb_supports static modes (where nb_supports is the number of supports
who undergo a different acceleration).

EXCIT
=_F (MULT_APPUI)

If one calculates the seismic response of a multimedia structure, MULT_APPUI = “OUI”, one
compare at every moment, the vector of absolute displacements of each point of shock
considered, in order to determine if there is shock and to calculate the corresponding forces of shock.
If not, MULT_APPUI = “NON”, one compares at every moment, the vector of relative displacements
of each node likely to shock.

/ACCE
=
ac,


VITE
=
VI,


DEPL
=
dp

Names of the functions acceleration (ACCE), speed (VITE) and displacement (DEPL) imposed at the time of
calculation of the seismic response of multimedia structures.

Note:

If the structure is mono-excited, the accélérogramme is defined by key word FONC_MULT.
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DIRECTION = (dx, Dy, dz, drx, dry, drz)

Components of the vector giving the direction of the seism in the total reference mark.


/
NOEUD

=
lno


/
GROUP_NO =
lgrno

List names of nodes (or group of nodes) corresponding to the supports concerned where
seism is imposed.

3.6 Taking into account of nonlocalized linearities of shock type,
friction and fluid blade

3.6.1 Not localized linearities of shock type and friction: key word CHOC

CHOC

This key word factor is used for the study of the response of structures (generally slim)
whose displacements are limited in one (or several) (S) - not specified a priori by the user
by the presence of an obstacle (the various types of obstacles available are described in
documentation [U4.44.21] of operator DEFI_OBSTACLE), another antagonistic structure or
of an effect of blade fluid.

3.6.1.1 Operand
INTITULE

INTITULE = int

Heading (eight characters to the maximum) allowing to name non-linearity. If nothing is specified
by the user, the heading is the name of the NOEUD_1.

3.6.1.2 Operands
NOEUD_1/NOEUD_2/GROUP_NO_1/GROUP_NO_2

NOEUD_1 or GROUP_NO_1

Node or name of the group of node of the structure to which the condition of non-linearity relates.
In the case of a non-linear calculation by dynamic under-structuring, one indicates under this key word
the node of shock pertaining to the first substructure (various substructures
do not belong to the same grid).

NOEUD_2 or GROUP_NO_2

Node or name of the group of node of the second structure to which the condition relates of
non-linearity. This operand is specific to the definition of a contact between two structures
mobiles.
In the case of a non-linear calculation by dynamic under-structuring, one specifies the node of
shock coinciding with the node indicated in NOEUD_1 (or GROUP_NO_1), but pertaining to
second substructure.

Note:

It is checked that the groups of nodes contain well one and only one node.

3.6.1.3 Operand
OBSTACLE

OBSTACLE = obs

Name of the concept of the obstacle type defining the geometry of an indeformable obstacle or
form envelope of the play between two antagonistic structures. It is produced by the operator
DEFI_OBSTACLE [U4.44.21].
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3.6.1.4 Operand
NORM_OBST

NORM_OBST = NOR

List of 3 realities defining the normal in the plan of cut of the obstacle, i.e. the vector xloc.
One advises that xloc is the direction of neutral fiber or a generator of the structure
studied.

3.6.1.5 Operand
ORIG_OBST

ORIG_OBST = ori

List of 3 realities defining the position of the origin of the obstacle in the total reference mark (key word
obligatory in the case of shocks between a mobile structure and a fixed wall). In the case of
shocks between two mobile structures, the code considers by defect that the origin is located at
medium of the two nodes of shock NOEUD_1 (or node of the GROUP_NO_1) and NOEUD_2 (or node of
GROUP_NO_2).

3.6.1.6 Operand
JEU

JEU = play

In the case of a shock enters a mobile structure and an indeformable obstacle, operand JEU
represent:

·
the half-distance inter-plans for obstacles of the type PLAN_Y and PLAN_Z
·
the radius of the circular obstacle for an obstacle of the type CERCLE

This key word is unutilised in the case of obstacles discretized by segments of the type DISCRET.

Note:

The obstacle of the type PLAN_Y or PLAN_Z comprises in fact two plane obstacles. Thus in
case where the user wishes to model the shock on a single level, not to be obstructed by
the rebound of the structure studied on the symmetrical level, one advises with the user of
to push back very far (cf [Figure 3.6.1.6-a]), J represents the real play between the studied structure and
the obstacle.

Yloc
Y
play
J
Zloc
K
X
orig_obs
m
no1

Appear 3.6.1.6-a: Système mass-arises impacting a fixed wall

Note:

Key word JEU is not used in the case of shock between mobile structures.

