Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
1/14
Organization (S): EDF-R & D/SINETICS
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.120
FORMA05 - Thermomechanical adaptive Maillage
on a fissured bolt
Summary:
In this case-test, it is a question of making sure of the not-regression of the TP n°2 associated the course “Indicateurs
of error and adaptation of grid; State of the art and establishment in Code_Aster “of the formation
“Non-linear static Analysis with Code_Aster”.
One “abuses” an elastic thermo calculation on a metal bolt fissured in forced modeling
plane (for the mechanical part) and lumpée (for the thermal part). In accordance with the “good practices”
of quality type of the studies, one uses two distinct grids: linear in thermics and quadratic in
mechanics.
One first of all carries out (modeling A) the thermal calculation on which one makes converge freely the grid
P1 with a coupling card of indicator of space errors (CALC_ELEM + “ERTH_ELEM_TEMP”)/refinement
déraffinement (MACR_ADAP_MAIL + “RAFF_DERA”).
In the second modeling (B), the two grids are adapted jointly according to the same process
during a chained thermomechanical calculation. For the free adaptation of the mechanical grid, one A resorts to
the indicator in pure residue “ERRE_ELGA_NORE”.
This case test makes it possible to test the not-regression of different coupling calculations from card of errors/procedure of
refinement-déraffinement into thermomechanical, and options the “pre one and postprocessings” of these calculations.
The entirety of the text of the TP is available on Internet site
http://www.code-aster.com/utilisation/formations.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
2/14
1
Problem of reference
1.1 Geometry
GM36
GM33
Y
ECHANGE= (1000 W/m2°C, 350°C)
OUTGOING FLOW
=-400 W/m2
8
4
GM34
20
10
GM35
3
6
3
X
GM37
55
ECHANGE= (5000 W/m2°C, 150°C)
Appear 1.1-a: Schéma of the thermal loadings and geometry (modelings A and B)
Be reproduced 1.1-b: Isovaleurs of the thermal field on the initial thermal grid (modelings A and B)
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
3/14
It is about one “
bolt
” metal fissured (steel 16MND5, E= 210.103 Mpa, v= 0.2,
C = 526.104 J/M3 C
°, =
5
,
33 W/m C
°).
p
In two modelings (A and B), one carries out an isotropic transitory linear calculation thermal
(THER_LINEAIRE or THER_NON_LINE) in modeling lumpée (PLAN_DIAG) on a grid
thermics TRIA3/SEG2.
In the second modeling, this calculation is chained with an elastic design (MECA_STATIQUE or
STAT_NON_LINE) in modeling forced plane (C_PLAN) on a mechanical grid in
TRIA6/SEG3.
GM36
GM33
ECHANGE= (1000 W/m2°C, 350°C)
OUTGOING FLOW
=-400 W/m2
GM34
GM35
PRES_REP= - 0.1N
GM39/GM40
DX=DY=0
GM37
ECHANGE= (5000 W/m2°C, 150°C)
Appear 1.1-c: Diagram of the mechanical thermo loadings and the geometry (modeling B)
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
4/14
Appear 1.1-d: Decrease of the potential energy of deformation
during the process of adjustment free of the grids (modeling B)
Appear 1.1-e: Deformation of the mechanical grid (modeling B)
The various key zones of calculation are indicated: GM38 for all the voluminal part in TRIA,
GM33 for the outgoing heat flux, GM36/37 for the conditions of exchange, GM39/40 for
embedding, GM34 for the pressure distributed and GM35 on the level of which one will measure the integral
temperature.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
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Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
5/14
1.2
Material properties
To all structure (GROUP_MA GM38), one applies the characteristics material
E = 210000 Mpa
= 2
.
0
C = 526.104 J/M3 C
°
p
=
5
.
33
W/m C
°
1.3
Boundary conditions and loadings
One can synthesize the decomposition of the loadings by zone in the shape of the following table:
Geometrical zones
Loadings
(GROUP_NO/GROUP_MA)
GM33
FLUX_REP
FLUN = - 400 W/M2
GM36 ECHANGE
COEF_H = 1000 W/m2°C
TEMP_EXT = 350 °C
GM37 ECHANGE
COEF_H = 5000 W/m2°C
TEMP_EXT = 150 °C
GM39/40 DDL_IMPO
DX = DY = 0.
