Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
1/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
Organization (S):
EDF-R & D/AMA, DeltaCAD
Instruction manual
U4.3- booklet: Function
Document: U4.32.05
Operator
INFO_FONCTION
1 Goal
To carry out mathematical operations on structures of data of the function type.
The following operations are currently available:
·
the search of the maxima of a function,
·
the calculation of the standard L
2
of a function,
·
the standard deviation of a function,
·
value RMS of a function,
·
the value of the indicator of harmfulness of seism.
Product a structure of data counts.
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
2/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
Count
matters
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
3/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
2 Syntax
Fr
= INFO_FONCTION
(
/MAX
= _F (
FUNCTION = F,
[function]
),
/STANDARD
=_F (
FUNCTION
=
F
,
[function]
),
/
ECART_TYPE
=
(
identical to the key word
RMS
)
[function]
/
RMS
=
_F (
FUNCTION
= F,
[function]
METHOD =
/“TRAPEZOID”,
[DEFECT]
/
“SIMPSON”,
INST_INIT= tdeb,
[R]
INST_FIN
= tfin,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION=/
0.001,
[DEFECT]
/
prec,
[R]
),
/
NOCI_SEISME
=
_F (
/FUNCTION =
F
,
[function]
OPTION
=
I
“ALL”
,
[DEFECT]
I
“MAXIMUM”,
COEFF =/0,
[DEFECT]
/r1
,
[R]
INST_INIT = tdeb,
[R]
INST_FIN = tfin,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
I
“INTE_ARIAS”,
INST_INIT = tdeb,
[R]
INST_FIN = tfin,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
I
“POUV_DEST”,
COEFF =
/
0, [DEFECT]
/
r1
,
[R]
INST_INIT = tdeb,
[R]
INST_FIN = tfin,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
I
“VITE_ABSO_CUMU”,
INST_INIT = tdeb,
[R]
INST_FIN = tfin,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
4/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
I
“DUREE_PHAS_FORT”,
INST_INIT = tdeb,
[R]
INST_FIN = tfin,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
BORNE_INF =/0.05,
[DEFECT]
/
binf,
[R]
BORNE_SUP =/0.95,
[DEFECT]
/
bsup,
[R]
I
“INTE_SPEC”,
AMOR_REDUIT
=
amndt,
[R]
FREQ_INIT
=/0.4,
[DEFECT]
/
fdeb,
[R]
FREQ_FIN
=/10.,
[DEFECT]
/
end,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
NORMALIZES
=
/
1., [DEFECT]
/
r2
,
[R]
I
“ACCE_SUR_VITE”,
COEFF =
/
0,
[DEFECT]
/
r1
,
[R]
/
SPEC_OSCI
=
sro
,
[function]
OPTION
=
I
“INTE_SPEC”,
[DEFECT]
AMOR_REDUIT
=
amndt,
[R]
NATURE
=
/
“ACCE”,
[DEFECT]
/
“QUICKLY”,
/
“DEPL”,
NORMALIZES
=
/
1., [DEFECT]
/
r2
,
[R]
FREQ_INIT
=/0.4,
[DEFECT]
/
fdeb,
[R]
FREQ_FIN
=/10.,
[DEFECT]
/
end,
[R]
CRITERION =/“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
PRECISION =/0.001,
[DEFECT]
/
prec,
[R]
FREQ =
lfre, [l_R]
LIST_FREQ
=
lfreq,
[listr8]
),
TITRATE
= T,
[l_Kn]
INFORMATION
=
/
1,
[DEFECT]
/
2,
)
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
5/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
3 Operands
3.1 Word
key
MAX
/MAX
=
Seek X-coordinates where the maximum and the minimum are reached.
This operation is available on functions of nature
function
or
tablecloth
.
FUNCTION = F
Name of the function of which one seeks the maxima.
If F is a function, the produced concept is a table whose parameters of access are:
FUNCTION, TYPE, the NOM_PARA of the function, the NOM_RESU of the function.
where the name of the function respectively is found,
MAXIMUM or MINI, the X-coordinate of the maximum/minimum,
the value of the minimum maximum/.
