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Titrate:
Operator CALC_FONCTION
Date:
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Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER Key
:
U4.32.04-I1 Page
: 1/20
Organization (S): EDF-R & D/AMA, DeltaCAD
Handbook of Utilization
U4.3- booklet: Function
Document: U4.32.04
Operator CALC_FONCTION
1 Goal
To carry out mathematical operations on structures of data of the function type.
The following operations are currently available:
·
the derivation of a function,
·
the integration of a function,
·
the reverse of a function,
·
the absolute value of a function,
·
the search of the envelope of several functions,
·
real or complex linear combination several functions,
·
the composition of two functions,
·
concatenation (put end to end with management of the overlappings) several functions,
·
the extraction of a real function starting from a complex function,
·
the calculation of the nth power of a function,
·
the calculation of direct or opposite FFT of a function,
·
correction of a accélérogramme measured for calculation of a seismic answer,
·
smoothing wraps one or more rough spectra of oscillator,
·
the calculation of the spectrum of oscillator of a accélérogramme (function of the frequency and of
damping) in the form of a tablecloth,
Product a structure of data function, or tablecloth, according to the key word factor used.
At output of the command, the function is reordered by increasing X-coordinates.
Handbook of Utilization
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Titrate:
Operator CALC_FONCTION
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:
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Contents
1 Goal ......................................................................................................................................................... 1
2 Syntax .................................................................................................................................................. 4
3 Operands ............................................................................................................................................. 7
3.1 Key word DERIVE ............................................................................................................................... 7
3.2 Key word INTEGRE ............................................................................................................................. 7
3.3 Key word INVERSE ............................................................................................................................. 8
3.4 Key word ABS ...................................................................................................................................... 8
3.5 Key word ENVELOPPE ......................................................................................................................... 8
3.5.1 Operand FUNCTION ............................................................................................................. 8
3.5.2 Operand CRITERION ............................................................................................................... 9
3.6 Key word COMB and operand LIST_PARA .......................................................................................... 9
3.7 Key word COMB_C and operand LIST_PARA ...................................................................................... 9
3.8 Key word COMPOSE ........................................................................................................................... 10
3.9 Key word ASSE .................................................................................................................................. 10
3.9.1 Operand FUNCTION ........................................................................................................... 10
3.9.2 Operand OVERLOADS ......................................................................................................... 10
3.9.3 Checks .......................................................................................................................... 10
3.10
Key word EXTRACTION ........................................................................................................... 11
3.10.1
Operand FUNCTION ............................................................................................... 11
3.10.2
Operand LEFT ................................................................................................... 11
3.11
