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Titrate:
Operator
DYNA_TRAN_MODAL
Date:
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Author (S):
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Key
:
U4.53.21-G
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, SINETICS















Instruction manual
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 pitch
adaptive time), an integral method '
ITMI
'and a method of integration implicit:
“NEWMARK”
are available. 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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Code_Aster
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Titrate:
Operator
DYNA_TRAN_MODAL
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Count
matters
1
......................................................................................................................................................... 1 drank
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, QUICKLY,
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
SHOCK
................................... 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 BUCKLING ......................................................................................................................... 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
FILING
.............................................................................................................. 25
3.14.1
Operand
LIST_ARCH
............................................................................................. 25
3.14.2
Operand
PAS_ARCH
............................................................................................... 26
3.15
Operand INFORMATION .................................................................................................................... 26
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Titrate:
Operator
DYNA_TRAN_MODAL
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U4.53.21-G
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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
TITRATE
................................................................................................................. 27
4
Production run ............................................................................................................................... 28
4.1
Checking on the matrices .......................................................................................................... 28
4.2
Checking and consulting on the choice of the pitch of time for the diagrams
EULER
,
DEVOGE
and
NEWMARK
:...................................................................................................................................... 28
4.3
Production run for the method
“ADAPT”
:............................................................................ 28
4.4
Production run for the 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 stop ......................................................................................... 31
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Titrate:
Operator
DYNA_TRAN_MODAL
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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]
METHOD
=
/
“EULER”,
[DEFECT]
/
“DEVOGE”,
/
“NEWMARK”,
/
“ADAPT”,
/
“ITMI”,
INCREMENT = _F (
INST
_
INIT =
to, [R]
INST
_
END =
tf,
[R]
NOT
=
dt,
[R]
VERI
_
NOT =
/
“YES”,
[DEFECT]
/
“NOT”,
# Operands specific to an integration by pitch of adaptive times
QUICKLY
_
MIN =
/
“STANDARD”, [DEFECT]
/
“MAXIMUM”,
COEFF
_
MULT
_
NOT =/1.1,
[DEFECT]
/
cmp
,
[R]
COEFF
_
DIVI
_
NOT =/1.33333334,
[DEFECT]
/
cdp
, [R]
NOT
_
LIMI
_
RELA =/1.E-6,
[DEFECT]
/
per
, [R]
NB
_
POIN
_
PERIOD =
/50, [DEFECT]
/
NR,
[I]
NMAX
_
ITER
_
NOT =/16,
[DEFECT]
/
NR, [I]
# End of the operands specific to an integration by pitch of adaptive times
),
STATE
_
INIT =
_
F (
/
RESU
_
GENE =
LMBO,
[tran_gene]
/
|
DEPL
_
INIT
_
GENE = C, [vect_asse_gene]
|
QUICKLY
_
INIT
_
GENE = vo, [vect_asse_gene]
INST
_
INIT =
to, [R]
CRITERION =
/“RELATIVE”, [DEFECT]
/
“ABSOULU”,
PRECISION =/1.E-3,
[DEFECT]
/
prec, [R]
),
EXCIT
= _F (
VECT
_
GENE
=
v,
[vect_asse_gene]
NUME
_
MODE
=
nmod,
[I]
/
FONC
_
MULT
=
F,
[function]
/
COEFF
_
MULT
=
has,
[R]
/
ACCE
=
ac,
[function]
QUICKLY
=
VI,
[function]
DEPL
=
dp,
[function]
# Operands and key words specific to the seismic analysis
[§3.5]
MULT
_
SUPPORT =/“NOT”,
[DEFECT]
/
“YES”,
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Titrate:
Operator
DYNA_TRAN_MODAL
Date:
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:
U4.53.21-G
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DIRECTION
= (dx, Dy, dz, drx, dry, drz), [l_R]
/
NODE
= lno, [l_noeud]
/
GROUP
_
NO
=
lgrno,
[l_groupe_no]
CORR
_
STAT
=
/
“NOT”
[DEFECT]
/
“YES”
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

