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Code_Aster
®
Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
Page
:
1/8
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA














Instruction manual
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
stresses.
The field theta is used within the framework of the breaking process in the controls
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 mesh:
·
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
type
fond_fiss
(produced by the 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 type
cham_no_DEPL_R
.
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Code_Aster
®
Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
Page
:
2/8
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
2 Syntax
theta [cham_no_DEPL_R] = CALC_THETA
(
OPTION
=
/
“CROWN”,
[DEFECT]
/
“TAPE”,
MODEL
=
Mo,
[model]
/
FOND_FISS
=
FF,
[fond_fiss]
THETA_3D =_F
(
/ALL = “YES”,
/
GROUP_NO
=
lgno
,
[l_gr_noeud]
/
NODE
=
lno
,
[l_noeud])
/
MODULATE =
, [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]
/
NODE
=
No
, [l_noeud])
MODULATE = module, [R]
R_INF = rinf,
[R]
R_SUP = rsup,
[R]
),
/
THETA_BANDE=_F (
MODULATE = 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
=
/
“NOT”,
[DEFECT]
/“YES”,
IMPRESSION=_F
(
FORMAT
=/“EXCEL”, [DEFECT]
/
“AGRAF”,
UNIT
=
/
8,
[DEFECT]
/
links,
[I]
)
)
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Code_Aster
®
Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
Page
:
3/8
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
3 Operands
3.1 Operand
OPTION
OPTION =/“CROWN”,
[DEFECT]
“TAPE”,
3.1.1
OPTION = “CROWN”
This manner of introducing the field
is geometrical [R7.02.01 §20]. It amounts being given
two radii R
inf
, R
sup
, 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
, identified by its curvilinear X-coordinate S, one
can define a normal plan P in 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) = C
you
in T (R
inf
)
·
vary linearly compared to the radius in the crown S (R
sup
)/T (R
inf
)
·
is continuous in S (R
sup
)
·
= 0 outside S (R
sup
)
S (R
sup
)
R
inf
R
= 0
T (R
inf
)
0
decrease linearly
P
= C
you
R
sup
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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
Page
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U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
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.
One aims at obtaining a field
being worth
K E
X
R
on the border and cancelling itself at a certain distance to
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 X-coordinate R
inf
corresponding to the straight line border,
·
the X-coordinate R
sup
corresponding to the straight line where the field is cancelled. There are R
sup
>
R
inf
.
3.2 Operand
MODEL
MODEL = 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 the aforementioned exists (case of one
nonsymmetrical problem).
X
R
inf
R
sup
= K E
X
R
= 0 Re
X
decrease linearly
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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
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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:
/
ALL =
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.
/
NODE =
taking into account of a under-part of the bottom of fissure made up of
list nodes specified.
Two radii defining the crown and the module of
can be introduced either by
constant actual values which are arguments of the single-ended spanner words
R_INF
,
R_SUP
and
MODULATE
or is by functions of the curvilinear X-coordinate on the directed bottom of fissure, which
are arguments of the single-ended spanner words
R_INF_FO
,
R_SUP_FO
and
MODULE_FO
.
3.3.3 Operands
DIRE_THETA
and
DIRECTION
The 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 one
AFFE_CHAM_NO
[U4.44.11] preliminary.
These options are optional: by defect these directions are calculated automatically from
concept
FF
resulting from the control
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
NODE
follow-up of the name
this node.
The module of
and the two radii are arguments of the single-ended spanner words
MODULATE
,
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 the option
BANDAGE
was retained. The 3 then are found
following single-ended spanner words:
MODULATE
=
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 mesh used.
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Code_Aster
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Version
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Titrate:
Operator
CALC_THETA
Date:
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E. CRYSTAL
Key
:
U4.82.02-F
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U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
R_SUP
= rsup
X-coordinate of the straight line where the field
cancel yourself. 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 area included/understood enters
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”,
/
“NOT”,
If the choice is '
NOT
', nothing occurs.
If the choice is '
YES
', 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
the aforementioned 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, the aforementioned 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”,
UNIT =/8,
[DEFECT]
/
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”
allows post-to treat the impression by Agraf.


4
Phase of checking
·
checking of the membership of the nodes or groups of nodes to the mesh,
·
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.
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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
Page
:
7/8
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
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 (MODEL = Mo,
THETA_2D
=_F (
NODE = (“NO29”),
MODULATE
=
1.,
R_INF
=
1., R_SUP
=
2.),
DIRECTION
= (1., 1., 0.),
IMPRESSION
=_F (UNIT
=
8),
)
with
Mo
the concept
model
product by the control
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.
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 (ALL
=
“YES”,
MODULATE
=
1., R_INF
=
2., R_SUP
=
5.),
DIRECTION
= (
1., 0., 0.),
IMPRESSION
=_F (UNIT
=
8),
)
with
Mo
the concept
model
product by the control
AFFE_MODELE
,
ff1
the concept of the type
fond_fiss
product by the control
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.
Direction of the field
is calculated with the nodes of the bottom of fissure.
THETA1 = CALC_THETA (OPTION = “CROWN”, MODELS = Mo, FOND_FISS =ff1,
THETA_3D
=
_F (GROUP_NO
=
GRN1,
MODULATE
=
1., R_INF
=
2., R_SUP
=
5.),
GROUP_NO
=
GRN2,
MODULE_FO=fo, R_INF_FO=f1, R_SUP_FO=f2),
IMPRESSION
=_F
(
UNIT
=
8)
)
with:
Mo
the concept
model
product by the control
AFFE_MODELE
.
ff1
the concept of the type
fond_fiss
product by the control
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 two radii of the crowns for
GRN2
products by the control
DEFI_FONCTION
.
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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_THETA
Date:
27/01/05
Author (S):
E. CRYSTAL
Key
:
U4.82.02-F
Page
:
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Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
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
Rsup
by function safe with the nodes
NO29
and
NO15
where one
affect
=
1
.
R_INF
=
2
.
R_SUP
=
3
. by constant actual values.
Direction of the field
is calculated with the nodes of the bottom of fissure.
THETA2 = CALC_THETA (OPTION = ' COURONNE', MODELS = Mo, FOND_FISS =ff3,
THETA_3D
=_F (ALL
= ' OUI'
MODULE_FO=fa, R_INF_FO=fb, R_SUP_FO=fc),
(NODE
= (
“NO29”,
“NO15”),
MODULATE
=
1., R_INF
=
2., R_SUP
=
3.
),
IMPRESSION=_F (
UNIT
=
8
)
)
with:
Mo
the concept
model
product by the control
AFFE_MODELE
.
ff3
the concept
fond_fiss
product by the control
DEFI_FOND_FISS
.
F
,
Bfr
,
FC
are respectively the functions defining I
I and two radii of the crowns for
all bottom of fissure, produced by the control
DEFI_FONCTION
.
Note:
The rule of overload applies here for the nodes of the bottom of fissure
NO29
and
NO15
.