Key word PUISSANCE .............................................................................................................. 11
3.12
Key word FFT ........................................................................................................................... 11
3.13
Key word CORR_ACCE .............................................................................................................. 12
3.13.1
Operand FUNCTION ............................................................................................... 12
3.13.2
Operand CORR_DEPL ............................................................................................. 12
3.14
Key word LISS_ENVELOP ....................................................................................................... 12
3.15
Key word SPEC_OSCI .............................................................................................................. 13
3.15.1
Operand FUNCTION ............................................................................................... 14
3.15.2
Operand METHOD ................................................................................................. 14
3.15.3
Operand AMOR_REDUIT ........................................................................................ 14
3.15.4
Operands FREQ/LIST_FREQ ............................................................................ 14
3.15.5
Operands NATURE/NATURE_FONC ................................................................... 14
3.15.6
Operand NORMALIZES ..................................................................................................... 14
3.16
Attributes of the concept function at output ................................................................................. 15
3.16.1
Default values .................................................................................................... 15
3.16.2
Overload attributes ............................................................................................ 16
3.16.2.1 Operand NOM_PARA .......................................................................................... 16
3.16.2.2 Operand NOM_RESU .......................................................................................... 16
3.16.2.3 Operand Interpol .......................................................................................... 16
3.16.2.4 Operands PROL_DROITE/PROL_GAUCHE .................................................... 16
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3.16.2.5 Operands NOM_PARA_FONC/INTERPOL_FONC/PROL_DROITE_FONC/
PROL_GAUCHE_FONC .............................................................................................. 16
3.17
Operand INFORMATION .................................................................................................................... 16
4 Examples ............................................................................................................................................. 17
4.1 Calculation of an envelope ................................................................................................................. 17
4.2 Calculation of derived from the function if ........................................................................................... 17
4.3 Concatenation of two functions .................................................................................................. 18
4.4 Composition of two functions ..................................................................................................... 19
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:
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2 Syntax
Fr
= CALC_FONCTION
(
/DERIVE
= _F (
FONCTION = F, [function]
METHOD = “DIFF_CENTREE”, [DEFECT]
),
/
INTEGRE
=
_F
(
FONCTION = F, [function]
METHOD =/“TRAPEZOID”,
[DEFAUT]
/
“SIMPSON”,
COEF =/0., [DEFAUT]
/R,
[R]
),
/
INVERSE
=
_F (
FONCTION = F, [function]
),
/
ABS
=
_F (
FONCTION = F, [function]
),
/
ENVELOPPE
=
_F (
FONCTION = F, [l_fonction]
CRITERE =
/“SUP”,
[DEFAUT]
/
“INF”,
),
/
COMB
=
_F
(
FONCTION
=
F
,
[function]
COEF = R,
[R]
),
/
COMB_C
=
_F
(
FONCTION
=
f_c,
[fonction_c]
/COEF_R
=
R
,
[R]
/
COEF_C
=
C
,
[C]
),
# if COMB or COMB_C
LIST_PARA
=
will lpara,
[listr8]
/
COMPOSE =
_F (
FONC_RESU
= f_resu
, [function]
FONC_PARA
= will f_para
, [function]
),
/
ASSE =_F (
FONCTION
=
l_f, [l_fonction]
SURCHARGE
=/“DROITE”,
[DEFAUT]
/
“GAUCHE”,
),
/
EXTRACTION=_F (
FONCTION
=
f_c, [fonction_c]
PARTIE
=/“REEL”,
/
“IMAG”,
/
“MODULE”,
/
“PHASE”,
),
/PUISSANCE = _F (
FONCTION
=
F
,
[function]
EXPOSANT
=/
N, [I]
/
1, [DEFAUT]
),
/
FFT
=
_F (
FONCTION
=
F
,