GM34 PRES_REP
CLOSE = - 0.1 NR
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
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Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
6/14
2
Reference solution
2.1
Method of calculation used for the reference solutions
On such a case of figure, it is not possible to exhume an analytical solution! The solution of
reference used for error analyzes on the integral of the temperature of GM35 (modeling A)
and on the potential energy of deformation (modeling A and B), is in fact an approximate solution
obtained after a series of three uniform refinements. This procedure of uniform refinement
can be controlled by a loop PYTHON and operator MACR_ADAP_MAIL option UNIFORME.
2.2
Result of reference
Modeling a:
Potential energy of deformation (purely thermal) = 2016.80291 J
Integral of the temperature on GM35 = 4080 °Cm
Modeling b:
Potential energy of deformation (thermomechanical) = 6.75073756. 105 J
2.3
Uncertainty on the solutions
They acts only of approximate solutions obtained on a “quasi-converged” grid.
2.4 References
bibliographical
[1]
X.DESROCHES. “Estimators of error of Zhu-Zienkiewicz in elasticity 2D”. [R4.10.01],
1994.
[2]
X.DESROCHES. “Estimator of error in residue”. [R4.10.02], 2000.
[3]
O.BOITEAU. “Indicating of space error in residue for transitory thermics”.
[R4.10.03], 2001.
[4]
O.BOITEAU. “Course and TP Indicateurs of error & Adaptation of grid; State of the art and
establishment in Code_Aster “.
http://www.code-aster.com/utilisation/formations, 2002.
[5]
O.BOITEAU. “FORMA04: Mechanical adaptive grid on a beam in inflection”.
[V6.03.119], 2002.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
7/14
3 Modeling
With
3.1
Characteristics of modeling
The grid is carried out with elements of the type TRIA3. Calculation is made in linear thermics
stationary isotropic with operator THER_LINEAIRE in lumpé (modeling PLAN_DIAG).
One calculates the cards of space errors of the indicator in pure residue (ERTH_ELEM_TEMP).
Beforehand it is necessary to have smoothed the heat flux of the points of Gauss to the nodes
(FLUX_ELNO_TEMP) and, post-to treat the card of error (via GIBI), it should be transformed of one
CHAM_ELEM by element with a CHAM_ELEM with the nodes by element. One determines also the value of
the integral of the temperature on GM35 (POST_RELEVE_T) and that of the potential energy of
deformation (POST_ELEM).
The whole is placed in a loop PYTHON allowing the installation of a procedure of
free refinement in nb_calc=4 levels (via MACR_ADAP_MAIL option LIBRE=' RAFF_DERA')
coupled on the card of error exhumed beforehand. One controls this process by the component
ERTREL of ERTH_ELEM_TEMP (component relative of the indicator in residue). With like criteria
CRIT_RAFF_PE=0.2 and CRIT_DERA_PE=0.1 (one refines 20% of the worst elements and one déraffine
10% of best).
One can thus note the convergence of the values of the temperature and energy, the increase of
their errors relative compared to the errors provided by the indicator (they same into relative and on
all the structure), variations of the indices of effectiveness of the indicator and its good checking of
the assumption of saturation.
In order to illustrate consultings of “good practice” for the quality of the studies, on the aspects
geometry with a grid, grid itself and standard of finite elements, one uses the options adhoc
LIRE_MAILLAGE, MACR_ADAP_MAIL and MACR_INFO_MAIL.
