Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 1/8
Organization (S): EDF-R & D/AMA
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.82.02
Operator CALC_THETA
1 Goal
To define a field theta for the calculation of the rate of refund of energy or the factors of intensity of
constraints.
The field theta is used within the framework of the breaking process in the commands
CALC_G_THETA_T [U4.82.03] and CALC_G_LOCAL_T [U4.82.04].
This operator allows to define on all the nodes of the grid:
·
the module of the field theta,
·
in 2D direction of propagation of the bottom of fissure (equalizes with that of the field theta) with
key word DIRECTION,
·
in 3D direction of the field theta calculated automatically starting from the directions of
propagation of the nodes in bottom of fissure. These directions are recovered by the concept of
fond_fiss type (produced by operator DEFI_FOND_FISS), or by the key words
DIRE_THETA or DIRECTION,
·
the Rinf radii and Rsup of the crowns surrounding the bottom of fissure and used in
method theta.
In 2D the bottom of fissure is tiny room to a node and the crowns are circular. In 3D radii
can be variable with the curvilinear X-coordinate of the bottom of fissure and Rinf, Rsup define then
two deformed and variable cylinders surrounding the bottom of fissure.
The rule of overload applies at the time of the assignment to the bottom of fissure.
This field theta is also used to represent the movement of a rectilinear border in
calculations 2D of sensitivity to the variations of field in linear thermics or mechanics.
The produced concept is of cham_no_DEPL_R. type.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 2/8
2 Syntax
theta [cham_no_DEPL_R] = CALC_THETA
(
OPTION
=
/
“COURONNE”,
[DEFAUT]
/
“BANDE”,
MODELE
=
Mo,
[model]
/FOND_FISS
=
FF,
[fond_fiss]
THETA_3D =_F
(
/ALL = “YES”,
/
GROUP_NO
=
lgno
,
[l_gr_noeud]
/
NOEUD
=
lno
,
[l_noeud])
/MODULE =, [R]
R_INF = R, [R]
R_SUP = R, [R]
/
MODULE_FO = Z, [function]
R_INF_FO = rz, [function]
R_SUP_FO = Rz, [function]
),
/
THETA_2D
=_F (
/GROUP_NO = gno,
[l_gr_noeud]
/
NOEUD
=
No
, [l_noeud])
MODULE = module, [R]
R_INF = rinf,
[R]
R_SUP = rsup,
[R]
),
/
THETA_BANDE=_F (
MODULE = module, [R]
R_INF = rinf,
[R]
R_SUP = rsup,
[R]
),
/DIRECTION
=
(d1, d2, d3),
[l_R]
/
DIRE_THETA =
chamno
,
[cham_no_DEPL_R]
GRAD_NOEU_THETA
=
/
“NON”,
[DEFAUT]
/“OUI”,
IMPRESSION=_F
(FORMAT
=/“EXCEL”, [DEFECT]
/
“AGRAF”,
UNITE
=
/
8,
[DEFAUT]
/
links,
[I]
)
)
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 3/8
3 Operands
3.1 Operand
OPTION
OPTION =/“CROWN”,
[DEFAUT]
“BANDE”,
3.1.1 OPTION = “CROWN”
This manner of introducing the field is geometrical [R7.02.01 §20]. It amounts being given
two radii Rinf, Rsup, and in each node of the bottom of fissure by the key word factor THETA_3D
or THETA_2D. One carries out calculations of distance from a knot slip at the bottom of fissure for
to determine the value of in this node.
More precisely, in any node of the bottom of fissure 0, located by its curvilinear X-coordinate S, one
a normal plan P can define into which the field is introduced in such way that after being
given 2 volumes T and S (deformed cylinders) surrounding the bottom of fissure, one a:
·
= O (S) = cte in T (Rinf)
·
vary linearly compared to the radius in the crown S (Rsup)/T (Rinf)
·
is continuous in S (Rsup)
·
= 0 outside S (Rsup)
P
S (Rsup)
T (Rinf)
Rinf
0
R
R
sup
= cte
decrease linearly
= 0
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 4/8
3.1.2 OPTION = “TAPE”
This manner of introducing the field is used to simulate the movement of a border
in calculations of sensitivity to the variations of field in linear thermics [U4.54.01] or in
linear mechanics [U4.51.01]. That is possible for the following configurations:
·
calculations in 2D or axisymmetric 2D,
·
rectilinear border, parallel with axis OY,
·
field of calculation on the right of the border.
R
One aims at obtaining a field being worth K E on the border and being cancelled at a certain distance to
X
interior; the module K is given in key word THETA_BANDE. Between these two situations,
field normalizes decrease linearly with the X-coordinate.
