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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
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U4.3- booklet: Function
HT-62/06/004/A
Organization (S):
EDF-R & D/AMA, DeltaCAD
Instruction manual
U4.3- booklet: Function
Document: U4.32.04
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 power N
ième
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 exit of the control, the function is reordered by increasing X-coordinates.
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Contents
Code_Aster
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Operator
CALC_FONCTION
Date:
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HT-62/06/004/A
3.16.2.5
Operands
NOM_PARA_FONC
/
INTERPOL_FONC
/
PROL_DROITE_FONC
/
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Date:
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2 Syntax
Fr
= CALC_FONCTION
(
/DRIFT
= _F (
FUNCTION = F,
[function]
METHOD = “DIFF_CENTREE”, [DEFECT]
),
/
JUST
=
_F
(
FUNCTION = F,
[function]
METHOD =/“TRAPEZOID”,
[DEFECT]
/
“SIMPSON”,
COEFF =/0., [DEFECT]
/R,
[R]
),
/
OPPOSITE
=
_F (
FUNCTION = F,
[function]
),
/
ABS
=
_F (
FUNCTION = F,
[function]
),
/
WRAP
=
_F (
FUNCTION = F,
[l_fonction]
CRITERION =
/“SUP”,
[DEFECT]
/
“INF”,
),
/
COMB
=
_F
(
FUNCTION
=
F
,
[function]
COEFF = R,
[R]
),
/
COMB_C
=
_F
(
FUNCTION
=
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]
),
/
ADZE =_F (
FUNCTION
=
l_f, [l_fonction]
OVERLOAD
=/“RIGHT”,
[DEFECT]
/
“LEFT”,
),
/
EXTRACTION=_F (
FUNCTION
=
f_c, [fonction_c]
PART
=/“REAL”,
/
“IMAG”,
/
“MODULE”,
/
“PHASE”,
),
/POWER = _F (
FUNCTION
=
F
,
[function]
EXPONENT
=/
N, [I]
/
1, [DEFECT]
),
/
FFT
=
_F (
FUNCTION
=
F
,
[function]
METHOD =
/“PROL_ZERO”,
[DEFECT]
/
“TRUNCATION”,
),
/
CORR_ACCE
=
_F (
FUNCTION
=
F
,
[function]
CORR_DEPL =/
“NOT”,
[DEFECT]
/“YES”,
),
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/LISS_ENVELOP
= _F (
,
TABLECLOTH
=
N,
[tablecloth]
FREQ_MIN
=
/
fmin,
[R]
/
0.2
[DEFECT]
FREQ_MAX
=
/
fmax,
[R]
/
35.5 [DEFECT]
ELARG
=
/elar,
[R]
/0.1,
[DEFECT]
TOLE_LISS
=
/
toleliss,
[R]
/0.25,
[DEFECT]
),
/
SPEC_OSCI
=
_F (
FUNCTION
=
F,
[function]
METHOD = “NIGAM”,
[DEFECT]
AMOR_REDUIT=
lam, [l_R]
/FREQ = lfre,
[l_R]
/LIST_FREQ = lfreq,
[listr8]
NATURE =/“ACCE”,
[DEFECT]
/
“QUICKLY”,
/
“DEPL”,
NATURE_FONC=
“ACCE”, [DEFECT]
NORMALIZES =/9.81,
[DEFECT]
/R,
[R]
),
NOM_PARA
=
para
,
[KN]
NOM_RESU
=
resu
,
[KN]
PROL_DROITE
=
/
“CONSTANT”,
/
“LINEAR”,
/
“EXCLUDED”,
PROL_GAUCHE
=
/
“CONSTANT”,
/
“LINEAR”,
/
“EXCLUDED”
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”,
/
“LINEAR”,
/
“EXCLUDED”,
PROL_GAUCHE_FONC
=/“CONSTANT”,
/
“LINEAR”,
/
“EXCLUDED”,
INFORMATION
=
/
1,
[DEFECT]
/
2,
)
If key word factor DERIVES
then Fr = [FUNCTION]
If JUST key word factor
then Fr = [FUNCTION]
If OPPOSITE key word factor
then Fr = [FUNCTION]
If key word factor ABS
then Fr = [FUNCTION]
If key word factor WRAPS
then Fr = [FUNCTION]
If key word factor COMB
then
Fr
=
[FUNCTION]
If key word factor COMB_C
then Fr = [FONCTION_C]
If key word factor COMPOSES
then Fr = [FUNCTION]
If key word factor ADZE
then
Fr
=
[FUNCTION]
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Date:
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HT-62/06/004/A
If key word factor EXTRACTION
then Fr = [FUNCTION]
If key word factor FFT
then Fr = [FUNCTION]
If key word factor CORR_ACCE
then Fr = [FUNCTION]
If key word factor POWER
then Fr = [FUNCTION]
If key word factor SPEC_OSCI
then Fr = [TABLECLOTH]
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Date:
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3 Operands
3.1 Word
key
DERIVES
/DRIFT
=
The function is derived
F ()
T
.