Appear 3.1-a: Isovaleurs of the component of exchange (TERME2) of the indicator of error
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
8/14
Appear 3.1-b: Décroissances of the relative errors of the deformation energy
and of the average temperature compared with that of the total component
relative of indicator (ERTREL)
3.2
Characteristics of the grid
Initially: 1619 TRIA3, 102 SEG2, 911 nodes
After a free refinement: 3088 TRIA3, 134 SEG2, 1681 nodes
After two free refinements: 6105 TRIA3, 180 SEG2, 3253 nodes
After three free refinements: 12345 TRIA3, 245 SEG2, 6462 nodes
After four free refinements: 25063 TRIA3, 347 SEG2, 12962 nodes
3.3 Functionalities
tested
Commands
DEFI_MATERIAU THER
LIRE_MAILLAGE INFORMATION
VERI_MAIL
MACR_INFO_MAIL QUALITY
INTERPENETRATION
TAILLE
CONNEXITE
DEFI_GROUP CREA_GROUP_NO
THERMAL AFFE_MODELE
PLAN_DIAG
AFFE_MATERIAU
AFFE_CHAR_THER EXCHANGE
FLUX_REP
STATIONARY THER_LINEAIRE
CALC_ELEM “FLUX_ELNO_TEMP”
“ERTH_ELEM_TEMP”
ERTH ELNO ELEM'
IMPR_RESU FORMAT=' CASTEM'
POST_ELEM ENER_POT
POST_RELEVE_T OPERATION=' MOYENNE'
IMPR_TABLE
MACR_ADAP_MAIL LIBRE=' RAFF_DERA'
QUALITE
NTERPENETRATION
TAILLE
CONNEXITE
Various PYTHON
Loop
Structure of control
Passage SD
ASTER - > PYTHON
Passage
SD
PYTHON - > ASTER
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
9/14
4
Results of modeling A
4.1 Values
tested
One tests the values of the relative errors in integral of the temperature and potential energy of
deformation compared to the reference solutions (cf [§2.2]). And this, on the initial grid and afterwards
four free refinements. Tests having to be multi-platforms, the relative tolerance, which is
on the initial errors fixed at 10 6%, is voluntarily slackened on the errors after four
refinements: 104%.
These tests are carried out on variables PYTHON (via TEST_FONCTION) inserted beforehand
in functions ASTER (via FORMULE).
Identification Valeurs Valeurs Tolérance Ecart relative
Variable
Variable
Code_Aster
of
(in %)
ASTER
PYTHON
reference
Ep (0)
0.491819%
idem
106% 1.101011
ERREEN0 eren0
~ 0%
Ep (4)
0.016287%
idem
104% 3.05
1012
ERREEN4 eren4
~ 0%
T (0)
0.921819%
idem
106% 2.42
1012
ERRETM0 ertm0
~ 0%
T (4)
0.208827%
idem
104% 6.65
1013
ERRETM4 ertm4
~ 0%
4.2
What it was necessary to retain of this part of the TP…
It is necessary well to keep in mind, that as a “simple postprocessing” of the problem
thermomechanical, the indicator cannot unfortunately provide more reliable diagnosis
in the zones where the resolution of the initial problem stumbles (fissure, corners, multi-material,
embedding, shock…). It is thus necessary to begin a process of adjustment (UNIFORME or LIBRE), with
a grid refined already a little “with the hand” close to the zones of discontinuities (materials,
geometrical…).
MACR_ADAP_MAIL does not have process of regularization, therefore a bad initial grid
will produce, even coupled to an indicator, probably a bad adapted grid!
As in mechanics, the thermal sequence “operators/MACR_ADAP_MAIL OPTION
“LIBRE”” makes it possible to make converge optimalement the grid.
One can, moreover, “to juggle” with the components of the thermal indicator and the conditions
limits, “fictitious” or not, to direct the construction of a grid refined or déraffiné by
zones (cf [§6.3] [R4.10.03]).
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
10/14
5 Modeling
B
5.1
Characteristics of modeling
Thermal grid (resp. mechanics) is carried out with elements of the type TRIA3
(resp. TRIA6). One chains a calculation of stationary linear thermics isotropic (via THER_LINEAIRE
in modeling PLAN_DIAG) and a calculation in linear elasticity (via STAT_NON_LINE in modeling
C_PLAN).
One calculates the cards of space errors of the indicators in thermal and mechanical pure residue
(ERTH_ELEM_TEMP and ERRE_ELGA_NORE). Beforehand it is necessary to have smoothed the heat flux and it
stress field of the points of Gauss to nodes (FLUX_ELNO_TEMP and SIEF_ELNO_ELGA) and,
post-to treat the card of error (via GIBI), it should be transformed of a CHAM_ELEM by element with one
CHAM_ELEM with the nodes by element. One determines also the value of the potential energy of
deformation (POST_ELEM).
The whole is placed in a loop PYTHON allowing the installation of a procedure of
free refinement in nb_calc=2 levels (via MACR_ADAP_MAIL option LIBRE=' RAFF_DERA')
coupled on the card of error exhumed beforehand. This process is controlled:
· by component ERTREL of ERTH_ELEM_TEMP (component relative of the indicator in
residue) for the thermal grid,
· by component NUEST of ERRE_ELGA_NORE (component relative of the indicator in
residue) for the mechanical grid.