One must thus give successively:
·
the module of the field on the border,
·
the Rinf X-coordinate corresponding to the straight line border,
·
the Rsup X-coordinate corresponding to the straight line where the field is cancelled. There is Rsup > Rinf.
= K er
decrease linearly
= 0 Re
X
X
X
Rinf
Rsup
3.2 Operand
MODELE
MODELE = Mo
Name of the concept models which defines the elements on which the field is calculated.
3.3
Breaking process - 3D problem
3.3.1 Operand
FOND_FISS
/
FOND_FISS = FF
Name of the concept FF of the type fond_fiss container:
·
the ordered list of the nodes describing the bottom of fissure,
·
the list of the meshs describing the upper lip of the fissure,
·
the list of the meshs of the lower lip of the fissure if this one exists (case of one
nonsymmetrical problem).
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 5/8
3.3.2 Operand
THETA_3D
THETA_3D =
Defines the nodes or the groups of nodes entirely describing the bottom of fissure where one
affect the radii of the crown and the module of.
The whole of the nodes of the bottom of fissure is specified by the operands:
/
TOUT =
taking into account of the totality of the nodes of the bottom of fissure.
/
GROUP_NO =
taking into account of a under-part of the bottom of fissure made up of
list groups of nodes specified.
/
NOEUD =
taking into account of a under-part of the bottom of fissure made up of
list nodes specified.
The two radii defining the crown and the module can be introduced either by
constant actual values which are arguments of single-ended spanner words R_INF, R_SUP and
MODULE or is by functions of the curvilinear X-coordinate on the directed bottom of fissure, which
are arguments of single-ended spanner words R_INF_FO, R_SUP_FO and MODULE_FO.
3.3.3 Operands
DIRE_THETA and DIRECTION
Operand DIRECTION makes it possible to define the three components (d1, d2, d3) of the field on the bottom
of fissure.
Operand DIRE_THETA makes it possible to introduce in 3D the direction of the field theta on all the nodes of
melts of fissure by a field with the nodes defined at the time of a AFFE_CHAM_NO [U4.44.11] preliminary.
These options are optional: by defect these directions are calculated automatically from
concept FF resulting from command DEFI_FOND_FISS [U4.82.01].
3.4
Breaking process - problem 2D
3.4.1 Operand
THETA_2D
/
THETA_2D =
Key word factor defining the node of the bottom of fissure is by GROUP_NO (if this node
belongs to a group of node which must be limited to this node) is by NOEUD followed by the name
this node.
The module of and the two radii are arguments of single-ended spanner words MODULE, R_INF,
R_SUP.
3.5
Sensitivity to the variations of field - problem 2D
3.5.1 Operand
THETA_BANDE
/
THETA_BANDE =
Key word factor defining the field if option BANDE were retained. The 3 then are found
following single-ended spanner words:
MODULE
=
modulate
It is the value of the module of the field theta on the line border.
R_INF = rinf
X-coordinate of the straight line border. Attention, it has no checking of the coherence there of
this value rinf with the grid used.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Code_Aster ®
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Titrate:
Operator CALC_THETA
Date:
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Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 6/8
R_SUP = rsup
X-coordinate of the straight line where the field is cancelled. This value must be strictly
higher than rinf. It must be lower than the maximum X-coordinate of the field of calculation.
In other words, the zone ranging between rinf and rsup must be completely included in
the field of calculation. That is not controlled by the operator.
3.6 Operand
GRAD_NOEU_THETA
GRAD_NOEU_THETA =/“YES”,
/
“NON”,
If the choice is “NON”, nothing occurs.
If the choice is “OUI”, the gradient of the field is calculated on all the nodes of the field.
calculation is obligatory if the options of sensitivity were activated in the thermal resolution or
mechanics.
3.7 Operand
DIRECTION/DIRE_THETA
DIRECTION = (d1, d2, d3),
List values of the three components of the direction of the field on the bottom of fissure when
this one is not calculated. In 2D this key word is obligatory: it is necessary to provide a vector of the form
(d1 d2 0).
DIRE_THETA = chamno,
Allows to introduce in 3D the direction of the field on all the nodes of the bottom of fissure by
skew of a preliminary AFFE_CHAM_NO. In the absence of DIRECTION and DIRE_THETA, this one is
calculated by the operator in each node of the bottom of fissure (normal at the bottom of fissure in
plan of the lips).
