Code_Aster ®
Version
8.2
Titrate:
Operator CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, Key S. GENIAUT
:
U4.82.04-H1 Page:
1/16
Organization (S): EDF-R & D/AMA
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.82.04
Operator CALC_G_LOCAL_T
1 Goal
To calculate the rate of refund of energy room and - under certain conditions factors of intensity of
constraints in 3D by the method théta.
This operator allows calculation in breaking process of the rate of refund of energy room
function of the curvilinear X-coordinate on the bottom of fissure G (S) in 3D by the method in the case of one
elastic thermo problem linear or not linear [R7.02.01] and [R7.02.03]. The problem can be is
statics, is dynamic [R7.02.02].
This operator also allows the extraction of the stress intensity factors function of
the curvilinear X-coordinate of the bottom of fissure K1 (S), K2 (S), K3 (S) in 3D by the method coupled with
method XFEM in the case of a linear elastic problem [R7.02.12].
Before a first use, it is advised to refer to the consulting and reference documents
of correspondents use, in particular the document [U2.05.01].
Functionalities concerning the rate of refund of energy room with Lagrangienne propagation
(i.e. for an extension of the fissure by using the same grid) in 3D in the case of one
thermo problem elastic linear are described in the document [R7.02.04].
The operator produces a concept of the type counts.
Handbook of Utilization
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Code_Aster ®
Version
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Titrate:
Operator CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, Key S. GENIAUT
:
U4.82.04-H1 Page:
2/16
2 Syntax
[tabl_ *]
=
CALC_G_LOCAL_T
(
MODELE
=
Mo,
[model]
CHAM_MATER = to subdue,
[cham_mater]
/FOND_FISS
= FF,
[fond_fiss]
/
FISSURE =
fiss,
[fiss_xfem]
# recovery of the field of displacements
/
DEPL =
depl,
[cham_no_DEPL_R]
/
VITE =
quickly,
[cham_no_DEPL_R]
ACCE = acce,
[cham_no_DEPL_R]
/
RESULTAT
=
resu,
/
[evol_elas]
/
[evol_noli]
/
[dyna_trans]
/
[mode_meca]
/TOUT_ORDRE = “YES”,
[DEFAUT]
/
NUME_ORDRE =
l_ordre,
[l_I]
/
LIST_ORDRE =
read
,
[listis]
/
INST =
l_inst, [l_R8]
/
LIST_INST
=
l_reel, [listr8]
| PRECISION
=/prec
/
1.0D-6
[DEFAUT]
| CRITERION =/“RELATIVE”, [DEFECT]
/
“ABSOLU”
,
# loading
EXCIT = (_F (CHARGE = load
, [char_meca]
[char_cine_meca]
FONC_MULT = fmult,
[function]
[formula]
),)
SYME_CHAR
=
/
“SANS”
,
[DEFAUT]
/“SYME”,
/“ANTI”,
# behavior
/COMP_ELAS
=_F
(
RELATION
=
/
“ELAS”, [DEFECT]
/
“ELAS_VMIS_LINE”,
/
“ELAS_VMIS_TRAC”,
DEFORMATION =/“SMALL”, [DEFECT]
/
“GREEN”,
/ALL = “YES”,
[DEFAUT]
/ | GROUP_MA
=
lgrma,
[l_gr_maille]
| MAILLE
= lma
,
[l_maille]
),
/
COMP_INCR
=_F
(
RELATION
=
/
“ELAS”, [DEFECT]
/
“VMIS_ISOT_TRAC”,
/
“VMIS_ISOT_LINE”,
DEFORMATION =/“SMALL”, [DEFECT]
/
“PETIT_REAC”,
/ALL = “YES”,
[DEFAUT]
/ | GROUP_MA
=
lgrma,
[l_gr_maille]
| MAILLE
= lma
,
[l_maille]
),
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, Key S. GENIAUT
:
U4.82.04-H1 Page:
3/16
ETAT_INIT
=_F
(
/DEPL = depl,
[cham_no_DEPL_R]
/SIGM =
sigm,
/
[carte_SIEF_R]
/
[cham_elem_SIEF_R]
),
# option requested: - calculation of G (S) traditional
-
calculation
of
G (S)
with
propagation
Lagrangian
OPTION
=
/
“CALC_G”,
[DEFAUT]
#
/“CALC_K_G”,
#
/“K_G_MODA”
,
#
/
“CALC_G_LGLO”,
PROPAGATION
=
alpha,
[R]
THETA
=
theta,
[theta_geom]
DIRE_THETA = dire_theta, [cham_no_DEPL_R]
#
/
“G_BILINEAIRE”,
#
/
“CALC_G_MAX”
,
BORNES=_F
(
NUME_ORDRE =
num, [I]
VALE_MIN
=
qmin
,
[R]
VALE_MAX
=
qmax
,
[R]
),
# method used for the discretization of in bottom of fissure
/LISSAGE_THETA
=
/
“LEGENDRE”,
[DEFAUT]
/
“LAGRANGE”,
/
LISSAGE_G
=
/
“LEGENDRE”,
[DEFAUT]