The various cases of plays are represented in the documentation of DEFI_OBSTACLE
[U4.44.21].
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3.6.1.7 Operand
ANGL_VRIL

ANGL_VRIL = gamma

, angle in degrees defining the angular position of the local reference mark of the obstacle in its plan.

By convention, normal N in the plan of cut of the obstacle, NORM_OBST defines the axis xloc
locate local. One passes from the total reference mark X Y Z to the reference mark of the plan of obstacle N y Z
2 2 by one
product of two rotations of angles around Z then around transformed y1 of Y.
The position of the obstacle in this plan is obtained by a rotation of angle around the direction
normal xloc (cf [Figure 3.6.1.7-a]).

Z2

Zloc
Z=Z1

Y

Y2 = Y1

Yloc
Obstacle of the type PLAN_Z
Xloc = N = X2

X1

X


Y
X1
Z2
Y1
X2
Zloc



X1
Z2
Yloc



X
Z1
Y2
Z=Z1
Y1=Y2
X2=Xloc

Appear 3.6.1.7-a: Rotations allowing to pass from the total reference mark to the local reference mark of the obstacle.
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The angles and are automatically given starting from the normal with obstacle N.
locate local X
, Y
, Z
loc
loc
loc
results then from the reference mark N, y
, Z

2
2 per rotation of an angle
of gimlet ANGL_VRIL around N.

Note:

· If the user does not specify anything, the angle of gimlet is calculated by the code in the case of shocks
between mobile structures with obstacles of the type BI_PLAN.
· With regard to the other types of obstacles, the default value of gamma is zero.

3.6.1.8 Operands
DIST_1/DIST_2

DIST_1 = dist1

Outdistance characteristic of matter surrounding NOEUD_1: no1 (or GROUP_NO_1).
Operand specific to the contact between two mobile structures.

DIST_2 = dist2

Outdistance characteristic of matter surrounding NOEUD_2: no2 (or GROUP_NO_2).
Operand specific to the contact between two mobile structures.

Note:

· DIST_1 and DIST_2 are defined within the meaning of the outgoing normals of the two solids in
opposite (DIST_1 and DIST_2 they are > 0 bus represent the thickness of the structures
studied).
· Because of the calculation of the normal distance from shock, the sum of DIST_1 and DIST_2 must
to be sufficiently large compared to the supposed amplitude of the relative displacement of
nodes of shocks (cf [R5.06.03]).

3.6.1.9 Operands
SOUS_STRUC_1/SOUS_STRUC_2

SOUS_STRUC_1 = ss1

Name of the substructure which contains the node of shock informing key word NOEUD_1 (or
GROUP_NO_1).

SOUS_STRUC_2
= ss2

Name of the substructure which contains the node of shock informing key word NOEUD_2 (or
GROUP_NO_2).

3.6.1.10 Operand LOCATES

REPERE = reference mark

Specify the reference mark in which the position of the obstacle is defined.

/
“GLOBAL”

The absolute position of the obstacle is defined independently of rotations and translations
which the various substructures are subjected.

/
nom_sst

Name of a substructure.
The position and the normal of the obstacle are given in the reference mark used to define them
co-ordinates of the nodes of the substructure nom_sst, the position and the normal finales of
the obstacle being the result of rotation and the translation to which is subjected
substructure.
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3.6.1.11 Operand RIGI_NOR

RIGI_NOR = kN

Value of the normal rigidity of shock (unit NR/m in USI).

3.6.1.12 Operand AMOR_NOR

AMOR_NOR = Cn

Value of the normal damping of shock (unit NR m/s in USI).

3.6.1.13 Operand RIGI_TAN

RIGI_TAN = kt

Value of the tangential rigidity of shock (unit NR/m in USI).

3.6.1.14 Operand AMOR_TAN

AMOR_TAN = ct

Value of the tangential damping of shock (unit NR m/s in USI).

Note:

If a stiffness kt is specified and that key word AMOR_TAN misses, the code calculates one
damping optimized in order to minimize the residual oscillations in adherence according to
the formula:
C = 2 (K + K) m - 2 K m
T
I
T
I
I
I
I

where I is the index of the dominating mode in the response of the structure.

3.6.1.15 COULOMB operand

COULOMB = driven

Value of the coefficient of friction of COULOMB.

3.6.2 Not localized linearities of fluid blade type

The operands following are specific to transitory calculation with localized non-linearity of blade type
fluid.