3.8 Operand
IMPRESSION
FORMAT
=/“EXCEL”, [DEFECT]
/
“AGRAF”,
UNITE =/8,
[DEFAUT]
/
links
,
Key word factor making it possible to print on the logical file of unit links (para defect 8) for
each node of the bottom of fissure rinf, rsup, the module and direction of the field theta. The format
“AGRAF” makes it possible post-to treat the impression by Agraf.
4
Phase of checking
·
checking of the membership of the nodes or groups of nodes to the grid,
·
checking of the membership of the nodes or groups of nodes at the bottom of fissure,
·
checking which the bottom of fissure is complete,
·
checking that direction of the field on the bottom of fissure (when it is given)
contains only three components.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 7/8
5 Examples
5.1
Assignment of a field in 2D by actual values
One affects on the node of the bottom of fissure = 1 R_INF = 1 and R_SUP = 2
THET2 = CALC_THETA (MODELE = Mo,
THETA_2D
=_F (
NOEUD = (“NO29”),
MODULE
=
1.,
R_INF
=
1., R_SUP
=
2.),
DIRECTION
= (1., 1., 0.),
IMPRESSION
=_F (UNITE
=
8),
)
with Mo the model concept produced by command AFFE_MODELE.
5.2
Assignment of a field in 3D by actual values
On the bottom of fissure one affects on all the nodes = 1., R_INF = 2. and R_SUP = 5. by values
real constants.
The direction of the field is given on each one of these nodes, it is worth (1. 0. 0.).
THET3 = CALC_THETA (OPTION = ' COURONNE', MODELS =MO, FOND_FISS =FF1,
THETA_3D
=_F (TOUT
=
“OUI”,
MODULE
=
1., R_INF
=
2., R_SUP
=
5.),
DIRECTION
= (
1., 0., 0.),
IMPRESSION
=_F (UNITE
=
8),
)
with Mo the model concept produced by command AFFE_MODELE,
ff1 the concept of the fond_fiss type produces by command DEFI_FOND_FISS.
5.3 Assignment of a field in 3D by actual values and function
with rule of overload
On the bottom of fissure one affects on the group of nodes GRN1, = 1. Rinf = 2. and Rsup = 5. by
constant actual values, and on the group of nodes GRN2, Rinf and Rsup by functions.
The direction of the field is calculated with the nodes of the bottom of fissure.
THETA1 = CALC_THETA (OPTION = “COURONNE”, MODELE = Mo, FOND_FISS =ff1,
THETA_3D
=
_F (GROUP_NO
=
GRN1,
MODULE
=
1., R_INF
=
2., R_SUP
=
5.),
GROUP_NO
=
GRN2,
MODULE_FO=fo, R_INF_FO=f1, R_SUP_FO=f2),
IMPRESSION
=_F
(
UNITE
=
8)
)
with:
Mo the model concept produced by command AFFE_MODELE.
ff1 the concept of the fond_fiss type produces by command DEFI_FOND_FISS.
GRN1 = {NO3 NO7 NO10}, GRN2 = {NO13 NO15}
The bottom of fissure is consisted of the nodes: NO3, NO7, NO10, NO13, NO15 in an ordered way.
f0, f1, f2 are respectively the functions defining and the two radii of the crowns for
GRN2 produced by command DEFI_FONCTION.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator CALC_THETA
Date:
27/01/05
Author (S):
E. Key CRYSTAL
:
U4.82.02-F Page
: 8/8
Note:
GRN1 and GRN2 must completely describe the bottom of fissure represented in the concept ff1.
On the bottom of fissure one affects, Rinf and safe Rsup by function with nodes NO29 and NO15 where one
affect = 1. R_INF = 2. R_SUP = 3. by constant actual values.
The direction of the field is calculated with the nodes of the bottom of fissure.
THETA2 = CALC_THETA (OPTION = ' COURONNE', MODELE = Mo, FOND_FISS =ff3,
THETA_3D
=_F (TOUT
= ' OUI'
MODULE_FO=fa, R_INF_FO=fb, R_SUP_FO=fc),
(NOEUD
= (
“NO29”,
“NO15”),
MODULE
=
1., R_INF
=
2., R_SUP
=
3.
),
IMPRESSION=_F (
UNITE
=
8
)
)
with:
Mo the model concept produced by command AFFE_MODELE.
ff3 the concept fond_fiss produces by command DEFI_FOND_FISS.
F, Bfrs, FC are respectively the functions defining II and the two radii of the crowns for
all bottom of fissure, produced by command DEFI_FONCTION.
Note:
The rule of overload applies here for the nodes of the bottom of fissure NO29 and NO15.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
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