Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
1/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Organization (S):
EDF-R & D/AMA
Instruction manual
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
stresses 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 agents use, in particular the document [U2.05.01].
Functionalities concerning the rate of refund of energy room with Lagrangian propagation
(i.e. for an extension of the fissure by using the same mesh) 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
count
.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
2/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
2 Syntax
[tabl_ *]
=
CALC_G_LOCAL_T
(
MODEL
=
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]
/
QUICKLY =
quickly,
[cham_no_DEPL_R]
ACCE =
acce,
[cham_no_DEPL_R]
/
RESULT
=
resu,
/
[evol_elas]
/
[evol_noli]
/
[dyna_trans]
/
[mode_meca]
/
TOUT_ORDRE =
“YES”,
[DEFECT]
/
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
[DEFECT]
|
CRITERION =/“RELATIVE”, [DEFECT]
/
“ABSOLUTE”
,
# loading
EXCIT = (_F (
CHARGE = load
, [char_meca]
[char_cine_meca]
FONC_MULT
=
fmult,
[function]
[formula]
),)
SYME_CHAR
=
/
“WITHOUT”
,
[DEFECT]
/“SYME”,
/“ANTI”,
# behavior
/COMP_ELAS
=_F
(
RELATION
=
/
“ELAS”, [DEFECT]
/
“ELAS_VMIS_LINE”,
/
“ELAS_VMIS_TRAC”,
DEFORMATION =/“SMALL”, [DEFECT]
/
“GREEN”,
/
ALL =
“YES”,
[DEFECT]
/
|
GROUP_MA
=
lgrma,
[l_gr_maille]
|
NET
= lma
,
[l_maille]
),
/
COMP_INCR
=_F
(
RELATION
=
/
“ELAS”, [DEFECT]
/
“VMIS_ISOT_TRAC”,
/
“VMIS_ISOT_LINE”,
DEFORMATION =/“SMALL”, [DEFECT]
/
“PETIT_REAC”,
/
ALL =
“YES”,
[DEFECT]
/
|
GROUP_MA
=
lgrma,
[l_gr_maille]
|
NET
= lma
,
[l_maille]
),
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
3/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
ETAT_INIT
=_F
(
/
DEPL =
depl,
[cham_no_DEPL_R]
/
SIGM =
sigm,
/
[carte_SIEF_R]
/
[cham_elem_SIEF_R]
),
# option requested: - calculation of G (S) conventional
-
calculation
of
G (S)
with
propagation
Lagrangian
OPTION
=
/
“CALC_G”,
[DEFECT]
#
/“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”,
[DEFECT]
/
“LAGRANGE”,
/
LISSAGE_G
=
/
“LEGENDRE”,
[DEFECT]
/
“LAGRANGE”,
/
“LAGRANGE_NO_NO”,
# degree of the polynomials of Legendre
DEGREE =/0,
/1,
/2,
/3,
/4,
/
5,
[DEFECT]
/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
TITRATE
=
titrate,
[l_Kn]
# impression
information
INFORMATION =
/
1,
[DEFECT]
/2,
)
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
4/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3 Operands
3.1 Operand
MODEL
MODEL =
Mo
Mo
is the name of the model on which the rate of refund of energy room is calculated
()
G S
. It is
product by the control
AFFE_MODELE
[U4.41.01].
The name of the model is:
· Optional if the field of displacement is given with the key word
RESULT
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
, in 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
direction does not have 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 the control
AFFE_MATERIAU
[U4.43.03].
The name of the material field is:
· Optional if the field of displacement is given with the key word
RESULT
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
,
·
Poisson's ratio
NAKED
,
·
thermal expansion factor
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”
.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
5/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Problem of the bimatériau:
1
er
case: There is a bimatériau but the point of fissure is in only one material.
material 1
E
1
,
1
,
1
material 2
E
2
,
2
,
2
R
R
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 the option
“CALC_G”
is possible.