SHOCK
=
_
F (
[§3.6.1]
ENTITLE =
int,
[l_Kn]
/
NODE
_
1
=
no1,
[node]
/
GROUP
_
NO
_
1
=
grno1,
[group_no]
/
NODE
_
2
=
no2,
[node]
/
GROUP
_
NO
_
2
=
grno2,
[group_no]
OBSTACLE
= obs,
[obstacle]
NORM
_
OBST
=
NOR,
[listr8]
ORIG
_
OBST
=
ori,
[listr8]
PLAY
=
/
1.,
[DEFECT]
/
play,
[R]
ENG
_
VRIL
=
gamma,
[R]
DIST
_
1
=
dist1,
[R]
DIST
_
2
=
dist2,
[R]
UNDER
_
STRUC_1
= ss1, [K8]
UNDER
_
STRUC_2 =
ss2,
[K8]
IDENTIFY
=
/
“TOTAL”,
[DEFECT]
/
nom_sst, [K8]
RIGI
_
NOR =
kN,
[R]
AMOR
_
NOR =
/
0.,
[DEFECT]
/
Cn,
[R]
RIGI
_
TAN =
/
0.,
[DEFECT]
/
kt,
[R]
AMOR
_
TAN =
/
0.,
[DEFECT]
/
ct,
[R]
COULOMB
=
/
0.,
[DEFECT]
/
driven,
[R]
# Operands and key words specific to the taking into account of a fluid blade
[§3.6.2]
BLADE
_
FLUID
=/
“NOT”,
[DEFECT]
/
“YES”,
ALPHA
=/
0.,
[DEFECT]
/
alpha,
[R]
BETA
=
/
0.,
[DEFECT]
/
beta, [R]
CHI
=
/
0.,
[DEFECT]
/
chi,
[R]
DELTA
=/
0.,
[DEFECT]
/
delta,
[R]
NMAX
_
ITER
=
/
20,
[DEFECT]
/
niter,
[I]
RESI
_
RELA
=
/
1.E-3,
[DEFECT]
/
residue, [R]
LAMBDA
=
/
10., [DEFECT]
/
lambda, [R]
),
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Titrate:
Operator
DYNA_TRAN_MODAL
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# End of the operands and key words specific to the taking into account of a fluid blade

VERI
_
SHOCK =
_
F (
[§3.7]
STOP
_
CRITERION
=/
“YES”,
[DEFECT]
/
“NOT”,
THRESHOLD =
/0.5,
[DEFECT]
/
S,
[R]
),

ANTI
_
SISM =
_
F (
[§3.8]
/
NODE
_
1
=
no1,
[node]
/
GROUP
_
NO
_
1
=
grno1,
[group_no]
/
NODE
_
2
=
no2, [node]
/
GROUP
_
NO
_
2
=
grno2,
[group_no]
RIGI
_
K1
=
/
0.,
[DEFECT]
/
kN,
[R]
RIGI
_
K2
=
/
0.,
[DEFECT]
/
kN,
[R]
THRESHOLD
_
FX =
/
0.,
[DEFECT]
/
Py,
[R]
C
=
/
0.,
[DEFECT]
/
C,
[R]
THEN
_
ALPHA
=
/
0.,
[DEFECT]
/
alpha,
[R]
DX
_
MAX
=
/
1.,
[DEFECT]
/
dx,
[R]
),

BUCKLING
=
_
F (
[§3.9]
/
NODE
_
1
=
no1,
[node]
/
GROUP
_
NO
_
1
=
grno1,
[group_no]
/
NODE
_
2
=
no2,
[node]
/
GROUP
_
NO
_
2
=
grno2,
[group_no]
OBSTACLE
=
obs,
[obstacle]
ORIG
_
OBST
=
ori,
[listr8]
NORM
_
OBST
=
NOR,
[listr8]
ENG
_
VRIL
=
/
0, [DEFECT]
/
gamma,
[R]
PLAY
=
/
1.,
[DEFECT]
/play,
[R]
DIST
_
1
=
dist1,
[R]
DIST
_
2
=
dist2,
[R]
IDENTIFY
=
/“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]
NODE
= Noah, [node]
SOUS_STRUC
=
S,
[K8]
NOM_CMP
=
nomcmp, [K8]
RELATION
= F,
[function]
),