/
“LAGRANGE”,
/
“LAGRANGE_NO_NO”,
# degree of the polynomials of Legendre
DEGRE =/0,
/1,
/2,
/3,
/4,
/
5,
[DEFAUT]
/6,
/7,
# lower radii and superiors defining the crowns
/
R_INF
=
R
,
[R]
R_SUP
=
R
,
[R]
/
R_INF_FO
=
rz
,
[function, formula]
R_SUP_FO
=
Rz
,
[function, formula]
# titrates
TITER
=
titrate,
[l_Kn]
# impression
information
INFO =/1,
[DEFAUT]
/2,
)
Handbook of Utilization
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Code_Aster ®
Version
8.2
Titrate:
Operator CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, Key S. GENIAUT
:
U4.82.04-H1 Page:
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3 Operands
3.1 Operand
MODELE
MODELE =
Mo
Mo is the name of the model on which the rate of refund of energy room G (S) is calculated. It is
product by command AFFE_MODELE [U4.41.01].
The name of the model is:
· Optional if the field of displacement is given with key word RESULTAT and if
structure of data resu is of type EVOL_ELAS, EVOL_NOLI:
- if the name of the model misses, the operator takes that which is present in
structure of data resu;
- if the name of the model is provided by the user, the operator checks if it is identical to
that present in the structure of data resu, the contrary case an error
fatal is emitted.
· Obligatory in all the other cases.
The calculation of the rate of refund of energy G (S) does not have a direction and is thus authorized only for
modeling 3D.
This modeling corresponds to hexahedrons with 8, 20 or 27 nodes, pentahedrons with 6 or
15 nodes, of the tetrahedrons with 4 or 10 nodes, of the pyramids with 5 or 13 nodes, of the faces with 3, 4, 8
or 9 nodes.
3.2 Operand
CHAM_MATER
CHAM_MATER =
to subdue
to subdue is the field of material generated by command AFFE_MATERIAU [U4.43.03].
The name of the material field is:
· Optional if the field of displacement is given with key word RESULTAT and if
structure of data resu is of type EVOL_ELAS, EVOL_NOLI:
if the name of the material field misses, the operator takes that which is present
in the structure of data resu;
if the name of the material field is provided by the user, the operator checks if it is
identical to that present in the structure of data resu. In the contrary case,
an alarm is emitted and calculation continues with the material field provided by
the user.
· Obligatory in all the other cases.
The material field makes it possible to recover the characteristics of material:
·
YOUNG modulus E,
·
NAKED Poisson's ratio,
·
thermal dilation coefficient ALPHA (for a thermomechanical problem),
·
elastic limit SY (for a nonlinear elastic problem),
·
slope of the traction diagram D_SIGM_EPSI (for a nonlinear elastic problem
with linear isotropic work hardening), or traction diagram.
These characteristics can depend on the geometry and the temperature for the option
“CALC_G” only.
Characteristics SY and D_SIGM_EPSI are treated only for one elastic problem not
linear with work hardening of von Mises and the option of calculation “CALC_G”.
Handbook of Utilization
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Code_Aster ®
Version
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Titrate:
Operator CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, Key S. GENIAUT
:
U4.82.04-H1 Page:
5/16
Problem of the bimatériau:
1st case: There is a bimatériau but the point of fissure is in only one material.
material 1
R
E
R
1, 1, 1
material 2
E2, 2, 2
If one is assured that the crown, definite enters the radii inferior R and higher R (
order CALC_THETA [U4.82.02]), has like support of the elements of same material, calculation is
possible some is the selected option. If not only option “CALC_G” is possible.