3.6.2.1 Operands
NMAX_ITER/RESI_RELA/LAMBDA

In this case, the projected system takes the form:

T .M.& + T.
C.& + T .K. = T .F (T) + T .F
(. .&.
T
T
T
E
fluid
T
T
& T)

&t is thus not given explicitly according to,
T
T
&. To obtain accelerations
generalized, one uses the algorithm of point fixes according to:
&0 = &
T
T1
-,
T
T
& are given. One repeats until convergence:

-
&
i+1
1
= [T.(M +.
T
T
I
T
T
I
T
I
My).].(.F
+. .M.
fluid
has
&
+ .F -.
C.
T
E
& - .K.
T
T
T)

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where:
My the diagonal contribution of the matrix of added mass represents resulting from
fluid blade,
is a parameter (higher than 1) used to guarantee the character contracting of the iterations
of fixed point. By defect = 10.

Convergence is tested by &i+1 - &i <. I
T
&

T
T where is the relative residue.

NMAX_ITER = niter

Numbers maximum iterations of the algorithm. By defect, niter = 20.

RESI_RELA = residue

Relative residue, noted above. By defect, = 10­3.

LAMBDA: lambda

Parameter of convergence, noted above. By defect, = 10.

3.6.2.2 Operands
LAME_FLUIDE/ALPHA/BETA/CHI/DELTA of the key word factor CHOC

LAME_FLUIDE = reference mark

Specify if the interaction enters the node and the obstacle or between the two nodes has involved place
of a fluid blade. By defect, the connection is supposed of dry contact type.
The force of reaction of the fluid blade [R5.06.05] takes the following general form:

X
X 2
X
X X
Fluid =.
&
.
&
.
&



+. &. &

X + H +

X + H + (X +h) 3 (X +h) 2

where H is the thickness of the fluid blade at rest.

ALPHA, BETA, CHI, DELTA

Parameters of the fluid force of blade.

3.7 Word
key
VERI_CHOC

Key word which makes it possible to evaluate a posteriori, the aptitude of the modal base to represent them correctly
impacts.

If VERI_CHOC is present, one calculates in each node of shock and for each mode, the rate of
2
N (T I. im
F Po)
reconstitution of the static solution: T = K

S
statics
and, for information, the rate of
K
i=1
I
N T I. im
F Po
reconstitution of the shearing action: T
T

NR =
.(im
F po.K.i). One calculates then them
K
i=1
I
values cumulated on the whole of the modes which constitute the modal base used.

It is checked that the report/ratio of the neglected flexibility (static flexibility minus static flexibility
reconstituted) on the flexibility of shock remains lower than the value given by operand SEUIL (SEUIL
0.5 per defect are worth) if not:

·
if STOP_CRITERE = “OUI” one stops the execution of the program (it is the case by defect);
·
if STOP_CRITERE = “NON” one continues the execution of the program with emission of one
alarm.
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Note:

· This functionality is available only for obstacles of the plane type or bi_plan.
· If the rate of reconstitution of the static solution is lower than the value of the threshold, one advises
with the user to supplement the modal base by the local modes at the points of shock which have
an important local flexibility.
· The formula is not applicable in the event of static modes (noninvertible matrix of rigidity).
Calculation continues then without checking of the criteria of shock and the user is informed by it.

3.8 Word
key
ANTI_SISM

Key word ANTI_SISM is incompatible with a calculation by dynamic under-structuring. It allows
to calculate the nonlinear force which exists if an antiseismic device is placed between the two nodes
antagonists whose names are specified by the key words (NOEUD_1 or GROUP_NO_1 and NOEUD_2
or GROUP_NO_2):
(K - K

1
2) X
X
F
K X
+ C sign (X
2
&) X
D =
+
&

2
X
K X
max
1 + 1

Py

RIGI_K1, RIGI_K2, SEUIL_FX, C, PUIS_ALPHA and DX_MAX

Parameters of the force due to the presence of an antiseismic device.

As example, values of the parameters for an antiseismic device of type JARRET
are:

K1 = 6. E+06 NR/m, K2 = 0.53 E+06 NR/m, Py = 1200., C = 0.07 E+05 Nm/S, alpha = 0.2 and
xmax = 0.03 m (if the problem is posed in USI).

3.9 Word
key
FLAMBAGE

This key word is used for the detection of possible buckling and the evaluation of the deformation
residual of an element at the time of a shock between two mobile structures or a mobile structure and
a fixed wall. The force of reaction at the time of a shock with taking into account of buckling can be
summarized by the following diagram:

F
Flim
kN
Fseuil
k2
compression

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It is considered that there is buckling if the force of reaction F reaches the value limits Flim defined by
the user. The normal rigidity of shock after buckling k2 is then different from front rigidity
buckling kN.

Only the operands specific to key word FLAMBAGE are detailed. The other key words allow
to define the places of shock and are identical to the operands of key word CHOC.

FNOR_CRIT = flim

Force normal limit which involves the buckling of the structure.

FNOR_POST_FL = fseuil
Force normal limit after buckling which causes a residual deformation of the structure.