[function]
METHODE =
/“PROL_ZERO”,
[DEFAUT]
/
“TRONCATURE”,
),
/
CORR_ACCE
=
_F (
FONCTION
=
F
,
[function]
CORR_DEPL =/
“NON”,
[DEFAUT]
/“OUI”,
),
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/LISS_ENVELOP
= _F (
,
NAPPE
=
N,
[tablecloth]
FREQ_MIN
=
/
fmin,
[R]
/
0.2
[DEFAUT]
FREQ_MAX
=
/
fmax,
[R]
/
35.5 [DEFAUT]
ELARG
=
/elar,
[R]
/0.1,
[DEFAUT]
TOLE_LISS
=
/
toleliss,
[R]
/0.25,
[DEFAUT]
),
/
SPEC_OSCI
=
_F (
FONCTION
=
F,
[function]
METHOD = “NIGAM”,
[DEFAUT]
AMOR_REDUIT=
lam, [l_R]
/FREQ = lfre,
[l_R]
/LIST_FREQ = lfreq,
[listr8]
NATURE =/“ACCE”,
[DEFAUT]
/
“VITE”,
/
“DEPL”,
NATURE_FONC=
“ACCE”, [DEFECT]
NORME =/9.81,
[DEFAUT]
/R,
[R]
),
NOM_PARA
=
para
,
[KN]
NOM_RESU
=
resu
,
[KN]
PROL_DROITE
=
/
“CONSTANT”,
/
“LINEAIRE”,
/
“EXCLU”,
PROL_GAUCHE
=
/
“CONSTANT”,
/
“LINEAIRE”,
/
“EXCLU”
Interpol
= I “FLAX”,
[l_Kn]
I “LOG”,
I “NOT”,
INTERPOL_FONC
=
I “FLAX”,
[l_Kn]
I “LOG”,
I “NOT”,
NOM_PARA_FONC
=
parf,
[KN]
PROL_DROITE_FONC
=/“CONSTANT”,
/
“LINEAIRE”,
/
“EXCLU”,
PROL_GAUCHE_FONC
=/“CONSTANT”,
/
“LINEAIRE”,
/
“EXCLU”,
INFO
=
/
1,
[DEFAUT]
/
2,
)
If key word factor DERIVE
then Fr = [FONCTION]
If key word factor INTEGRE
then Fr = [FONCTION]
If key word factor INVERSE
then Fr = [FONCTION]
If key word factor ABS
then Fr = [FONCTION]
If key word factor ENVELOPPE
then Fr = [FONCTION]
If key word factor COMB
then
Fr
=
[FONCTION]
If key word factor COMB_C
then Fr = [FONCTION_C]
If key word factor COMPOSE
then Fr = [FONCTION]
If key word factor ASSE
then
Fr
=
[FONCTION]
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:
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If key word factor EXTRACTION
then Fr = [FONCTION]
If key word factor FFT
then Fr = [FONCTION]
If key word factor CORR_ACCE
then Fr = [FONCTION]
If key word factor PUISSANCE
then Fr = [FONCTION]
If key word factor SPEC_OSCI
then Fr = [NAPPE]
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3 Operands
3.1 Word
key
DERIVE
/DERIVE
=
The function F (T) is derived.
FONCTION = F
Name of the function which one wishes to derive.
Do not apply to the concepts of the tablecloth type.
METHODE =
Name of the METHODE which one wishes to use: the only method available is currently
DIFF_CENTREE (by defect).
Note:
See key word INTEGRE.
3.2 Word
key
INTEGRE
/INTEGRE
=
The function F (T) is integrated.
FONCTION = F
Name of the function which one wishes to integrate.
Do not apply to the concepts of the tablecloth type.
METHODE =
Name of the METHODE which one wishes to use.
Two methods are available: method of the “TRAPEZE” (by defect) and method of
“SIMPSON”.
The method of “SIMPSON” is to be employed with precaution because it can involve
oscillations. It is to better discretize F (T) finely and to integrate with the method of
“TRAPEZE”. In particular it is disadvised using method “SIMPSON” for
the interpretation of a accélérogramme.
COEF = R
Constant of integration, by defect 0.
Note:
· For INTEGRE as for DERIVE, the NOM_PARA of the produced function is
unchanged: one does not have for example to expect only NOM_RESU=' ACCE'
NOM_RESU=' VITE' in the integrated function produces. The user with the faculty of
to modify by the key word of the same name in CALC_FONCTION.
· Concerning the prolongations, the produced function has by defect of the prolongations
EXCLU on the left and on the right, some are those of the starting function. Not
to thus expect that a linear prolongation becomes constant in the function
derived… Là still, the user is a Master of his prolongations for the function
produced by key words PROL_DROITE and PROL_GAUCHE.
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3.3 Word
key
INVERSE
/INVERSE
=
The function F (T) is reversed.
FONCTION = F
Name of the function which one wishes to reverse, it is necessary that this one is bijective
(strictly increasing or strictly decreasing).
Do not apply to the concepts of the tablecloth type.
Note:
· The labels of the parameters are not reversed! The care is left with the user
to affect the correct values by the key words NOM_PARA and NOM_RESU.Par defect,
the NOM_PARA is unchanged and NOM_RESU is affected with “TOUTRESU”.
· The modes of interpolations are inverted: e.g. (“LIN”, “LOG”) becomes
(“LOG”, “FLAX”).
· Prolongations EXCLU and LINEAIRE are unchanged. On the other hand, one
prolongation CONSTANT is changed into EXCLU.
3.4 Word
key
ABS
/ABS
=
Provides the absolute value of a function or a tablecloth.
FONCTION = F
Name of the function which one wishes the absolute value.
Note:
· Parameters (prolongations, interpolations, NOM_PARA and NOM_RESU) of
produced function are the same ones as those of the starting function.