2nd case: There is a bimatériau where the point of fissure is with the interface.
material 1
E1, 1, 1
R
R
material 2
E2, 2, 2
To date, only the option of calculation of the rate of refund of energy (option “CALC_G”) is available.
3.3 Operands
FOND_FISS/FISSURE
/FOND_FISS
= FF,
FF is the bottom of fissure defined by command DEFI_FOND_FISS [U4.82.01]. It allows
to recover:
·
the ordered list of the nodes of the bottom of fissure,
·
meshs of the lips of the fissure or the normal with the fissure,
·
directions of propagation of the bottom of fissure at the ends.
It is starting from these entities that are calculated automatically the curvilinear X-coordinates S
and directions of propagation of the bottom of fissure in each node [R7.02.01 §2.2]. This word
key is obligatory, except if OPTION = “CALC_K_G” or “K_G_MODA”.
/FISSURE = fiss,
fiss is the fissure defined by command DEFI_FISS_XFEM [U4.82.08]. It allows
to recover within the framework of method X-FEM:
·
the ordered list of the points of the bottom of fissure,
·
gradients of the level-sets,
·
the local base at the bottom of fissure
·
the statute of the nodes (enrichment or not) and numbers of the enriched meshs.
These entities contain in particular the curvilinear X-coordinates S and the directions of
propagation of the bottom of fissure in each node. This word is obligatory only in
case where OPTION = “CALC_K_G” or “K_G_MODA”.
Handbook of Utilization
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Titrate:
Operator CALC_G_LOCAL_T
Date:
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Author (S):
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:
U4.82.04-H1 Page:
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3.4 Operands
DEPL/QUICKLY/ACCE/RESULT
These operands make it possible to recover the field of displacement (and speed and acceleration for
a calculation in dynamics) starting from a field with the nodes or extract of a result.
3.4.1 Operand
DEPL
/DEPL = depl
depl is a field with the nodes solution of calculation on Mo.
3.4.2 Operand
QUICKLY/ACCE
/
VITE = quickly
ACCE = acce
quickly and acce is respectively a field speed and a field of acceleration. It is
fields with the nodes solution of a dynamic calculation on Mo.
These two operands must be simultaneously present to calculate the rate of refund
energy into elastodynamic [R7.02.02].
3.4.3 Operand
RESULTAT
/RESULTAT = resu
Name of a concept result of the evol_elas type, evol_noli, mode_meca or dyna_trans.
3.4.3.1 Operands TOUT_ORDRE/NUME_ORDRE/LIST_ORDRE/INST/LIST_INST/
PRECISION/CRITERION
See document [U4.71.00].
3.5 Word
key
EXCIT and operands CHARGE/FONC_MULT
EXCIT = _F (LOAD
= load
FONC_MULT = fmult)
Key word EXCIT makes it possible to recover a list of loadings charges, resulting from the commands
Multiplying AFFE_CHAR_MECA or AFFE_CHAR_MECA_F [U4.44.01], and coefficients fmult.
Key word EXCIT is optional.
If displacements are provided by key word RESULTAT and that the structure of
data resu is of type EVOL_ELAS, EVOL_NOLI the loading taken into account is is that
provided by the user, that is to say that extracted from resu if it misses command. If the loading
provided in resu (coherence of the name and the number of loads is different from that present, of
couples load-function), an alarm is emitted and calculation continues with the loading indicated
by the user.
In all the cases, it should be taken care that the loads indicated here were indeed taken into account
in the preceding mechanical calculation which produced the field of displacements.