RIGI_NOR_POST_FL = k2
Value of normal rigidity after buckling.

Note:

The calculation of shock with buckling does not allow the taking into account of the fluid blade and of
the damping of shock.

3.10 Word
key
RELA_EFFO_DEPL

RELA_EFFO_DEPL

Key word factor allowing to define a relation force-displacement or moment-rotation on one
degree of freedom given in the shape of a nonlinear curve.

3.10.1 Operand NODE

NOEUD = No

Name of the node of the structure to which the relation relates.

3.10.2 Operand SOUS_STRUC

SOUS_STRUC = S

Name of the substructure containing the node informing operand NOEUD.

3.10.3 Operand NOM_CMP

NOM_CMP = nomcmp

Name of the component of the node of the structure to which the relation relates.

3.10.4 Operand RELATION

RELATION = F

Name of the nonlinear function.
The nonlinear relation is defined starting from the linear limit of behavior.

Note:

Contrary to key word RELA_TRANSIS, there is not linear limit, the definite function
under key word RELATION is thus defined on] -, + [.
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The equilibrium equation, for the modelled structure, subjected to a horizontal acceleration of ground
ax in direction X, and having terms of correction coming from non-linearities is written:

MX & + Cx & + Kx = - My + F
X
C

where FC is the corrective force due to nonthe linearity of the ground. It can, for example, be defined by
the following relation (cf case test SDND103):

F (X
)

X
F (X)
threshold
F (X
C
=
-
) with, if X > X
() = K 1 -
. X.
X
threshold, F X
0
threshold

x0

In example Ci above, one thus imposes, under operand RELATION the function:

K
F (X) = 0 X.[X - X
C
threshold].
x0

3.11 Word
key
RELA_TRANSIS

RELA_TRANSIS

This key word factor was introduced in order to ensure a compatibility with the preceding versions. It
corresponds in fact to key word RELA_EFFO_DEPL of version 4. It thus allows, just like
current key word RELA_EFFO_DEPL to impose a relation force-displacement on a degree of
freedom of a node given in the form of a nonlinear function. The nonlinear relation being
defined starting from the linear limit of behavior.

Operands NOEUD, SOUS_STRUC, NOM_CMP and RELATION have the same direction for
key words RELA_EFFO_DEPL, RELA_TRANSIS and RELA_EFFO_VITE. They are thus not
detailed in this paragraph.

3.12 Word
key
RELA_EFFO_VITE

RELA_EFFO_VITE

Key word factor allowing to define a relation force-speed on a degree of freedom of a node
given in the form of a nonlinear function.

Operands NOEUD, SOUS_STRUC, NOM_CMP and RELATION have the same direction for
key words RELA_EFFO_DEPL, RELA_TRANSIS and RELA_EFFO_VITE. They are thus not
detailed in this paragraph.

3.13 Response of mechanical systems very slightly deadened with
couplings fluidelastic

One describes Ci below the key words specific to the calculation of the response of mechanical systems
linear very slightly deadened with couplings fluidelastic possibly associated with
non-linearities located with the nodes of the shocks type and frictions.

METHOD = “ITMI”

This diagram of integration by integral method allows, for the slightly deadened systems,
to obtain an exact response by taking account of the variations of fluidelastic forces obtained
in the presence of shocks.
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Note:

This diagram of integration is not usable in continuation and does not allow calculation by
dynamic under-structuring.
The presence of key word CHOC is imperative even for simulations of phases without shocks
known as “phases of flight”.
The taking into account of non-linearities of the fluid blade type was not introduced to date into
diagram of integration

BASE_ELAS_FLUI = mix

Modal base used for calculation.

Concept of the melasflu type produces by the operator CALC_FLUI_STRU [U4.66.02] who contains
the whole of the modal bases calculated for different the rate of flow definite. It
key word is obligatory for method “ITMI”.

NUME_VITE_FLUI = Nvitf

Rate of flow retained for calculation (sequence number).

Allows to extract in the concept melasflu the modal base corresponding at the speed
of flow retained (cf [U4.66.02]). This key word is obligatory for method “ITMI”.

ETAT_STAT
=

For the systems very slightly deadened, this option makes it possible to avoid an expensive calculation of
linear phase preceding the first shock. This phase, called thereafter “transitional stage”
precede the establishment by a mode made up of a succession of nonlinear phases of shocks
and/or of linear phases called of “flight” according to functions' of excitation of the mechanical system
applied. The time of transient corresponds to a displacement equal to the play of a thrust. It can
to be relatively important (50 to 100 seconds).

ETAT_STAT = “YES”: the passage in only one step of calculating time of the phase allows
transient.