· Except for prolongation LINEAIRE: systematically changed into EXCLU by
precaution. Indeed, linear prolongation on the right of a decreasing function
conduit for sufficiently large X-coordinates with negative values:
responsibility is thus left with the user affect itself
PROL_DROITE=' LINEAIRE' (and respectively on the left).
3.5 Word
key
ENVELOPPE
/
ENVELOPPE
=
Calculation of the envelope of several functions.
This operation is available on operands of nature function or tablecloth.
3.5.1 Operand
FONCTION
FONCTION = F
List functions or tablecloths which one seeks the envelope.
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3.5.2 Operand
CRITERE
CRITERE =
/
“SUP”
The higher envelope is sought.
/
“INF”
The lower envelope is sought.
Remarks for the search of the envelope:
·
the functions all must be of comparable nature (function or tablecloth),
·
Case of the simple functions: for the prolongations, interpolations, NOM_PARA and
NOM_RESU, they are the parameters of the first of the functions in the list which are
retained. The support of X-coordinates of the function envelope will be the meeting of the lists
X-coordinates of all the functions.
·
Case of the tablecloths: the parameters (prolongations, interpolations, NOM_PARA, NOM_RESU,
NOM_PARA_FONC) must imperatively be identical between the provided tablecloths.
supports of X-coordinates (values of the parameters and X-coordinates of the functions of the tablecloths)
are homogenized to be able to calculate the envelope. The produced tablecloth will have this
discretization for X-coordinates.
3.6 Word
key
COMB and operand LIST_PARA
/COMB =
Real linear combination several concepts of nature function or tablecloth.
FONCTION = F
Name of the function to be combined.
COEF= R
Value of the coefficient.
LIST_PARA= will lpara
List values of the parameters for which the combination of the functions will be discretized. If
this key word is not indicated, a list by defect is built by taking the union of the lists of
values of the parameters of each function.
Caution:
It is not a key word of the key word factor COMB.
Remarks for the combination:
See the remarks for key word ENVELOPPE
3.7 Word
key
COMB_C and operand LIST_PARA
/COMB_C
=
Linear combination complexes several concepts of nature fonction_c.
FONCTION =
f_c
Name of the function to be combined. It can be with complex or real values.
/COEF_R = R,
/COEF_C = C,
Value of the multiplying coefficient, either in real form R, or in form complexes C.
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LIST_PARA = will lpara
List values of the parameters for which the combination of functions will be discretized. If it
key word is not indicated, a list by defect is built by taking the union of the lists of
values of the parameters of each function.
Remarks for the combination:
See the remarks for key word ENVELOPPE
3.8 Word
key
COMPOSE
Key word factor allowing to calculate the made up one of two functions F (G (T)).
Do not apply to the concepts of the tablecloth type.
/
COMPOSE
=
FONC_RESU = f_resu
Function f_resu (X)
FONC_PARA = will f_para
Function will f_para (T)
It is checked that the NOM_PARA of f_resu corresponds to the NOM_RESU of will f_para.
3.9 Word
key
ASSE
/
ASSE
=
Key word factor allowing to create a real function by concaténant two real functions
tabulées.
Do not apply to the concepts of the tablecloth type.
3.9.1 Operand
FONCTION
FONCTION = l_f
Functions with concaténer. Two functions exactly are awaited.
3.9.2 Operand
SURCHARGE
SURCHARGE
=/“DROITE”,
/“GAUCHE”,
The points of discretization of the function created are those of the whole of the two functions,
modulo effects of overload.
If the fields of definition of the functions overlap, one of the functions impose its
points on the zone of recovery and for the prolongations:
OVERLOAD =/“RIGHT”: it is the function which has large the xmax which is chosen,
OVERLOAD =/“LEFT”: it is the function which has smallest xmin which is selected.
3.9.3 Checks
One checks that all the functions have the same NOM_PARA, as well as the same interpolations.
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3.10 Word
key
EXTRACTION
/
EXTRACTION
=
Key word factor making it possible to build starting from a function complexes (standard fonct_c),
a real function representative either the real part, or the imaginary part, or the module,
that is to say the phase of the complex function.
3.10.1 Operand FUNCTION
FONCTION = f_c
Complex function.