Handbook of Utilization
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Titrate:
Operator CALC_G_LOCAL_T
Date:
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Author (S):
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:
U4.82.04-H1 Page:
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The loadings taken into account in the calculation of G are as follows:
Loading
Options
Modeling
key word of
AFFE_CHAR_MECA (_F)
CALC_G
3D
TEMP_CALCULEE
CALC_K_G
FORCE_INTERN
K_G_MODA
PRES_REP
G_BILINEAIRE
FORCE_FACE
CALC_G_MAX
PESANTEUR
ROTATION
Note:
The loadings not supported by an option are ignored. To date, loadings
following being able to have a direction in breaking process is not treated:
·
FORCE_NODALE
·
FORCE_ARETE
·
EPSI_INIT
·
DDL_IMPO on the lips of the fissure
·
FACE_IMPO
It is important to note that the only loadings taken into account in a calculation of mechanics
rupture with the method are those supported by the elements inside the crown
(between Rinf and Rsup [R7.02.01 §3.3]). Only types of load likely to influence it
calculation of G are thus the voluminal loadings (gravity, rotation), a field of
nonuniform temperature or of the efforts applied to the lips of the fissure.
Caution:
·
A loading of comparable nature (for example voluminal force) can appear only in
only one load. In the contrary case, calculation finishes in error.
·
It is not possible to date to associate a load defined as a function
(AFFE_CHAR_MECA_F) and a multiplying coefficient (FONC_MULT). In this case, it
calculation finishes in error.
·
If one makes a calculation in great transformations (key word DEFORMATION = “GREEN” under
the key word factor COMP_ELAS) the supported loadings must be loads
died, typically an imposed force and not a pressure [R7.02.03 §2.4].
·
For option CALC_K_G, if a loading is imposed on the lips of the fissure
(PRES_REP or FORCE_CONTOUR), then it is obligatorily necessary to direct them correctly
meshs of those (by using ORIE_PEAU_3D) before the calculation of K.
3.6 Operand
SYME_CHAR
SYME_CHAR
=/“SANS”
, [DEFAUT]
/
“SYME”
,
/
“ANTI”
,
This key word makes it possible to indicate if the loading is symmetrical or antisymmetric if one
model that half of the solid compared to the fissure. The values of G (S) are then
automatically multiplied by 2.
3.7 Word
key
COMP_ELAS
COMP_ELAS
=
This key word factor makes it possible to define the relation of behavior of material used for it
postprocessing of breaking process.
By defect the relation of behavior is elastic linear in small deformations with
characteristic defined in CHAM_MATER.
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Titrate:
Operator CALC_G_LOCAL_T
Date:
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:
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Note:
· The calculation of the rate of refund of energy G or not has direction only in linear elasticity
linaire (COMP_ELAS). It is however possible to calculate in elastoplasticity
(COMP_INCR) a parameter G then defined as the total flow of energy (plasticity and
rupture) through the defect. In the case of elastoplasticity, the defect must be modelled
by a notch.
· Nothing prohibits to affect a behavior different during calculation from displacements (by
elastoplastic example) then to carry out this postprocessing with another relation (by
non-linear elastic example). The user is responsible for interpretation for
results obtained [R7.02.03].
· If the loading is perfectly radial monotonous, calculations in nonlinear elasticity and
in elastoplasticity lead to the same results. For this type of loading (and
only in this case), it is also possible to make an elastoplastic calculation on
a fissure.
For more precise details, to refer to [U2.05.01].
3.7.1 Operand
RELATION
RELATION
=
/
“ELAS”
Relation of elastic behavior linear i.e. the relation between the deformations
and the constraints considered is linear [R7.02.01 §1.1].
/
“ELAS_VMIS_LINE”
Relation of nonlinear elastic behavior, von Mises with isotropic work hardening
linear. The data materials necessary of the field material are provided in
operator DEFI_MATERIAU (cf the operator STAT_NON_LINE [U4.51.03] and the key word
VMIS_ISOT_LINE) [R7.02.03 §1.1] and [R5.03.20].
/
“ELAS_VMIS_TRAC”
Relation of nonlinear elastic behavior, von Mises with isotropic work hardening not
linear. The data materials necessary of the field material are provided in
operator DEFI_MATERIAU (cf the operator STAT_NON_LINE [U4.51.03] and the key word
VMIS_ISOT_TRAC) [R7.02.03 §1.1] and [R5.03.20].
3.7.2 Operand
DEFORMATION
DEFORMATION =
/
“PETIT”
The deformations used in the relation of behavior are the linearized relations:
(
1
U)
ij
=
(iu J + uj I)
2
,
,
/
“GREEN”
The deformations used in the relation of behavior are the deformations of
Green-Lagrange [R7.02.03 §2.1]:
(
1
U)
ij
=
(iu J + uj I + ku I ku J)
2
,
,
,
,
Caution:
·
The supported loadings are those supported in linear rubber band provided that it
are died loads, i.e independent of the configuration: an imposed load
is a dead load whereas the pressure can be a following loading.