The passage of the transitional stage is carried out by supposing the mechanical system in “flight”.
time necessary to the passage of the transient is estimated by the algorithm according to
mechanical characteristics of the system in `'flight ''. This estimate is based on a criterion where
intervene parameter PREC_DUREE and the durations of excitations due to the turbulent efforts.

Note:

If one asks for a simulation with calculation in a step of time of the transitional stage, it
will be necessary to take care to introduce one duration of sufficiently long excitation. This duration must
to correspond to the duration necessary to the passage of the transient increased by the duration of
simulation in established mode wished. This total duration of simulation will be indicated via
two operands INST_INIT and INST_FIN under the key word factor INCREMENT.

ETAT_STAT = “NOT”: Simulation does not distinguish the transitory state from the established mode.

PREC_DUREE = prec

Allows to define the precision chosen to determine the duration of the transitional stage according to
formulate:
-
(
Ln prec)
T =
where
and
tr
reduced damping and the pulsation indicate respectively
2
0
0
0
0
of each mode considered. The default value of this parameter is 1%.
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CHOC_FLUI
=

Determine the processing carried out by the algorithm during the phases of shock with respect to the forces
fluidelastic.
By defect, variation of the fluidelastic forces in phase of shock related to the modification of
rigidity and of the damping of the mechanical system (impact on the thrust) is not taken in
count.

NB_MODE = Nmode

A number of modes of the modal base retained for dynamic calculation.
The preserved modes correspond to increasing frequencies (first modes). If
NB_MODE is not specified, one takes all the modes of the modal base of the concept of the type
melasflu.

NB_MODE_FLUI = Nmodef

A number of modes of the modal base disturbed by the fluidelastic phenomena of coupling
in phase of shock (lower than the number of modes retained for dynamic calculation).
The preserved modes correspond to Nmodef first increasing frequencies (first
modes). If NB_MODE_FLUI is not specified, one takes the number of modes retained for
dynamic calculation.

TS_REG_ETAB = tsimu

Duration of desired simulation.

In the case of a simulation without preliminary calculation and in a step of time of the transitional stage
(ETAT_STAT = “NON”), this duration corresponds to the duration of simulation whatever the state of
system enters the moments of beginning and end of simulation. Consequently one will have to ensure oneself
that: TS_REG_ETAB INST_FIN - INST_INIT

By defect, one will have TS_REG_ETAB = INST_FIN - INST_INIT

In the case of a simulation with calculation of the transitional stage (ETAT_STAT = “OUI”), this
duration corresponds to the duration of really desired simulation when the phase of shocks is
established from the numerical point of view. Consequently one will have to make sure that:

TS_REG_ETAB INST_FIN - INST_INIT - “time considered transitory”

If this last condition is not observed, the user is informed with
precision of the minimum time of excitation necessary for its calculation INST_FIN - INST_INIT.
By defect, one a: TS_REG_ETAB = INST_FIN - INST_INIT - “time considered transitory”

3.14 Word
key
ARCHIVAGE

ARCHIVAGE

Key word factor defining filing.

3.14.1 Operand LIST_ARCH

·
Methods “EULER”, “DEVOGE”, “NEWMARK”:

/LIST_ARCH = l_arch

List entireties defining the moments of calculation for which the solution must be filed
in the concept tran_gene result.
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3.14.2 Operand PAS_ARCH

PAS_ARCH = ipa

· Methods “EULER”, “DEVOGE”, “NEWMARK”, “ITMI”:
Entirety defining the periodicity of filing of the solution of transitory calculation in the concept
tran_gene result.
If ipa = 5 one files all the 5 steps of calculation.
Whatever the option of filing chosen, one files the last step of time and all the fields
associated to allow a possible recovery.
By defect one files all the steps of calculation.

·
Method “ADAPT”:
Entirety which makes it possible to calculate the interval between two moments of filing in the concept
result, equal to PAS_ARCH * PAS. With this convention, the step of filing is always
superior or equal to the maximum step used by calculation.

With a variable step, the moments of filing do not correspond exactly to steps of
calculation. The algorithm thus files the sizes with the steps of calculation closest to the moments
of filing indicated by the user (in Tn on this diagram):