3.10.2 LEFT operand
PARTIE
=
/“REEL”
: extraction of the real part of f_c,
/“IMAG”
: extraction of the imaginary part of f_c,
/“MODULE”: extraction of the module of f_c,
/“PHASE”: extraction of the phase (in degree) of f_c.
3.11 Word
key
PUISSANCE
This key word makes it possible to build the nth power of a function or a whole of functions
provided in the form of a tablecloth.
FONCTION = F
Name of the function F concerned (standard function or tablecloth).
EXPOSANT = N
The function result calculated will be X F (X) N. By defect, N = 1.
3.12 Word
key
FFT
/FFT
=
One calculates the transform of Fourier direct or opposite of a function (algorithm FFT).
FONCTION = F
Name of the function on which the operation is carried out.
If the NOM_PARA of the function is INST, then the direct FFT is calculated.
If the NOM_PARA of the function is FREQ, then the opposite FFT is calculated.
Do not apply to the concepts of the tablecloth type.
METHODE =
Algorithm FFT accepts in input only one signal of which the number of samples is one
power of 2.
Method “PROL_ZERO” (by defect) proposes to prolong the input signal with zeros
until having a total number of sample which is the first power of 2 whose value is
higher than the initial number of samples.
Method “TRONCATURE” will consider only the first samples of which the total number
is the greatest power of two whose value is lower than the initial number of sample.
For example, on a signal of 601 values, method “PROL_ZERO” will supplement the signal for
to have 1024 samples, whereas method “TRONCATURE” will consider only them
the first 512 moments.
If the input signal to a number of sample which is a power of two, two methods
are obviously equivalent: one takes into account the signal without modifying it.
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3.13 Word
key
CORR_ACCE
/
CORR_ACCE
=
Key word factor allowing to correct a accélérogramme measured for calculation of
seismic response of a system.
One removes the drift of the signal, calculated by linear smoothing within the meaning of least squares
on the totality of the signal, in order to make the accélérogramme more realistic. Drift speed
relative corresponding is also removed.
One turns over at output the corrected accélérogramme.
3.13.1 Operand FUNCTION
FONCTION = F
Measured real Accélérogramme.
Do not apply to the concepts of the tablecloth type.
3.13.2 Operand CORR_DEPL
CORR_DEPL
=
/
“NON”
One does not correct the drift of relative displacement, it is the default value.
/
“OUI”
One removes also the drift of relative displacement. This option is to be used with
precaution, because one does not know a priori the value of final displacement after the seism.
3.14 Word
key
LISS_ENVELOP
The data of origin make up of a tablecloth of spectra SRO gross definite on large
a number of points for a level of floor given.
The first stage consists, for each spectrum, with widening in frequency (shift on the left
and) followed on the right by a reduction in the number of point of definition. These operations carried out, one
ensure yourself of the character wraps spectrum smoothed compared to the initial spectrum. This stage, each
spectrum has its own base of frequency.
The second stage consists in homogenizing the base of frequency of the whole of the spectra of
tablecloth while ensuring itself of nonthe recovery of the spectra between them.
NAPPE = N
Name of the tablecloth of input formed of the rough spectra associated each level of damping.
FREQ_MIN and FREQ_MAX
Range of definition in frequency of the smoothed spectrum.
The frequencies mentioned under FREQ_MIN and FREQ_MAX must be selected among
frequencies of discretization of the rough spectrum.
By defect, one considers the complete spectrum.
ELARG
Widening relates to the whole of the spectrum,
It is given expressed as a percentage and is worth 0.1 (10%) per defect.
For each Fi frequency of the rough spectrum, one defines two new values of frequencies
such as:
·
F - = I
F (1 - G) with 0< G <1,
·
F + = I
F (1+ D) with 0< D <1.
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The parameters G and D represent the amplitude of widening in frequency.
Values of the offset frequencies
-
F and +
F do not correspond to values I
F of
the list of definition of the rough spectrum. J thus is defined
F and K
F such as:
-
·
J
F: value belonging to the list, immediately below or equalizes with F,
·
K
F: value belonging to the list, immediately below or equalizes with +
F.