·
Displacements and rotations can be large but it is preferable
to limit to small deformations if one wishes a coherence with actual material.
For more precise details to refer to [R7.02.03 §2.5].
Handbook of Utilization
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Titrate:
Operator CALC_G_LOCAL_T
Date:
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:
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3.7.3 Operands
ALL/GROUP_MA/MESH
/
TOUT =
“OUI”,
/ |
GROUP_MA = lgrma,
|
MAILLE
=
lma,
Specify the meshs or the nodes on which the relation of behavior is used.
3.7.4 Relation of behavior available for each option
“CALC_G”
“CALC_K_G”
COMP_ELAS “ELAS”
“PETIT”
“PETIT”
“GREEN”
“ELAS_VMIS_LINE”
“PETIT” not
disp.
“GREEN”
“ELAS_VMIS_TRAC”
“PETIT” not
disp.
“GREEN”
It is possible for these relations of behavior to calculate the rate of refund of energy G in
great transformations [R7.02.03 §2] with the proviso of having only dead loads.
3.8 Word
key
COMP_INCR
COMP_INCR
=
The relation of behavior elastoplastic is associated a criterion of von Mises with
isotropic or kinematic work hardening.
RELATION
=
/“ELAS”: relation of elastic behavior incremental [U4.51.03]
/“VMIS_ISOT_LINE”
: von Mises with linear isotropic work hardening ([U4.51.03] and
[R5.03.20])
/“VMIS_ISOT_TRAC”
: von Mises with isotropic work hardening given by a curve of
traction [U4.32.01]
DEFORMATION
=
linearized deformations: = (U
) = 1/2 U
+ U
ij
ij
(I, J
J, I)
/“PETIT”:
U
U
I
J
1/2
/“PETIT_REAC”
:
ij =
+
(
[U4.32.01]
X + U)
(X + U)
J
I
ALL/GROUP_MA/MESH
The meshs or the nodes specify on which the incremental relation of behavior is
used.
3.9 Word
key
ETAT_INIT
ETAT_INIT
=
Initial State of reference selected. By defect, all the fields are identically null. The data
of an initial state does not have direction (and is not thus taken into account) only for the treated part of the field
in incremental behavior (COMP_INCR): if calculation is elastic (COMP_ELAS) that does not have
no incidence.
If one wants to take into account an initial state in elasticity, it is key word ELAS located under
COMP_INCR which should be used.
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Date:
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:
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3.9.1 Operand
SIGM/DEPL
/SIGM =
sig,
/DEPL
=
depl,
Respectively, displacement and stress fields taken in an initial state. They can by
being example resulting from command RECU_CHAMP, or to be read in a file with
format I-DEAS by command LIRE_RESU. Either one gives an initial displacement, or one
initial deformation. Attention, if the load transmitted in operand CHARGE contains one
initial deformation (key word EPSI_INIT of AFFE_CHAR_MECA_F), this one will be taken in
count in the same way that depl displacement provided here; it is then illicit to give one
initial state with key word DEPL.
3.10 Operand
OPTION
OPTION
=
/
“CALC_G”
,
[DEFAUT]
/
“CALC_K_G”,
/
“K_G_MODA”,
/
“CALC_G_LGLO”
,
/
“G_BILINEAIRE”,
/
“CALC_G_MAX”
,
3.10.1 OPTION = “CALC_G” [R7.02.01] and [R7.02.03]
It is the default option. It allows the calculation of the rate of refund of energy G (S) by the method
théta in 3D for a or not linear problem thermo elastic linear. G (S) is solution of
the variational equation [R7.02.01 §2.2].
G (S) (
S). m (S) ds G (),
=
O
where 0 are the bottom of fissure and m the normal at the bottom of fissure in the tangent plan of its lips.
3.10.2 OPTION = “CALC_K_G” [R7.02.12]
This option allows calculation by the method théta in 3D of the rate of refund of energy G (S) and of
factors of intensity of the constraints K (
1 S), K (
2 S), K (
3 S) for a linear elastic problem. It is
a generalization of the case 2D [R7.02.05].