2
ème
case: There is a bimatériau where the point of fissure is with the interface.
material 1
E
1
,
1
,
1
material 2
E
2
,
2
,
2
R
R
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 the control
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 the control
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”.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
6/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
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
/
QUICKLY = quickly
ACCE = acce
quickly
and
acce
are 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
RESULT
/RESULT = resu
Name of a concept result of the type
evol_elas
,
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 (
CHARGE
= load
FONC_MULT = fmult)
The key word
EXCIT
allows to recover a list of loadings
charge
, resulting from the controls
AFFE_CHAR_MECA
or
AFFE_CHAR_MECA_F
[U4.44.01], and multiplying coefficients
fmult
.
The key word
EXCIT
is optional.
If displacements are provided by the key word
RESULT
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 control. If the loading
provided is different from that present in
resu
(coherence of the name and the number of loads, 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.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
7/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
The loadings taken into account in the calculation of G are as follows:
Options
Modeling
Loading
key word of
AFFE_CHAR_MECA (_F)
CALC_G
CALC_K_G
K_G_MODA
G_BILINEAIRE
CALC_G_MAX
3D
TEMP_CALCULEE
FORCE_INTERN
PRES_REP
FORCE_FACE
GRAVITY
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 R
inf
and R
sup
[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
=/“WITHOUT”
, [DEFECT]
/
“SYME”
,
/
“ANTI”
,
This key word makes it possible to indicate if the loading is symmetrical or antisymmetric if one
modelize that half of the solid compared to the fissure. 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
.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
8/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
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 modelized
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 stresses 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
the 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
the 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 =
/
“SMALL”
The deformations used in the relation of behavior are the linearized relations:
()
(
)
ij
I J
J I
U
U
U
=
+
1
2
,
,
/
“GREEN”
The deformations used in the relation of behavior are the deformations of
Green-Lagrange [R7.02.03 §2.1]:
()
(
)
ij
I J
J I
K I
K J
U
U
U
U
U
=
+
+
1
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].
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
9/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3.7.3 Operands
ALL/GROUP_MA/MESH
/
ALL =
“YES”,
/
|
GROUP_MA = lgrma,
|
NET
=
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”
“SMALL”
“SMALL”
“GREEN”
“ELAS_VMIS_LINE”
“SMALL” not
disp.
“GREEN”
“ELAS_VMIS_TRAC”
“SMALL” 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
=
/“SMALL”:
linearized deformations:
(
)
I
J
J
I
ij
ij
U
U
U
,
,
2
/
1
)
(
+
=
=
/“PETIT_REAC”
:
(
)
(
)
ij
I
J
J
I
U
X U
U
X U
=
+
+
+
1 2
/
[U4.32.01]
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 angle of attack.
If one wants to take into account an initial state in elasticity, it is the key word
ELAS
located under
COMP_INCR
that it is necessary to use.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
10/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
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 the control
RECU_CHAMP
, or to be read in a file with
format I-DEAS by the control
LIRE_RESU
. Either one gives an initial displacement, or one
initial deformation. Attention, if the load transmitted in the operand LOAD contains one
initial deformation (key word EPSI_INIT of AFFE_CHAR_MECA_F), the aforementioned 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”
,
[DEFECT]
/
“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
S ds
O
=
.
,
m
G
where
0
is 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 stresses
)
(
3
),
(
2
),
(
1
S
K
S
K
S
K
for a linear elastic problem. It is
a generalization of the case 2D [R7.02.05].
The factors of intensity of the stresses 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 stresses
,
i.e factors
of intensity of the stresses 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 RESULT of the mode_meca type
only. The rate of conventional refund of energy G is also calculated.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
11/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3.10.4
OPTION = “CALC_G_LGLO”
Also the calculation of the rate of refund of energy allows
()
G S
but with Lagrangian propagation
[R7.02.04].
3.10.5
OPTION = “G_BILINEAIRE”
[R7.02.01]
For a series of displacements
(
,…,
)
U
U
N
1
, this option allows the calculation of the bilinear form
(
)
G U U
I
J
,
for
I
J
; if
I
J
=
then
()
()
G U U
G U
,
=
. The results are stored in a table
comprising two indices
I
and
J
in reference to displacements
U
I
and
U
J
ordered in the list
contained in the structure of data result under the key word
RESULT
.