(jF, I)
For each frequency I
F, two points of co-ordinates
and (K
F, I) are defined
where I represents acceleration at frequency I
F. Two new spectra resulting from
shift of the rough spectrum on the axis of the frequencies are thus built.
TOLE_LISS
Bearing expressed as a percentage criterion on the elimination of the points during smoothing. This tolerance is
fixed at 0.25 times the default value.
Smoothing is carried out on the envelope of the spectra rough, shifted on the right and on the left.
An example of application is proposed in the case ZZZZ100e test.
3.15 Word
key
SPEC_OSCI
/SPEC_OSCI
=
Calculate the spectrum of oscillator of a accélérogramme, function of nature function [R4.05.03].
The spectrum of oscillator is calculable only on the functions of NOM_RESU = “ACCE” and of
NOM_PARA = “INST”.
For any I and any J one considers J
IQ the solution of the differential equation:
&
Q J
J
J
I + 2
2
ji &q + Q = F (T)
I
I
I
J
J
with Q ()
0 =
()
0 = ()
&q
F
I
I
0 and = 2
I
I
The concept produces Fr is a tablecloth (function with two variables) made up of the functions
(Fr,…, Fr,)…
I
J
with Fr J function defined in items I with:
Fr (I) = Max Q J
(T) and D = {T/F
J
I
}
defined
T D
By defect for the calculation of the spectrum of oscillator
·
one considers for reduced depreciation the values:
0.02 0.05 0.10
·
one considers for the frequencies, the 150 values following in Hz,
first is to 0.2 Hz and one deduces the following ones by the rule;
2nd with the 57ème: by step of
0.05 Hz
58
65
0.075
Hz
66
79
0.10
Hz
80
103
0.125
Hz
104
131
0.25
Hz
132
137
0.5
Hz
138
141
1.
Hz
142
150
1.5
Hz
·
the spectrum is normalized with G (either with the value 9.81 ms-2).
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A
Code_Aster ®
Version
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Titrate:
Operator CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER Key
:
U4.32.04-I1 Page
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3.15.1 Operand FUNCTION
FONCTION =
F
Name of the function on which the operation is carried out.
Do not apply to the concepts of the tablecloth type.
3.15.2 Operand METHOD
METHODE =
Name of the METHODE which one wishes to use: the only method usable currently is
“NIGAM” (by defect) which is detailed in the document [R5.05.01].
3.15.3 Operand AMOR_REDUIT
AMOR_REDUIT = lam
lam = (
1,…,
,)
…
I
List reduced depreciation: example 0.01, 0.05,….
3.15.4 Operands FREQ/LIST_FREQ
/
FREQ = lfre
lfre = (
1,…,
,)
…
I
. List frequencies.
/
LIST_FREQ = lfreq
List frequencies provided under a concept listr8.
3.15.5 Operands NATURE/NATURE_FONC
NATURE =
Nature of the size of the tablecloth created by command CALC_FONCTION.
2
“ACCE”: spectrum the pseudo one - acceleration
(
U T) =
(
U T)
&
I
“VITE”: spectrum of pseudovelocity
(
U T) =
(
U T)
&
I
“DEPL”: spectrum of displacement
(
U T)
NATURE_FONC = “ACCE”
Nature of the function which is used to build the spectrum. For the moment only value “ACCE” is
available. This key word makes it possible to overload the NOM_RESU of the function specified under
key word FONCTION when this one is created by RECU_FONCTION [U4.32.03].
3.15.6 Operand NORMALIZES
NORME = R
The spectrum of oscillator will be normalized with the value R (value of pseudo-acceleration), this
value is recalled in the file of message.
Handbook of Utilization
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Titrate:
Operator CALC_FONCTION
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:
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3.16 Attributes of the concept function at output
3.16.1 Default values
By defect the attributes of the concept function at output of command CALC_FONCTION are for
various options (cf commands DEFI_FONCTION [U4.31.02] and DEFI_NAPPE [U4.31.03]).