RELA
_
STIFF =
_
F (
[§3.11]
NODE
= Noah, [node]
SOUS_STRUC
=
S,
[K8]
NOM_CMP
=
nomcmp, [K8]
RELATION
= F,
[function]
),
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Code_Aster
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Titrate:
Operator
DYNA_TRAN_MODAL
Date:
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:
U4.53.21-G
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:
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RELA
_
EFFO
_
QUICKLY =
_
F (
[§3.12]
NODE
= 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
_
QUICKLY
_
FLUI =
Nvitf, [I]
STATE
_
STAT
=
/
“NOT”,
[DEFECT]
/
“YES”,
PREC
_
DURATION
=
/
1.E-2,
[DEFECT]
/
prec,
[R]
SHOCK
_
FLUI
=
/
“NOT”,
[DEFECT]
/
“YES”,
NB
_
MODE =
Nmode,
[I]
NB
_
MODE
_
FLUI
=
Nmodef, [I]
TS
_
REG.
_
ETAB
=
tsimu,
[R]
# End of the key words only associated with method “ITMI”

FILING
=
_
F (
/LIST
_
ARCH
=
l_arch, [l_I]
[§3.14]
/NOT
_
ARCH = ipa,
[I]
),

INFORMATION =
/
1,
[DEFECT]
/2,

IMPRESSION
=
_
F (
/ALL = “YES”,
[DEFECT]
/
LEVEL
=
|
'DEPL
_
LOC',
|
'QUICKLY
_
LOC',
|
'FORC
_
LOC',
|
'RATE
_
CHOC',
INST
_
INIT
=
Ti,
[R]
INST
_
END
=
tf,
[R]
),