FUNCTION = F
Name of the function which one wishes to derive.
Do not apply to the concepts of the tablecloth type.
METHOD =
Name of
METHOD
that one wishes to use: the only method available is currently
DIFF_CENTREE
(by defect).
Note:
See JUST key word.
3.2 Word
key
JUST
/JUST
=
The function is integrated
F ()
T
.
FUNCTION = F
Name of the function which one wishes to integrate.
Do not apply to the concepts of the tablecloth type.
METHOD =
Name of
METHOD
that one wishes to use.
Two methods are available: method of
“TRAPEZOID”
(by defect) and method of
“SIMPSON”
.
Method of
“SIMPSON”
is to be employed with precaution because it can involve
oscillations. It is to better discretize finely
F ()
T
and to integrate with the method of
'
TRAPEZOID
'. In particular it is disadvised using the method
“SIMPSON”
for
the interpretation of a accélérogramme.
COEFF = R
Constant of integration, by defect
0
.
Note:
· For JUST as for DRIFT, 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
EXCLUDED 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… There 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
OPPOSITE
/OPPOSITE
=
The function is reversed
F ()
T
.
FUNCTION = F
Name of the function which one wishes to reverse, it is necessary that the aforementioned 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. (“FLAX”, “LOG”) becomes
(“LOG”, “FLAX”).
· The prolongations EXCLUDED and LINEAR are unchanged. On the other hand, one
CONSTANT prolongation is changed from of EXCLUDED.
3.4 Word
key
ABS
/ABS
=
Provides the absolute value of a function or a tablecloth.
FUNCTION = 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 the LINEAR prolongation: systematically changed from of EXCLUDED 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
WRAP
/
WRAP
=
Calculation of the envelope of several functions.
This operation is available on operands of nature
function
or
tablecloth
.
3.5.1 Operand
FUNCTION
FUNCTION = F
List functions or tablecloths which one seeks the envelope.
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3.5.2 Operand
CRITERION
CRITERION =
/
“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
.
FUNCTION = 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 the key word WRAPS
3.7 Word
key
COMB_C and operand LIST_PARA
/COMB_C
=
Linear combination complexes several concepts of nature fonction_c.
FUNCTION =
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 the key word WRAPS
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
ADZE
/
ADZE
=
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
FUNCTION
FUNCTION = l_f
Functions with concaténer. Two functions exactly are awaited.
3.9.2 Operand
OVERLOAD
OVERLOAD
=/“RIGHT”,
/
“LEFT”,
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 area 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
FUNCTION = f_c
Complex function.
3.10.2 LEFT operand
PART
=
/“REAL”
: 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
POWER
This key word makes it possible to build power N
ième
of a function or a whole of functions
provided in the form of a tablecloth.
FUNCTION = F
Name of the function F concerned (standard function or tablecloth).
EXPONENT = 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).
FUNCTION = 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.
METHOD =
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
“TRUNCATION”
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, the method
“PROL_ZERO”
will supplement the signal for
to have 1024 samples, whereas method
“TRUNCATION”
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 exit the corrected accélérogramme.
3.13.1 Operand
FUNCTION
FUNCTION = F
Measured real Accélérogramme.
Do not apply to the concepts of the tablecloth type.
3.13.2 Operand
CORR_DEPL
CORR_DEPL
=
/
“NOT”
One does not correct the drift of relative displacement, it is the default value.
/
“YES”
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.
TABLECLOTH = 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 frequency F
I
rough spectrum, one defines two new values of frequencies
such as:
·
(
)
G
I
F
F
-
=
-
1
with 0<
G
<1,
·
(
)
D
I
F
F
+
=
+
1
with 0<
D
<1.
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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
.