·
Option DERIVES:
Interpolation: data by the function in input
Left prolongation: EXCLU
Right prolongation: EXCLU
NOM_PARA = “INST” (example) given by the function in input
NOM_RESU = “VITE” (example) given by the function in input
·
JUST option:
Even rules that for DERIVE
·
Options COMB/COMB_C:
Attributes of the first combined function.
·
Option SPEC_OSCI: the result is a tablecloth
Attributes of the tablecloth:
NOM_PARA = “AMOR”
NOM_RESU = “DEPL” or “VITE” or “ACCE”
Interpolation: “LOG”
Left prolongation: “EXCLU”
Right prolongation: “EXCLU”
Attributes of each function:
NOM_PARA = “FREQ”
Interpolation: “LOG”
Left prolongation: “EXCLU”
Right prolongation: “CONSTANT”
·
Option WRAPS:
Attributes of the first function given.
·
Option FFT:
NOM_PARA = FREQ if NOM_PARA of the function is INST
If not it is the reverse
·
Option COMPOSES:
NOM_PARA: that of function FONC_PARA
NOM_RESU: that of function FONC_RESU
Interpol: that of function FONC_RESU
Prolongation: that of function FONC_RESU
·
Option EXTRACTION:
Attributes identical to those of the function given in input
·
Option ADZE:
NOM_PARA: that of the functions
NOM_RESU: that of the functions
Interpol: linear
Prolongation: “EXCLU”
Handbook of Utilization
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:
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3.16.2 Overload attributes
The user can overload the attributes given by defect by using the following key words:
3.16.2.1 Operand NOM_PARA
NOM_PARA = para
He indicates the name of the parameter (variable or X-coordinate) of the function or the tablecloth.
values currently authorized for para are:
/
“TEMP”
/
“INST”
/
“EPSI”
/
“X”
/
“Y”
/
“Z”
/
“FREQ”
/
“PULS”
/
“AMOR”
/
“DX”/
“DY”/
“DZ”
/
“DRX”
/
“DRY”
/
“DRZ”
/
“ABSC”
3.16.2.2 Operand NOM_RESU
NOM_RESU = resu
It makes it possible to document, the function created by giving a name (8 characters) to the function.
Except exception (cf [§3.1], [3.2], [§3.5]), this name is not tested.
3.16.2.3 Operand Interpol
Interpol
Type of interpolation of the function enters the values of the parameter of the field of definition.
Behind this key word one awaits a parameter list (two to the maximum) among “NON”,
“FLAX”, “LOG”. If only one value is given the interpolation will be identical for
X-coordinates and ordinates. If two values are given, the first corresponds to
the interpolation of the X-coordinates and the second with the interpolation of the ordinates.
3.16.2.4 Operands PROL_DROITE/PROL_GAUCHE
PROL_DROITE and PROL_GAUCHE
They define the type of prolongation on the right (on the left) of the field of definition of
variable:
·
“CONSTANT” for a prolongation with the last (or first) value of
function,
·
“LINEAIRE” for a prolongation along the first definite segment
(PROL_GAUCHE) or of the last definite segment (PROL_DROITE),
·
“EXCLU” if the extrapolation of the values apart from the field of definition of
parameter is prohibited.
3.16.2.5 Operands NOM_PARA_FONC/INTERPOL_FONC/PROL_DROITE_FONC/PROL_GAUCHE_FONC
These key words make it possible to modify the attributes of the functions which intervene in the definition of
tablecloths. They thus have the same significance as the key words without suffix FONC.
3.17 Operand
INFO
INFO
=
Specify the options of impression on 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.
Handbook of Utilization
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Titrate:
Operator CALC_FONCTION
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:
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4 Examples
4.1
Calculation of an envelope
The command file which follows:
DEPI=2. * pi
PAS0=DEPI/200.