No calculation
T
Tn+1
N
No filing
Moments of filing


3.15 Operand
INFO

INFO = imp
Entirety allowing to specify the level of impression in file MESSAGE.
If INFORMATION: 1, one prints following information in file MESSAGE:
<I> <nom of the routine where information suivantes> is written
If <I> <MDTR74>, one recalls that it is a transitory calculation on modal basis “traditional”,
if not <I> <SSDT74> it is a transitory calculation on modal basis by under-structuring
dynamics.
<---------------------------------------------->
CALCULATION BY MODAL SUPERPOSITION
----------------------------------------------
! The BASE OF PROJECTION EST a >type of the base of projection<
! NB Of EQUATIONS EAST: Nb
! METHOD UTILISEE EAST: >nom of the method of integration <
! BASE UTILISEE EAST: >nom of the modal base <
! NB OF BASIC VECTORS EAST: nbv
! THE INITIAL TIME NO EAST: step value of initial time
(only if method ADAPT requested)
! THE TIME NO OF CALCULATION EAST: step value of calculating time
! NB OF CALCULATION EAST NO: nbc
! NB OF FILE EAST NO: nba
! THE NUMBER OF PLACE (X) OF SHOCK EAST: nbchoc
! THE NUMBER OF RELA_EFFO_DEPL EAST: nbrelaed
(only if the number of relations is nonnull)
! THE NUMBER OF RELA_EFFO_VITE EAST: nbrelaev
(only if the number of relations is nonnull)
----------------------------------------------

If INFORMATION: 2, one prints, in addition to written information if INFO is worth 1, them
following information in file MESSAGE:
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For each obstacle:

· The number and type of the obstacle;
· The name and co-ordinates in the total reference mark of the node of shock (of the nodes of shock
in the case of a shock between mobile structures);
· Orientation, in the total reference mark, of the normal to the obstacle;
· The value of the angle of gimlet;
· The value of the initial play;

And for each node of shock and each mode, the number of the mode, values of
local stiffnesses of shock and the rate of local flexibility and the local flexibility.
One also prints at the end, for each node of shock:

RATE OF RESTIT FLEXIBILITY: 9.9539E-01 is 99.53% of local flexibility;
RATE OF RESTIT SHARP EFFORT: 1.8979E-02 is 1.89% of the sharp effort.

One prints these quantity overall for the whole of the modes and each mode.

One prints moreover:

·
for each node of shock, local the flexibility reports/ratios on flexibility of shock and
static flexibility minus local flexibility on flexibility of shock,
·
for each mode, its participation on the deformations statics in the nodes of shock. It is worth
the report/ratio of the number of conditioning of the matrix closed by the modal vector and them
static deformations on the number of conditioning of the matrix of the deformations
statics.

3.16 Operand
IMPRESSION

IMPRESSION

Key word factor which makes it possible to print in file RESULTAT of the sizes, nonprintable
by an operator of impression, such as local displacement, local speed, the forces of
contact with the nodes of shock and the value cumulated on all the modes of the modal base of
projection of the rate of reconstitution of the static solution.

3.16.1 Operands ALL/LEVEL

Key word NIVEAU makes it possible to print one or more table (X) among “DEPL_LOC”, “VITE_LOC”,
“FORC_LOC” and “TAUX_CHOC”. With TOUT = “OUI” (default value), one prints the four
tables.

3.16.2 Operands INST_INIT/INST_FIN

These two key words make it possible the user to filter the impressions in each loop on the steps
time.

3.17 Operand
TITER

TITER = title

Titrate structure of data result [U4.03.01].
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4 Phase
of execution

4.1
Checking on the matrices

In the case of a calculation by modal recombination, one checks that the generalized matrices are well
exits of a projection on a common basis and with the same number of basic vectors. In
case of a calculation per dynamic under-structuring, one checks that the generalized matrices are well
exits of the same generalized classification.

4.2 Checking and consulting on the choice of the step of time for
diagrams EULER, DEVOGE and NEWMARK:

One makes sure that the step of selected time checks the stability conditions of the numerical diagram (criterion
CFL):

· in the case of NEWMARK, stability are always assured but the going beyond of the criterion can
to induce a lack of precision on the result and is announced by a message; calculation
continues (with the risk to produce a not very precise or false result).
· in the case of diagrams of EULER and DEVOGE, if operand VERI_PAS is worth “OUI” (value by
defect), the execution is stopped, a step of minimum time is proposed. If the operand
VERI_PAS is worth “NON” or if it is about diagram ADAPT, a message of alarm is transmitted and it
calculation continues (with the risk to produce a not very precise or false result).

In a transitory analysis without non-linearity, it should be taken care that the step of time is such as:

dt < 0,1/fn for NEWMARK and DEVOGE
dt < 0,05/fn for EULER

fn being the highest frequency of the modes of the modal base considered.

Note:

It is mentioned that with nonlocalized linearities the step of selected time must be sometimes very
lower than this advised value.

4.3
Production run for method “ADAPT”:

The execution is stopped when the step of time reaches a minimal step equal to
NOT X PAS_LIMI_RELA.

Note:

The diagram of the centered differences does not restore in an exact way the own pulsations of one
system, which leads to important computational errors in the two following cases:
·
Calculation of a very great number of free periods of oscillations;
·
Calculation of the oscillations of a system very slightly deadened (<
-
10 3) excited on one
frequency of resonance.
In these two cases, it is often necessary to increase parameter NB_POIN_PERIODE.