TITRATE
=
titrate,
[l_Kn]
)
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Titrate:
Operator
DYNA_TRAN_MODAL
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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
the operator
PROJ_MATR_BASE
[U4.63.12] or by the macro-control
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 the 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 type
matr_asse_gene_R
.
RIGI_GENE = laughed
Stamp rigidity of the generalized system.
Concept of the type
matr_asse_gene_R
.
/AMOR_GENE = amndt
Stamp damping of the generalized system.
Concept of the type
matr_asse_gene_R
.
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
METHOD
METHOD
=
Choice of the numerical method of resolution.
In the case of a conventional 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 pitch 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”:
F
X
X
X
X
APt
T
T
T
T
=
-
-
-
-
1
2
1
1
&&
&&
One specifies Ci after the operands specific to the method of integration per pitch 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, the aforementioned can
to become very high, which leads to an unjustified refinement of the pitch of time. To cure it,
the algorithm uses the following criterion:
(
)
X
X
T
V
F
X
X
V
T
N
N
AP N
N
N
-
=
-
-
-
1
1
1
2
min
min
&&
&&
V
min
can be calculated in two ways different according to the value from
VITE_MIN
:
“NORM”
=
()
()
V
T
V T
N
N
min
= 100
for all the degrees of freedom.
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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.
“MAXIMUM”
=
()
(
)
V
T
Max V T
I
N
T
T
I
p
p
N
min
()
=
< <
0
100
for the degrees of freedom I.
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 pitch of time per pitch of calculation. It is by defect equal to 16, it
who limits the coefficient of reduction of the pitch to
0 75
10
16
2
.
=
-
by iteration (when the pitch of time
is too high, one takes again calculation with a weaker pitch:
=
T
T
N
N
0 75
.
).
NMAX_ITER_PAS
can be:
·
increased to allow the pitch time to fall in a more brutal way,
·
decreased if the pitch of time seems excessively refined, for example in presence
discontinuities (solid friction, discontinuous excitation,…).
COEF_MULT_PAS = cmp
Coefficient of increase in the pitch when the error is sufficiently weak:
T
Nf
T
T
N
APn
N
N
<
=
+
0 75
1
.
cmp
.
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 pitch 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 pitch of minimal time is not
not reached:
T
Nf
NR
NR
T
T
T
T
N
AP N
iter
iter
N
initial
N
N
<
<
>
=
1. ,
.
_max
E
T
plr
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 pitch of initial time to define the limit of refinement and thus the pitch of
minimal time:
The default value is 1.33333334, that is to say a reduction of a factor 0.75.
T
T
initial
min
.
=
plr
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 the key word
ETAT_INIT
cf [§3.3]: under this key word, the initial moment is recovered with the operand
INST_INIT
or taken
equal to the last moment of filed preceding calculation. The 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 pitch 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
NOT = dt
·
Methods
“EULER”, “DEVOGE”, “NEWMARK”
:
No the time of transitory calculation.
·
Method
“ADAPT”:
Indicate at the same time the pitch of initial time and the pitch 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 pitch 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 pitch of time appointed for the first pitch of calculation (after possible passage of
transient). Thereafter, the algorithm automatically manages the pitch of calculation according to
rigidity of the structure and the areas of transition flight/shock.
VERI_PAS = item
Checking of the pitch of calculating time relative to the pitch 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 the operator
RECU_GENE
[U4.71.03] applied to a calculation
precedent.
3.3.1 Operands
RESU_GENE/DEPL_INIT_GENE/VITE_INIT_GENE
/RESU_GENE = tran
Concept of the type
tran_gene
resulting from a preceding calculation with
DYNA_TRAN_MODAL
.
/
I
DEPL_INIT_GENE = C
Concept of the type
vect_asse_gene
, initial generalized displacements.
I
VITE_INIT_GENE = vo
Concept of the type
vect_asse_gene
, 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
CRITERION
CRITERION
Indicate with which precision the search of the moment must be done:
“RELATIVE”
: interval of search
[(1-prec) .instant, (1+prec) .instant]
“ABSOLUTE”
: interval of search
[moment-prec, instant+prec]
The criterion is
“RELATIVE”
by defect.
3.3.4 Operand
PRECISION
PRECISION
=/1.E-03
[DEFECT]
/
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
generalized loading
F
I
. 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 type
vect_asse_gene
.
The generalized vectors must be establish by the 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 type
mult_elas
product by the macro-control
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 = “YES”
allows to take into account the contribution
modal correction a posteriori for each occurrence of the 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 the 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
the operator
DYNA_TRAN_MODAL
.
· With the ième occurrence of the key word
EXCIT
the ième elastic solution corresponds of
MODCOR
.
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
,
QUICKLY
, and
DEPL
;
DIRECTION
and
NODE
or
GROUP_NO
) specific to the taking into account of the multimedia character must be simultaneously
present.
MODE_STAT = psi
Concept of the type
mode_stat
product by the control
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
= “YES”
, 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
= “NOT”
, one compares at every moment, the vector of relative displacements
of each node likely to shock.
/
ACCE
=
ac,
QUICKLY
=
VI,
DEPL
=
dp
Names of the functions acceleration (
ACCE
), speed (
QUICKLY
) 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 the 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.
/
NODE
=
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
SHOCK
SHOCK
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
ENTITLE
ENTITLE = 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
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 mesh).
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
concept of the type
obstacle
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
X
loc
.
One advises that
X
loc
that is to say 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
GROUP_NO_1
) and
NOEUD_2
(or node of
GROUP_NO_2
).