If F is a tablecloth, the produced concept is a table whose parameters of access are:
FUNCTION, TYPE, the NOM_PARA of the tablecloth, the name of the parameter of the functions
(NOM_PARA_FONC), the NOM_RESU of the functions.
3.2 Word
key
NORMALIZES
This key word makes it possible to follow convergence in accordance with the standard L
2
of a continuation of function
NR
F
data
in the form of a tablecloth. The table result comprises a line by function, the parameters of input
are STANDARD and FUNCTION.
FUNCTION = F
Name of the tablecloth whose standard must be evaluated.
3.3 Word
key
ECART_TYPE
/ECART_TYPE
=
The standard deviation of the function is calculated
F ()
T
who is defined by:
(
)
(
)
dt
T
2
tfin
tdeb
F
)
F (
1
tdeb
tfin
-
-
=
where
F
is the average on [T
deb.
, T
end
]
The key words are identical to those provided under the key word factor RMS.
The produced concept is a table whose parameters of access are:
FUNCTION, METHOD, AVERAGE, INST_INIT, INST_FIN, ECART_TYPE
.
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
6/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
3.4 Word
key
RMS
/RMS
=
One calculates value RMS of the function
F ()
T
who is defined by:
(
)
()
RMS
T dt
=
-
1
2
tfin
tdeb
tdeb
tfin
F
FUNCTION = F
Name of the function which one calculates value RMS.
Do not apply to the concepts of the tablecloth type.
METHOD =
Name of
METHOD
that one uses to calculate the integral.
Two methods are available: method of
“TRAPEZOID”
(by defect) and method of
“SIMPSON”
.
INST_INIT = tdeb,
INST_FIN = tfin,
Limits lower and higher of the interval of integration.
If these values are not indicated, the points of discretization inferior and superior (
relation of command being defined compared to the parameter in X-coordinate) are taken as limits
the interval of integration.
PRECISION =/0.001,
/
prec,
CRITERION =
/“ABSOLUTE”,
/
“RELATIVE”, [DEFECT]
One seeks a point of discretization of the function in an interval defined by the position
absolute or relative around a value of the parameter of the X-coordinates for which the function
must be estimated:
·
[inst (1-prec), inst (1+prec)] if
CRITERION = “RELATIVE”
·
[inst - prec, inst + prec]
if
CRITERION = “ABSOLUTE”
The produced concept is a table whose parameters of access are:
FUNCTION, METHOD, INST_INIT, INST_FIN, RMS
.
3.5 Word
key
NOCI_SEISME
/NOCI_SEISME
=
/FUNCTION = F,
/SPEC_OSCI
= sro
,
Name of the function or the tablecloth considered which must be defined in
DEFI_FONCTION
[U4.31.02] with
NOM_RESU=' ACCE'
.
If a tablecloth is considered, only the calculation of spectral radiant intensity is available.
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
7/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
/OPTION =
Allows to choose one or more of the six following indices of harmfulness:
|
“ALL”
give all six index of harmfulness,
|
“MAXIMUM”
give the maximum of acceleration, speed and displacement
[]
{}
)
(
max
,
T
PGA
F
I
T
T
T
=
,
[]
{}
)
(
max
,
T
v
PGV
F
I
T
T
T
=
[]
{}
)
(
max
,
T
X
PGD
F
I
T
T
T
=
|
“INTE_ARIAS”
give the intensity of Arias
=
F
I
T
T
With
dt
T
G
I
)
(
2
2
|
“POUV_DEST”
give the destroying capacity
=
=
F
I
T
T
C
With
dt
T
v
G
I
Pd
2
3
0
)
(
2
|
“VITE_ABSO_CUMU”
give the cumulated absolute value speed
=
F
I
T
T
dt
T
CAV
)
(
|
“DUREE_PHAS_FORT”
duration of strong phase:
Minimal duration
inf
sup
T
T
-
such as:
With
T
T
With
I
B
dt
T
G
I
B
×
×
sup
)
(
2
inf
sup
inf
2
|
“INTE_SPEC”
spectral radiant intensity
=
end
fdeb
v
H
df
F
N
F
S
I
2
)
,
(
|
“ACCE_SUR_VITE”
ratio Amax/Vmax
[]
{}
[]
{}
)
(
max
)
(
max
,
,
T
v
T
F
I
F
I
T
T
T
T
T
T
=
ITE
ACCE_SUR_V
.