Method “ADAPT” can be used in under-structuring.

The step of time can be recovered by operator RECU_FONCTION, with following syntax:
not = RECU_FONCTION (
RESU_GENE = dynamoda
NOM_CHAM = PTEM
….)

For more clearness, it is in fact the decimal logarithm of the step of time which is stored in
concept result of RECU_FONCTION.
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4.4
Production run for method “ITMI”

The execution is stopped:

·
when the duration of excitation chosen by the user is incompatible with the time of
simulation wished (mode established + simulation after obtaining the established mode). In it
case, the user is informed with precision of the minimum time of excitation necessary for sound
calculation,
·
when the algorithm does not succeed in finding a solution converged at the time of the diagonalisation
matrix of stiffness,
·
when the phases of transition flight/shock cannot be given with a precision
sufficient.

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5 Examples
of use

5.1
Calculation of the linear response of a system

One presents an example partial of use of a linear calculation of response with static correction.

# Description of the loading

condlim = AFFE_CHAR_MECA (MODELE = model,
DDL_IMPO=_F (GROUP_NO=' A2',
DX=0., DY=0., DZ=0., DRX=0., DRY=0., DRZ:0.)
)

charge = AFFE_CHAR_MECA (model MODELE=,
FORCE_NODALE=_F (GROUP_NO=' B2', FX=1.0D6)
)

v_elem = CALC_VECT_ELEM (OPTION=' CHAR_MECA', CHARGE= charges)

v_asse = ASSE_VECTEUR (VECT_ELEM = v_elem, NUME_DDL=NUM)
#
# Calculation of the static loading
#
modcor = MACRO_ELAS_MULT (model MODELE=, NUME_DDL= NUM,
CARA_ELEM = champcar,
CHAM_MATER= champmat,
CHAR_MECA_GLOBAL= condlim,
CAS_CHARGE= _F (NOM_CAS= “CAS1”,
CHAR_MECA= charges)
)
#
# Calculation dynamic by modal superposition
# One projects on the first 9 modes of the base
#
MACRO_PROJ_BASE (BASE = MODES, NB_VECT = 9,
MATR_ASSE_GENE =_F (MATRICE = mass_gen, MATR_ASSE = m_asse),
MATR_ASSE_GENE =_F (MATRICE = rigi_gen, MATR_ASSE = k_asse),
VECT_ASSE_GENE =_F (VECTEUR = vect_gen, VECT_ASSE = v_asse)
)
#
# Response with static correction
#
tran_gen = DYNA_TRAN_MODAL (
MASS_GENE = mass_gen,
RIGI_GENE = rigi_gen,
METHOD = “DEVOGE”,
MODE_CORR = modcor,
EXCIT = _F (VECT_GENE = vect_gen,
CORR_STAT = “YES”,
FONC_MULT = depl,
D_FONC_DT = quickly, D_FONC_DT2 = gamma
),
INCREMENT = _F (INST_INIT= 0.,
INST_FIN: 0.1,
PAS = 0.00001),
FILING = _F (PAS_ARCH = 100)
)
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5.2
Calculation of the nonlinear response of a system

One presents the file of execution for the dynamic calculation of a steam generator with
thrusts side and frontal tilted with 22° limiting its displacements (see [Figure 5.2-a]).

POMPE
Y
PRIMAIRE
Connect out of U
Cold branch
Frontal thrust
Side thrust
dimensioned PP
GENERATEUR
D E vapor
Connect Chaud E
Side thrust
CUVE
dimensioned opposite PP
22°
X

Appear 5.2-a: Schéma of a primary education branch of circuit

5.2.1 Modeling of the side thrust

The side thrust in Générateur of Vapor is parallel to the axis of the hot branch. One selected one
obstacle of the type BI_PLAN_Z, the normal direction of shock is thus Zloc (cf [Figure 5.2.1-a])

BI_PLAN_Z
Zloc
Y
Yloc
Steam Generator
22°
Center hot branch
Side thrust
X
Appear 5.2.1-a: Description of the side thrust of Steam Generator

One chooses that the normal direction in the plan of Xloc cut is axis Z of the total reference mark:
NORM_OBST = (0., 0., 1.).
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·
Calculation of Yloc and Zloc in the total reference mark

According to the figure [Figure 3.6.1.7-a],

Xloc = cos cos X + cos sin Y - sin Z


Yloc = (- sin cos + sin cos sin) X + (cos cos + sin sin sin) Y + cos sin Z

Zloc =

(sin sin + sin cos cos) X + (- cos sin + sin sin cos) Y +cos cos Z

Xloc = Z thus = 90° (2) and is unspecified, one takes = 0

Xloc = Z

Yloc = - sin X + cos Y
Zloc = - cos X - sin Y


In the example [Figure 5.2.1-a], the side thrust in Générateur of Vapor is parallel to the axis of
the hot branch, it even tilted of 22° compared to axis X: Yloc = cos22 X + sin22 Y. One
has then: ANGL_VRIL = -
°
68.