3.6.1.6 Operand
PLAY
PLAY = play
In the case of a shock enters a mobile structure and an indeformable obstacle, the operand
PLAY
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
RING
This key word is unutilised in the case of obstacles discretized by segments of the type
DISCRETE
.
Note:
The obstacle of the type
PLAN_Y
or
PLAN_Z
comprise in fact two plane obstacles. Thus in
case where the user wishes to modelize 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.
K
m
Y
X
Yloc
Zloc
play
orig_obs
J
no1
Appear 3.6.1.6-a: System mass-arises impacting a fixed wall
Note:
The key word
PLAY
in the case of shock between mobile structures is not used.
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, the normal
N
in the plan of cut of the obstacle,
NORM_OBST
the axis defines
X
loc
identify local. One passes from the total reference mark
X Y Z
with the reference mark of the plan of the obstacle
N y Z
2 2
by one
product of two rotations of angles
around
Z
then
around transformed
y
1
of
Y
.
The position of the obstacle in this plan is obtained by a rotation of angle
around the direction
normal
X
loc
(cf [Figure 3.6.1.7-a]).
Zloc
Xloc = N =
X2
Yloc
Z
=
Z1
X1
Y2
=
Y1
Z2
X
Y
Zloc
Obstacle of the type PLAN_Z
Zloc
Yloc
Z2
Z
=
Z1
X1
Y1
X
Y
Y1
=
Y2
Z2
X2
Z1
X1
X2
=Xloc
Y2
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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Angles
and
are automatically given starting from the normal with the obstacle
N
.
identify local
X
Y
Z
loc
loc
loc
,
results then from the reference mark
N, y
Z
,
2
2
by rotation of an angle
of spin
ANGL_VRIL
around
N
.
Note:
· If the user does not specify anything, the angle of spin 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 of
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 the key word
NOEUD_1
(or
GROUP_NO_1
).
SOUS_STRUC_2
= ss2
Name of the substructure which contains the node of shock informing the key word
NOEUD_2
(or
GROUP_NO_2
).

3.6.1.10 Operand
IDENTIFY
IDENTIFY = item
Specify the reference mark in which the position of the obstacle is defined.
/
“TOTAL”
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 the 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
K
K m
K m
T
I
T
I
I
I
I
=
+
-
2
2
where I is the index of the dominating mode in the response of the structure.

3.6.1.15 Operand
COULOMB
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
T
T
T
T
T
T
E
T
fluid
T
T
T
T
….
&&
….
&
….
.
()
.
(.
.
&.& &)
M
C
K
F
F
+
+
=
+
&&
T
is thus not given explicitly according to
T
T
,
&
. To obtain accelerations
generalized, one uses the algorithm of point fixes according to:
&&
&&
T
T
0
1
=
-
,
T
T
,
&
are given. One repeats until convergence:
(
)
[
]
(
)
&&
.
.
.
.
.
.
.
.
&&
.
….
&
….
Ti
T
has
T
fluid
T
has
Ti
T
E
T
Ti
T
Ti
+
-
=
+
+
+
-
-
1
1
M
M
F
M
F
C
K
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where:
M
has
represent the diagonal contribution of the matrix of added mass 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
&&
&&
.
&&
Ti
T
I
Ti
+
-
<
1
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,
= 10
­ 3
.
LAMBDA: lambda
Parameter of convergence, noted
above. By defect, = 10.

3.6.2.2 Operands
LAME_FLUIDE/ALPHA/BETA/CHI/DELTA
key word factor
SHOCK
LAME_FLUIDE = item
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:
(
)
(
)
F
fluid
X
X H
X
X H
X
X H
X X
X H
=
+




+
+




+
+
+
+
.
&&
.
&
.
&
. &. &
2
3
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
reconstitution of the static solution:
(
)
T
K
K
S
statics
I
I
N
=
=
T
impo
F
I
.
2
1
and, for information, the rate of
reconstitution of the shearing action:
(
)
T
K
NR
I
T
I
N
=
=
T
impo
impo
F
.
F
.K.
I
I
.
1
. One calculates then them
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 the operand THRESHOLD (THRESHOLD
0.5 per defect are worth) if not:
·
if STOP_CRITERE = “YES” one stops the execution of the program (it is the case by defect);
·
if STOP_CRITERE = “NOT” 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 type
plan
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
):
(
)
F
X
X
X
X X
X
X
D
=
+
-
+
+
K
K
K
K
P
C sign (&) &
y
max
2
1
2
1
2
1
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 BULGE type
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
BUCKLING
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
Fseuil
kN
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 the key word BUCKLING are detailed. The other key words allow
to define the places of shock and are identical to the operands of the key word SHOCK.
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
NODE = 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 the operand
NODE
.
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 the key word
RELA_TRANSIS
, there is not linear limit, the definite function
under the key word RELATION is thus defined on] -, + [.
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The equilibrium equation, for the modelized structure, subjected to a horizontal acceleration of ground
has
X
in the direction
X
, and having terms of correction coming from non-linearities is written:
MX
Cx
Kx
My
F
& & &
+
+
= -
+
X
C
where
F
C
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
F
F X
C
=
-
(X
)
X
()
threshold
threshold
with, if
X > X
threshold
,
F X
X
X
()
K
X.
=
-