According to the option, one must inform certain parameters, if one does not indicate an option, by defect, one
thus calculate all the indices it is necessary all to inform.
The method of integration is the method of
“TRAPEZOID”
INST_INIT = tdeb,
INST_FIN = tfin,
Limits lower and higher of the interval of time.
If these values are not indicated, the points of discretization inferior and superior (
relation of command being defined compared to the parameter in X-coordinate) are taken as limits
the interval.
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
8/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
PRECISION =/0.001,
/
prec,
CRITERION =
/“ABSOLUTE”,
/
“RELATIVE”, [DEFECT]
One seeks a point of discretization of the function in an interval defined by the position
absolute or relative around a value of the parameter of the X-coordinates for which the function must
to be estimated:
·
[inst * (1-prec), inst * (1+prec)] if
CRITERION = “RELATIVE”
·
[inst - prec, inst + prec]
if
CRITERION = “ABSOLUTE”
·
[freq * (1-prec), freq * (1+prec)] if
CRITERION = “RELATIVE”
·
[freq - prec, freq + prec]
if
CRITERION = “ABSOLUTE”
COEFF = r1
Constant of integration, by defect
0
. In the option
'
MAXIMUM
'
, one calculates speed and it
displacement by two successive integrations of damping, it is thus necessary to inform
COEFF if one does not want to take it by defect.
FREQ_INIT = fdeb,
FREQ_FIN = fine,
Frequencies representing the two terminals of integration for the calculation of the spectral radiant intensity.
Those must lie between the extréma base of frequencies defining
tablecloth SRO, if not poses a problem of interpolation. By defect, these two frequencies
0,4Hz and 10Hz are worth.
AMOR_REDUIT = amndt
Reduced damping, for the calculation of the spectral radiant intensity.
FREQ = lfre
fre
=
(
)
1
,…,…
I
. List frequencies.
LIST_FREQ = lfreq
List frequencies provided under a concept
listr8
.
= r2 NORMALIZES
The spectrum of oscillator will be normalized with the value r2 (value of pseudo-acceleration).
BORNE_INF = binf,
BORNE_SUP = bsup,
Terminals limiting the share of intensity Arias defining the moments initial and final of the strong phase
(between (binf) % and (bsup) % of (I
With
)
max
) of the seism.
3.6 Operand
TITRATE
TITRATE = T
Titrate
attache with the concept produced by this operator [U4.03.01].
3.7 Operand
INFORMATION
INFORMATION
=
Specify the options of impression on the file
MESSAGE
.
1
no impression
2
impression of the descriptor of the function (default option) and of the list of the 10 first
values of each function in the order ascending of the first 10 parameters.
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
9/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
4 Examples
4.1
Seek extrema of a function
A5=DEFI_FONCTION (
NOM_RESU=' SIGM',
NOM_PARA=' EPSI',
VALE= (0.002, 400.0,
0.003, 500.0,
0.0045, 550.0,
0.0065, 580.0,
0.008, 590.0,
0.01, 600.0,
0.02, 600.0,
),
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' LINEAIRE',
)
= INFO_FONCTION (MAX=_F (FONCTION=A5),)
IMPR_TABLE (TABLE=tab)
give on the file “RESULT”.
#
# ASTER 8.02.00 CONCEPT the 24/01/2006 A 16:14 CALCULATES:04 OF TYPE
# TABLE_SDASTER
STANDARD FUNCTION EPSI SIGM
MINI A5 2.00000E-03 4.00000E+02
MAXIMUM A5 1.00000E-02 6.00000E+02
MAXIMUM A5 2.00000E-02 6.00000E+02
Code_Aster
®
Version
8.2
Titrate:
Operator
INFO_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., F. LEBOUVIER
Key
:
U4.32.05-A1
Page:
10/10
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
Intentionally white left page.