For each frequency I
F
, two points of co-ordinates
()
I
J
F
,
and
(
)
I
K
F
,
are defined
where I
represent 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 all
I
and all
J
one considers
ji
Q
the solution of the differential equation:
()
&&
Q
&q
Q
F
ij
J I
ij
I
ij
T
+
+
=
2
2
with
()
()
()
Q
&q
F
ij
ij
0
0
0
=
=
and
I
I
= 2
The produced concept
Fr
is a tablecloth (function with two variables) made up of the functions
(
)
Fr,…, Fr,…
I
J
with
Fr
J
function defined in the points
I
with:
()
()
{
}
Fr
Max Q
D
T/F
J
ij
I
T D
T
=
=
and
defined
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 with
0.2
Hz and one deduce the following ones by the rule;
2nd
with
57ème
: by pitch 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
).
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER
Key
:
U4.32.04-I1
Page
:
14/20
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
3.15.1 Operand
FUNCTION
FUNCTION =
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
METHOD =
Name of
METHOD
that 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 the control
CALC_FONCTION
.
()
()
()
()
()
“ACCE”
“QUICKLY”
“DEPL”
:
& &
:
&
:
spectrum of pseudo acceleration
spectrum pseudo speed
spectrum of displacement
-
-
=
=
U T
U T
U T
U T
U T
I
I
2
NATURE_FONC = “ACCE”
Nature of the function which is used to build the spectrum. For the moment only the value
“ACCE”
is
available. This key word makes it possible to overload it
NOM_RESU
function specified under
key word
FUNCTION
when the aforementioned is created by
RECU_FONCTION
[U4.32.03].
3.15.6 Operand
NORMALIZES
= R NORMALIZES
The spectrum of oscillator will be normalized with the value
R
(value of pseudo-acceleration), this
value is recalled in the file of message.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER
Key
:
U4.32.04-I1
Page
:
15/20
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
3.16 Attributes of the concept function at exit
3.16.1 Default values
By defect attributes of the concept function at exit of the control
CALC_FONCTION
are for
various options (cf controls
DEFI_FONCTION
[U4.31.02] and
DEFI_NAPPE
[U4.31.03]).
·
Option
DERIVES
:
Interpolation: data by the function in input
Left prolongation: EXCLUDED
Right prolongation: EXCLUDED
NOM_PARA
=
“INST”
(example) given by the function in input
NOM_RESU
=
“QUICKLY”
(example) given by the function in input
·
Option
JUST
:
Even rules that for
DERIVES
·
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
“QUICKLY”
or
“ACCE”
Interpolation:
“LOG”
Left prolongation:
“EXCLUDED”
Right prolongation:
“EXCLUDED”
Attributes of each function:
NOM_PARA
=
“FREQ”
Interpolation:
“LOG”
Left prolongation:
“EXCLUDED”
Right prolongation:
“CONSTANT”
·
Option
WRAP
:
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
COMPOSE
:
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:
“EXCLUDED”
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER
Key
:
U4.32.04-I1
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:
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Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
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”
/
“SWEATERS”
/
“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
“NOT”
,
“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,
·
“LINEAR”
for a prolongation along the first definite segment
(
PROL_GAUCHE
) or of the last definite segment (
PROL_DROITE
),
·
“EXCLUDED”
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 the suffix
FONC
.
3.17 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
CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER
Key
:
U4.32.04-I1
Page
:
17/20
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
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 = FORMULA (NOM_PARA=' INST', VALE=' cos (INST) ')
SIa = FORMULA (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 controls which follow
der1 = CALC_FONCTION (DERIVE=_F (FONCTION= if),)
inst1 = 20. * not
TEST_FONCTION (
VALEUR=
_F (
FUNCTION = der1, NOM_PARA = “inst”,
VALE_PARA=
inst1,
VALE_REFE=
COa (INST1),
)
)
produce on the file
“RESULT”
:
---- FUNCTION: DER1
OK INST RELA - 0.016% VALE: 8.0888392298046D-01
6.28319E-01 SHEET 0.100% REFE: 8.0901699437495D-01
Code_Aster
®
Version
8.2
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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Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
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 (
FUNCTION = (DFC2, DFC1,),
OVERLOAD = “RIGHT”)
)
DFC4=CALC_FONCTION (ASSE=_F (
FUNCTION = (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.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER
Key
:
U4.32.04-I1
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:
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Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
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.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FONCTION
Date:
31/01/06
Author (S):
COURTEOUS Mr., D. THOMASSON, F. LEBOUVIER
Key
:
U4.32.04-I1
Page
:
20/20
Instruction manual
U4.3- booklet: Function
HT-62/06/004/A
Intentionally white left page.