LI1=DEFI_LIST_REEL (DEBUT=0.,
INTERVALLE=_F (JUSQU_A = DEPI, NOT = PAS0))
COa = FORMULE (NOM_PARA=' INST', VALE=' cos (INST) ')
SIa = FORMULE (NOM_PARA=' INST', VALE=' sin (INST) ')
CO = CALC_FONC_INTERP (FONCTION=COa, LIST_PARA=LI1,
NOM_PARA=' INST',
NOM_RESU=' DEPL',
PROL_GAUCHE=' EXCLU', PROL_DROITE=' LINEAIRE',
INTERPOL=' LIN',
TITER=' FUNCTION COSINUS')
IF = CALC_FONC_INTERP (FONCTION=SIa, LIST_PARA=LI1,
NOM_PARA=' INST',
NOM_RESU=' DEPLACEMENT',
PROL_GAUCHE=' EXCLU',
PROL_DROITE=' CONSTANT',
INTERPOL=' LIN',
TITER=' FUNCTION SINE ')
ENV1=CALC_FONCTION (ENVELOPPE=_F (FUNCTION = (IF, CO,),
CRITERION = “SUP”))
4.2
Calculation of derived from the function if
The commands which follow
der1 = CALC_FONCTION (DERIVE=_F (FONCTION= if),)
inst1 = 20. * not
TEST_FONCTION (
VALEUR=
_F (
FONCTION = der1, NOM_PARA = “inst”,
VALE_PARA=
inst1,
VALE_REFE=
COa (INST1),)
)
produce on file “RESULTAT”:
---- FONCTION: DER1
OK INST RELA - 0.016% VALE: 8.0888392298046D-01
6.28319E-01 SHEET 0.100% REFE: 8.0901699437495D-01
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A
Code_Aster ®
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Titrate:
Operator CALC_FONCTION
Date:
31/01/06
Author (S):
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:
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4.3
Concatenation of two functions
DFC1=DEFI_FONCTION (NOM_PARA=' X', NOM_RESU=' Y',
VALE= (0., 10.,
4.,
14.,
6.,
16.,),
PROL_DROITE=' LINEAIRE',
PROL_GAUCHE=' LINEAIRE'
)
#
DFC2=DEFI_FONCTION (NOM_PARA=' X', NOM_RESU=' Y',
VALE= (5., 25.,
7.,
27.,
8.,
28.,),
PROL_DROITE=' LINEAIRE',
PROL_GAUCHE=' LINEAIRE'
)
#
DFC3=CALC_FONCTION (ASSE=_F (
FONCTION = (DFC2, DFC1,),
OVERLOAD = “RIGHT”)
)
DFC4=CALC_FONCTION (ASSE=_F (
FONCTION = (DFC1, DFC2,),
OVERLOAD = “LEFT”)
)
The values of the function dfc3 are:
X
=
0.
4.
5.
7.
8.
y
=
10.
14.
25.
27.
28.
The values of the function dfc4 are:
X
=
0.
4.
6.
7.
8.
y
=
10.
14.
16.
27.
28.
Handbook of Utilization
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Titrate:
Operator CALC_FONCTION
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:
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4.4
Composition of two functions
FONC1 = DEFI_FONCTION (NOM_PARA = “X”,
NOM_RESU
=
“F”,
VALE =
(
0.,
0.,
2.,
5.,
3.,
10.,
5.,
15.,
7.,
13.,
8.,
10.,
10.,
9.,
12.,
8.,
13.,
5.,
15.,
1.,
20.,
0.
)
)
FONC2 = DEFI_FONCTION (NOM_PARA = “INST”,
NOM_RESU
=
“X”,
VALE =
(
0.,
0.,
0.1,
2.,
0.2
,
4.,
0.3
,
6.,
0.4
,
8.,
0.5
, 10.,
0.6
, 12.,
0.7
, 14.,
0.8
, 16.,
0.9
, 18.,
1.0
, 20.
)
)
COMP1 = CALC_FONCTION (COMPOSES = _F (FONC_RESU = FONC1,
FONC_PARA
=
fonc2
)
)
The values of the function comp1 are:
inst = 0.
0.1
0.2.0.3.0.4 0.5 0.6
0.7
0.8
0.9
1.0
F = 0.
5.
12.5 14.
10.
9.
8.
3.
0.8
0.4
0.
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A
Code_Aster ®
Version
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Titrate:
Operator CALC_FONCTION
Date:
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:
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