The factors of intensity of the constraints are calculated starting from the symmetrical bilinear form of the rate
of restitution. This formulation uses the explicit expressions of the fields of displacements
singular known for a plane fissure at right bottom in an infinite medium. Singular displacements
are calculated while placing itself on the assumption of the plane deformations.
Caution:
·
For this option, only linear elastic designs (elements HEXA8, PENTA6 and
TETRA4) without initial state are available to date. Moreover, narrower terms dependant
with the mechanical loading on the lips of the fissure are not calculated.
·
This formulation being recent in Code_Aster, it is recommended to check, with
each time that is possible, the coherence of the results with those of the operator
POST_K1_K2_K3.
3.10.3 OPTION = “K_G_MODA”
This option allows the calculation of the modal coefficients of intensity of constraints, i.e the factors
of intensity of the constraints associated with the clean modes with vibration with the structure.
Calculations are carried out in thermo linear elasticity by the method of the singular fields (use
bilinear form of G), starting from a structure of data RESULTAT of the mode_meca type
only. The rate of traditional refund of energy G is also calculated.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Code_Aster ®
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Titrate:
Operator CALC_G_LOCAL_T
Date:
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Author (S):
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:
U4.82.04-H1 Page:
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3.10.4 OPTION = “CALC_G_LGLO”
Also the calculation of the rate of refund of energy G allows (S) but with Lagrangian propagation
[R7.02.04].
3.10.5 OPTION = “G_BILINEAIRE” [R7.02.01]
For a series of displacements (U,…, U), this option allows the calculation of the bilinear form
1
N
G (U, U for I J; if I = J then G (U, U) = G (U). The results are stored in a table
I
J)
comprising two indices I and J in reference to displacements U and U ordered in the list
I
J
contained in the structure of data result under key word RESULTAT.
Caution:
Only combinations of discretization of G (S) and the field, cf [§3.12] and [§ 3.13]:
LEGENDRE-LEGENDRE or LAGRANGE-LAGRANGE are available for this option.
3.10.6 OPTION = “CALC_G_MAX” [R7.02.05]
This option relates to only the maximization of G under constraints terminals [R7.02.05]. It
is necessary to provide the value of the constraints terminals behind key word BORNES. The results are printed
in the structure of data result. The value of G_MAX not being single one also determines
the maximum value of G_MAX.
Caution:
Only combinations of discretization of G (S) and the field, cf [§3.12] and [§3.13]:
LEGENDRE-LEGENDRE or LAGRANGE-LAGRANGE are available for this option.
3.11 Key word
BORNES
BORNES
=
This key word factor is obligatory if one uses option “CALC_G_MAX”. If not it is not used. It
allows to define couples of constraints terminals (Q, q+
I
I) for each sequence number of
structure of data result. One then seeks to define the combination of loading more
penalizing in term of rate of refund D `energy:
NR
max G Q Q = max
I I
ij
G qiq J where IQ are the NR associated unit loadings
Q Q q+
I
I
I
I
I, j=1
with the various Ui displacements contained in the structure of data result, and
G = G (U, U
ij
I
J) bilinear form of G.
NUME_ORDRE = num
Sequence number in the structure of data result associated with the values of constraints
terminals.
VALE_MIN = qmin
Value minimal of the coefficient applied to the loading associated with the result stored in
sequence number num of the structure of data resu.
VALE_MAX = qmax
Value maximum of the coefficient applied to the loading associated with the result stored in
sequence number num of the structure of data resu.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Code_Aster ®
Version
8.2
Titrate:
Operator CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, Key S. GENIAUT
:
U4.82.04-H1 Page:
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Note:
·
The user must as many give couples of terminals of sequence numbers contained
in the structure of data result under penalty of fatal error.
·
This option of calculation is valid only for elastic designs linear where
superposition of loading by linear combination is possible.
·
An example of use of this option is given in the document [U4.82.03]
(CALC_G_THETA_T).
3.12 Operands
PROPAGATION/THETA/DIRE_THETA
PROPAGATION = alpha,
THETA
=
theta,
DIRE_THETA = dire_theta
Operands PROPAGATION and THETA are obligatory if one uses option “CALC_G_LGLO” of
Lagrangian propagation. If not they are not used. alpha is the value of
propagation, defined by the field theta [R7.02.04].