Caution:
Only combinations of discretization of
()
G S
and of 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 stresses terminals [R7.02.05]. It
is necessary to provide the value of the stresses terminals behind the key word
TERMINALS
. 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 of the field
,
cf [§3.12] and [§3.13]:
LEGENDRE-LEGENDRE
or
LAGRANGE-LAGRANGE
are available for this option.
3.11 Key word
TERMINALS
TERMINALS
=
This key word factor is obligatory if the option is used
“CALC_G_MAX”
. If not it is not used. It
allows to define couples of stresses 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:
max
max
,
Q
Q Q
I I
I
ij I J
I J
NR
I
I
I
G
Q Q
G Q Q
-
+
=
=
1
where
Q
I
are them
NR
associated unit loadings
with various displacements
U
I
contents 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 stresses
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.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
12/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
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
The operands PROPAGATION and THETA are obligatory if the option is used
'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”
), that is to say 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 Deg
max
) or deg
max
is the maximum degree given under the key word
DEGREE
(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”,
[DEFECT]
/
“LAGRANGE”,
/
“LAGRANGE_NO_NO”,
()
G S
can be discretized either according to the polynomials of Legendre (
“LEGENDRE”
), that is to say according to
functions of form of the nodes of the bottom of fissure (
“LAGRANGE”
). Method
“LAGRANGE_NO_NO”
is resulting from method LAGRANGE-LAGRANGE but it is simplified
[R7.02.01].
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
13/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
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
LEGENDRE
LISSAGE_THETA= “LEGENDRE”
LISSAGE_G = “LEGENDRE”
LISSAGE_THETA=' LAGRANGE'
LISSAGE_G= “LEGENDRE”
()
G S
Functions of
form
LISSAGE_THETA = “LAGRANGE”
LISSAGE_G = “LAGRANGE”
or “LAGRANGE_NO_NO”
3.15 Operand
DEGREE
DEGREE
= 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 the discretizations are retained
LISSAGE_THETA = ' LAGRANGE'
and
LISSAGE_G = “LEGENDRE”
,
one must have
N
NO
[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
NO
.
If
N
is too large in comparison with
NO
the results are poor [U2.05.01 §2.4];
·
oscillations can appear with the Théta method: Lagrange, in particular if it
mesh comprises quadratic elements. If the mesh 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 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.
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
14/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
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 the control successively
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
INFORMATION
INFORMATION
=
/1,
[DEFECT]
/2,
Level of messages in the file
“MESSAGE”
. If
INFORMATION
is worth 2, one generates the impression of
G-values
I
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
TITRATE
[U4.03.01].
3.20 Count
produced
The control
CALC_G_LOCAL_T
product a concept of the type
count
.
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 the 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 stresses K
1
, K
2
, K
3
buildings and of G local in each
not.
The table can be printed by
IMPR_TABLE
[U4.91.03].
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
15/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
4 Examples
4.1 Calculation
of ()
G S
conventional in linear elasticity (option
“CALC_G”
)
G1LOC
=
CALC_G_LOCAL_T
(
MODEL
=
Mo,
CHAM_MATER =
chma,
DEPL =
depl,
FOND_FISS
=
FF,
R_INF
=
1.,
R_SUP
=
2.,
EXCIT
=
_F (LOAD
=
CH,),
DEGREE
=
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 modelizes only half of the solid compared to the bottom of fissure, one can add the key word:
SYME_CHAR=' SYME'
who allows to obtain the intrinsic values automatically of
()
G S
(value
multiplied by 2.). To note that the load
CH
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] Thermoelasticity 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 (RESULT = resu,
NUME_ORDRE=
(1,
10,
20),
FOND_FISS
=
FF,
R_INF_FO
=
rinf,
R_SUP_FO
=
rsup,
LISSAGE_THETA
= “LEGENDRE”,
DEGREE
=
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
).
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_G_LOCAL_T
Date:
31/01/06
Author (S):
E. CRYSTAL, S. GENIAUT
Key
:
U4.82.04-H1
Page:
16/16
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Intentionally white left page.