0
0
1
.
In example Ci above, one thus imposes, under the operand RELATION the function:
()
[
]
F X
X X
X
C
threshold
=
-
K
X
.
0
0
.
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.
The operands NODE, 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.
The operands NODE, 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 the key word SHOCK 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 type
melasflu
product by the operator
CALC_FLUI_STRU
[U4.66.02] which contains
the whole of the modal bases calculated for different the rate of flow definite. It
key word is obligatory for the 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 the 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 stop. It can
to be relatively important (50 to 100 seconds).
ETAT_STAT = “YES”: the passage in only one pitch 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 pitch 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:
(
)
T
Ln prec
2
tr
0 0
0
0
= -
where
and
reduced damping and the pulsation indicate respectively
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 amendment of
rigidity and of the damping of the mechanical system (impact on the stop) 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 pitch of time of the transitional stage
(ETAT_STAT = “NOT”), 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 = “YES”), 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 has
: TS_REG_ETAB = INST_FIN - INST_INIT -
“time considered transitory”
3.14 Word
key
FILING
FILING
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 result
tran_gene
.
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3.14.2 Operand
PAS_ARCH
PAS_ARCH = ipa
· Methods
“EULER”
,
“DEVOGE”
,
“NEWMARK”
, “ITMI”:
Entirety defining the interval of filing of the solution of transitory calculation in the concept
result
tran_gene
.
If
ipa = 5
all the 5 pitches of calculation are filed.
Whatever the option of filing chosen, one files the last pitch of time and all the fields
associated to allow a possible recovery.
By defect one files all the pitches 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 * NOT
. With this convention, the pitch of filing is always
superior or equal to the maximum pitch used by calculation.
With a variable pitch, the moments of filing do not correspond exactly to pitches of
calculation. The algorithm thus files the sizes with the pitches of calculation closest to the moments
of filing indicated by the user (in Tn on this diagram):
No filing
Moments of filing
T
n+1
No calculation
T
N
3.15 Operand
INFORMATION
INFORMATION = imp
Entirety allowing to specify the level of impression in the file
MESSAGE
.
If INFORMATION: 1, one prints following information in the file
MESSAGE
:
<I> <nom of the routine where information suivantes> is written
If <I> <MDTR74
>, it is reminded the meeting that it is a transitory calculation on modal basis “conventional”,
if not
<I> <SSDT74>
it is a transitory calculation on modal basis by under-structuring
dynamics.
<---------------------------------------------->
CALCULATION BY MODAL SUPERPOSITION
----------------------------------------------
! THE BASE OF PROJECTION EAST ONE >
type of the base of projection
<
! NB Of EQUATIONS EAST: Nb
! METHOD UTILISEE EAST: >
name of the method of integration
<
! BASE UTILISEE EAST: >
name 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
INFORMATION
is worth 1, them
following information in the 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 spin;
· 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
that is to say 99.53% of local flexibility;
RATE OF RESTIT SHARP EFFORT: 1.8979E-02
that is to say 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 the file
RESULT
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
The key word LEVEL makes it possible to print one or more table (X) among
“DEPL_LOC”
,
“VITE_LOC”,
“FORC_LOC”
and
“TAUX_CHOC”
. With
ALL = “YES”
(default value), the four are printed
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 pitches
time.
3.17 Operand
TITRATE
TITRATE = 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 pitch of time for
diagrams
EULER
,
DEVOGE
and
NEWMARK
:
One makes sure that the pitch of selected time checks the stability conditions of the numerical diagram (criterion
CFL):
· in the case of
NEWMARK
, stability is 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 the operand
VERI_PAS
is worth
“YES”
(value by
defect), the execution is stopped, a pitch of minimum time is proposed. If the operand
VERI_PAS
is worth
“NOT”
or if it is about the 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 pitch of time is such as:
dt < 0,1/F
N
for
NEWMARK
and
DEVOGE
dt < 0,05/F
N
for
EULER
F
N
being the highest frequency of the modes of the modal base considered.
Note:
It is mentioned that with nonlocalized linearities the pitch of selected time must be sometimes very
lower than this advised value.
4.3
Production run for the method
“ADAPT”
:
The execution is stopped when the pitch of time reaches a minimal pitch 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 the parameter
NB_POIN_PERIODE
.
Method
“ADAPT”
can be used in under-structuring.
The pitch of time can be recovered by the 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 pitch of time which is stored in
concept result of RECU_FONCTION.
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4.4
Production run for the 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 (MODEL = 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 (MATRIX = mass_gen, MATR_ASSE = m_asse),
MATR_ASSE_GENE =_F (MATRIX = rigi_gen, MATR_ASSE = k_asse),
VECT_ASSE_GENE =_F (VECTOR = 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,
NOT = 0.00001),
FILING = _F (PAS_ARCH = 100)
)
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Key
:
U4.53.21-G
Page
:
31/34
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
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
stops side and frontal tilted with 22° limiting its displacements (see [Figure 5.2-a]).