3.13 Operand
LISSAGE_THETA
/LISSAGE_THETA
=
/
“LEGENDRE” [DEFECT]
/
“LAGRANGE”
The trace of the field on the bottom of fissure can be discretized either according to the base of
NR first polynomials of Legendre (“LEGENDRE”), is according to the linear functions of form
associated the discretization of the bottom of fissure (“LAGRANGE”) [R7.02.01].
LISSAGE_THETA = ' LEGENDRE': (S) is discretized on a basis of polynomials of Legendre
()
J S of degree J (0 J Degmax) or Degmax is the maximum degree given under key word DEGRE
(between 0 and 7).
LISSAGE_THETA = ' LAGRANGE': (S) is discretized on the functions of form of the node K of
melts of fissure: ()
K S.
3.14 Operand
LISSAGE_G
/LISSAGE_G
=
/
“LEGENDRE”,
[DEFAUT]
/
“LAGRANGE”,
/
“LAGRANGE_NO_NO”,
G (S) can be discretized either according to the polynomials of Legendre (“LEGENDRE”), or according to
functions of form of the nodes of the bottom of fissure (“LAGRANGE”). Method
“LAGRANGE_NO_NO” results from method LAGRANGE-LAGRANGE but it is simplified
[R7.02.01].
Handbook of Utilization
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Titrate:
Operator CALC_G_LOCAL_T
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Author (S):
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:
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If the smoothing of théta by polynomials of Legendre were retained with the preceding key word, then it
smoothing of G must also be to him of Legendre type. The options available in Aster are
summarized in the following table:
Théta
Polynomials of LEGENDRE
Functions of form
Polynomials of LISSAGE_THETA= “LEGENDRE” LISSAGE_THETA=' LAGRANGE'
G (S) LEGENDRE
LISSAGE_G = “LEGENDRE”
LISSAGE_G= “LEGENDRE”
Functions of
LISSAGE_THETA = “LAGRANGE”
form
LISSAGE_G = “LAGRANGE”
or “LAGRANGE_NO_NO”
3.15 Operand
DEGRE
DEGRE = N
N is the maximum degree of the polynomials of Legendre used for the decomposition of the field in
melts of fissure [§3.12] (when LISSAGE_THETA = ' LEGENDRE').
By defect N is assigned to 5. The value of N must lie between 0 and 7.
If one retains the discretizations LISSAGE_THETA = ' LAGRANGE' and LISSAGE_G = “LEGENDRE”,
one must have N NNO [R7.02.01 §2.3].
The Councils on smoothing:
·
it is difficult to give a preference to one or the other method of smoothing. In theory
both give equivalent numerical results. Nevertheless the Théta method:
Lagrange is a little more expensive in time CPU than the Théta method: Legendre;
·
the Théta method: Legendre is sensitive to the maximum degree of the selected polynomials.
maximum degree must be defined according to the number of nodes in bottom of fissure NNO.
If N is too large taking into consideration NNO the results are poor [U2.05.01 §2.4];
·
oscillations can appear with the Théta method: Lagrange, in particular if it
grid comprises quadratic elements. If the grid is radiant in bottom of
fissure, it is then recommended to define crowns R_INF and coinciding R_SUP
with the borders of the elements. A smoothing of the type “LAGRANGE_NO_NO” allows
to limit these oscillations;
·
the use of the two methods with several crowns of integration and the comparison
results makes it possible to consolidate the validity of the model.
3.16 Operands
R_INF/R_SUP
/R_INF = R
R_SUP = R
R and R are the lower and higher radii, presumedly constant over the entire length
fissure, make it possible to determine the crown on which the fields will have one
linear decrease.
3.17 Operands
R_INF_FO/R_SUP_FO
/
R_INF_FO = rz
R_SUP_FO = Rz
Functions defining the radii of the crowns varying according to the curvilinear X-coordinate on
melts of fissure.
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Titrate:
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:
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The Councils:
·
To avoid using crowns with a radius lower no one. Fields of displacements
are singular in bottom of fissure and introduce results vague in postprocessing
of breaking process.