·
Command file
#
# Calculation of the clean modes
#--------------------------------------------------------------------
#
modejeu = MODE_ITER_INV (MATR_A = mkassjeu,
MATR_B = mmassjeu,
CALC_FREQ = _F (OPTION = “ADJUSTS”,
FREQ = (0.1, 40.),
NMAX_FREQ = 150,
)
)
#
# Definition of the excitation
#--------------------------------------------------------------------
#
INCLUDE (UNIT = 38)
#
accelx = CALC_FONCTION (COMB = _F (FONCTION = accdirx,
COEF = 3.)
)
dirxj = CALC_CHAR_SEISME (MATR_MASS = mmassjeu,
DIRECTION = (1., 0., 0. ),
MONO_APPUI = “YES”)
#
# Calculation of the matrices of generalized mass and stiffness
# of a generalized effort
#--------------------------------------------------------------------
#
numgenej = NUME_DDL_GENE (BASE = modejeu,
STORAGE = “FULL”
)
rigigenj = PROJ_MATR_BASE (BASE = modejeu,
NUME_DDL_GENE = numgenej,
MATR_ASSE = mkassjeu
)
massgenj = PROJ_MATR_BASE (BASE = modejeu,
NUME_DDL_GENE = numgenej,
MATR_ASSE = mmassjeu
)
seismexj = PROJ_VECT_BASE (BASE = modejeu,
NUME_DDL_GENE = numgenej,
VECT_ASSE = dirxj)
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#
# definition of an obstacle of the type BI_PLAN_Z
#--------------------------------------------------------------------
#
biplanz = DEFI_OBSTACLE (TYPE = “BI_PLAN_Z”)
#
# calculation transitory generalized with presence of an obstacle to node NO10
#------------------------------------------------------------------------
#

Zloc
GV2INFL2
BUT11
DIST_1
J
abtgv122
Yloc
DIST_2
Y
Steam Generator
Center hot branch
X

repbasnl = DYNA_TRAN_MODAL (METHODE = “ADAPT”,
MASS_GENE = massgenj,
RIGI_GENE = rigigenj,
LIST_AMOR = lamorjeu,
INCREMENT = _F (INST_INIT = T0,
PAS = not,
INST_FIN = tf
),
FILING = _F (PAS_ARCH = 10),
EXCIT = _F (VECT_GENE = seismexj,
FONC_MULT = accelx,
DIRECTION = (1., 0., 0., 0., 0., 0.),
GROUP_NO = “SOL1”
),
SHOCK = _F (ENTITLES = “GV2INFL2”,
GROUP_NO_1 = “BUT11”,
GROUP_NO_2 = “abtgvl22”,
OBSTACLE = biplanz,
NORM_OBST = (0., 0., 1.),
ANGL_VRIL = - 68.,
DIST_1 = 1.7749,
DIST_2 = 1.7749,
RIGI_NOR = 14.3E8,
AMOR_NOR = 7.E5,
),
)
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#
# Statistical Post processing of the shocks
#--------------------------------------------------------------------
tabchoc = POST_DYNA_MODA_T (RESU_GENE = repbasnl,
SHOCK = _F (NB_BLOC = 10,
OPTION = “IMPACT”,
),
TITRATE = “RESULTS SHOCKS STEAM GENERATOR”,
)
#
# Restitution on physical basis
#--------------------------------------------------------------------
#
repnl = REST_BASE_PHYS (RESU_GENE = repbasnl,
TOUT_CHAM = “YES”,
)
#
# Extraction of the curves
#--------------------------------------------------------------------
#
n2175axn = RECU_FONCTION (RESULTAT = repnl,
NOM_CHAM = “ACCE”,
NOEUD = “N2175”,
NOM_CMP = “DX”,
TITRATE = “AX NULL PLAY LCUVV”
)
#
# Impression of the curves
#--------------------------------------------------------------------
#
IMPR_COURBE (FILE = “GNUPLOT”,
FORMAT = “AGRAF”,
TITRATE = “ACCELERATIONS NONLINEAR CASE X IN LCUVV”,
LABEL_X = “TEMPS (S)”,
LABEL_Y = “ACCELERATION (M/S2)”,
CURVE = _F (COLOR = “RED”,
FONCTION = n2175axn
),
)
#
FIN ()

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