FERMENT
PUMP
PRIMARY EDUCATION
GENERATOR
D E VAPOR
Cold branch
Connect Chaud E
Connect out of U
Side stop
dimensioned opposite PP
Frontal stop
Side stop
dimensioned PP
Y
X
22°
Appear 5.2-a: Diagram of a primary education branch of circuit
5.2.1 Modeling of the side stop
The side stop with the Steam generator 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])
22°
Y
X
Yloc
Zloc
Center
the bran
che cha
ude
Butted L
atérale
BI_PLAN_Z
Steam Generator
Appear 5.2.1-a: Description of the side stop 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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Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_TRAN_MODAL
Date:
18/02/05
Author (S):
E. BOYERE, Fe. WAECKEL
Key
:
U4.53.21-G
Page
:
32/34
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
·
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 stop with the Steam generator 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 (FUNCTION = accdirx,
COEFF = 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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Code_Aster
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Version
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Titrate:
Operator
DYNA_TRAN_MODAL
Date:
18/02/05
Author (S):
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Key
:
U4.53.21-G
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:
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
#
# definition of an obstacle of the type BI_PLAN_Z
#--------------------------------------------------------------------
#
biplanz = DEFI_OBSTACLE (STANDARD = “BI_PLAN_Z”)
#
# calculation transitory generalized with presence of an obstacle to node NO10
#------------------------------------------------------------------------
#
Steam Generator
Y
X
Yloc
Zloc
Center
the bran
che cha
ude
BUT11
DIST_1
DIST_2
J
abtgv1
22
GV2INFL2

repbasnl = DYNA_TRAN_MODAL (METHOD = “ADAPT”,
MASS_GENE = massgenj,
RIGI_GENE = rigigenj,
LIST_AMOR = lamorjeu,
INCREMENT =
_
F (INST_INIT = T0,
NOT = 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,
),
)
background image
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_TRAN_MODAL
Date:
18/02/05
Author (S):
E. BOYERE, Fe. WAECKEL
Key
:
U4.53.21-G
Page
:
34/34
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
#
# 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 (RESULT = repnl,
NOM_CHAM = “ACCE”,
NODE = “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 = “TIME (S)”,
LABEL_Y = “ACCELERATION (M/S2)”,
CURVE =
_
F (COLOR = “RED”,
FUNCTION = n2175axn
),
)
#
END ()