·
It is advised to use successively command CALC_G_LOCAL_T with at least
3 different couples of crowns to ensure itself of the stability of the results. In the event of
important variation (higher than 5-10%) it is necessary to wonder about the good taking into account
of all modeling.
3.18 Operand
INFO
INFO
=
/1,
[DEFAUT]
/2,
Level of messages in file “MESSAGE”. If INFO is worth 2, one generates the impression of
Gi coefficients of G (S) in the base of the polynomials of Legendre, the value of G elementary
G (I) before smoothing, then G (S) on all the nodes of the bottom of fissure.
3.19 Operand
TITER
[U4.03.01].
3.20 Count
produced
Command CALC_G_LOCAL_T produces a concept of the type counts.
This table contains, for each node of the bottom of fissure:
·
the name of the node,
·
its curvilinear X-coordinate along the bottom of fissure,
·
the value of G local to the node.
For option CALC_K_G, the table contains:
· the number of the point of the bottom of fissure (see [U4.82.08]),
· its curvilinear X-coordinate along the bottom of fissure,
· the value of the factors of intensity of the constraints K1, K2, K3 buildings and of G local in each
not.
The table can be printed by IMPR_TABLE [U4.91.03].
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Version
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Titrate:
Operator CALC_G_LOCAL_T
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:
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4 Examples
4.1 Calculation
of
G (S) traditional in linear elasticity (option “CALC_G”)
G1LOC
=
CALC_G_LOCAL_T
(
MODELE
=
Mo,
CHAM_MATER =
chma,
DEPL =
depl,
FOND_FISS
=
FF,
R_INF
=
1.,
R_SUP
=
2.,
EXCIT
=
_F (CHARGE
=
CH,),
DEGRE
=
4.,
LISSAGE_THETA
= ' LAGRANGE')
One calculates the rate of refund of energy room G (S) on the bottom of fissure FF by approximating it by
polynomials of Legendre of degree 4. The base of the fields of propagation corresponds to
functions of form of the nodes of the bottom of fissure (LISSAGE_THETA=' LAGRANGE'). Radii of
crown calculation are constant.
If one models only half of the solid compared to the bottom of fissure, one can add the key word:
SYME_CHAR=' SYME' which makes it possible automatically to obtain the intrinsic values of G (S) (value
multiplied by 2.). To note that the CH load is taken into account only if it applies inside
crown defined by R_SUP.
One can find examples of use in the following tests:
SSLV110 [V3.04.110] semi-elliptic Fissure in infinite medium
SSLV112 [V3.04.112] circular Fissure in infinite medium
HPLV103 [V7.03.103] Thermoélasticité with circular fissure in infinite medium
4.2 Calculation
of
G (S) in nonlinear elasticity in great transformations
(option “CALC_G”)
G2LOC = CALC_G_LOCAL_T (RESULTAT = resu,
NUME_ORDRE=
(1,
10,
20),
FOND_FISS
=
FF,
R_INF_FO
=
rinf,
R_SUP_FO
=
rsup,
LISSAGE_THETA
= “LEGENDRE”,
DEGRE
=
7.,
COMP_ELAS
=_F (RELATION=' ELAS_VMIS_LINE'
DEFORMATION=' GREEN'),
)
One calculates the rate of refund of energy room G (S):
·
on the bottom of fissure FF;
·
starting from the model, field of material and loadings extracted the structure of
data resu;
·
the relation between the strains and the stresses is a nonlinear elastic relation of
von Mises with linear isotropic work hardening;
·
the deformations are those of Green-Lagrange (behavior hyperelastic), the large ones
displacements and great rotations are authorized. In this case, the loadings are thus
inevitably dead loads;
·
G (S) is approximated by polynomials of Legendre of maximum degree 7;
·
the base of the fields of propagation is the base of the polynomials of Legendre
(LISSAGE_THETA=' LEGENDRE');
·
the radii defining the crown are functions of the curvilinear X-coordinate;
·
calculation is carried out for 3 sequence numbers (one recovers displacements with the numbers
of command 1, 10 and 20 starting from the concept resu resulting from a calculation with STAT_NON_LINE).
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_G_LOCAL_T
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Author (S):
E. CRYSTAL, Key S. GENIAUT
:
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