With like criteria CRIT_RAFF_PE=0.2 and CRIT_DERA_PE=0.1 (one refines 20% of the elements them
worse and one déraffine 10% of best).
After each thermal calculation one of course projects the field of temperature of the thermal grid
on the mechanical grid (via PROJ_CHAMP).
One can thus note the convergence of energy, the increase of his relative error per report/ratio
with the errors provided by the indicators (they same into relative and on all the structure), the variations
indices of effectiveness of the indicators and their good checking of the assumption of saturation.
5.2
Characteristics of the grid
Thermal grid
Initially: 1619 TRIA3, 102 SEG2, 911 nodes
After a free refinement: 3088 TRIA3, 134 SEG2, 1681 nodes
After two free refinements: 6105 TRIA3, 180 SEG2, 3253 nodes
Mechanical grid
Initially: 1619 TRIA6, 102 SEG3, 3443 nodes
After a free refinement: 2881 TRIA6, 152 SEG3, 6065 nodes
After two free refinements: 5319 TRIA6, 180 SEG3, 11097 nodes
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
11/14
5.3 Functionalities
tested
Commands
DEFI_MATERIAU THER
ELAS
LIRE_MAILLAGE
DEFI_GROUP CREA_GROUP_NO
THERMAL AFFE_MODELE
PLAN_DIAG
MECANIQUE
C_PLAN
AFFE_MATERIAU
AFFE_CHAR_THER EXCHANGE
FLUX_REP
AFFE_CHAR_MECA TEMP_CALCULEE DDL_IMPO
PRES_REP
STATIONARY THER_LINEAIRE
STAT_NON_LINE COMPR_INCR=' ELAS'
CALC_ELEM “FLUX_ELNO_TEMP”
“ERTH_ELEM_TEMP”
“ERTH_ELNO_ELEM”
“SIEF_ELNO_ELGA”
`ERRE_ELGA_NORE4
“ERRE_ELNO_ELGA”
IMPR_RESU FORMAT=' CASTEM'
POST_ELEM ENER_POT
IMPR_TABLE
MACR_ADAP_MAIL LIBRE=' RAFF_DERA'
QUALITE
INTERPENETRATION
TAILLE
CONNEXITE
Various PYTHON
Loop
Structure of control
Passage SD
ASTER - > PYTHON
Passage
SD
PYTHON - > ASTER
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
12/14
6
Results of modeling B
6.1 Values
tested
One tests the relative error values in potential energy of deformation compared to the solution
of reference (cf [§2.2]). And this, on the initial grid and after two free refinements. Tests
in front of being multi-platforms, the relative tolerance, which on the initial errors is fixed at 10 6%, is
voluntarily slackened on the errors after two refinements: 104%.
These tests are carried out on variables PYTHON (via TEST_FONCTION) inserted beforehand
in functions ASTER (via FORMULE).
Identification Valeurs Valeurs Tolérance Ecart relative
Variable
Variable
Code_Aster
of
(in %)
ASTER
PYTHON
reference
Ep (0)
10.077761% idem 106% 4.7912
ERREEN0 eren0
~ 0%
Ep (2)
0.459330%
idem
104% 1.03
1012
ERREEN2 eren2
~ 0%
6.2
What it was necessary to retain of this part of the TP…
Into thermomechanical, various strategies of adaptation of grid are offered to the user:
· to adapt the grid only according to one thermal criterion,
· idem according to a mechanical criterion,
· to adapt initially according to a thermal criterion, then according to a mechanical criterion (two
separate loops of adaptation).
· to adapt jointly according to a thermal criterion then mechanical (a loop as in
this TP),
· to adapt according to a thermomechanical criterion.
In Code_Aster, one does not have access to indicators explicitly thermo mechanics, although
the mechanical indicators can comprise incidentally a thermal dependence via
loading TEMP_CALCULEE.
According to the needs for the study (rather thermal or rather mechanics, to make converge a grid
broadly, better taken into account of certain CLs…) one can set up in the code,
one of the first four strategies.
Good practice during a thermomechanical calculation being to use the P1 elements lumpés in
thermics and P2 in mechanics, that resulted in using two grids (as in this TP) and
to interpolate the thermal field linear solution on the quadratic mechanical network (via
PROJ_CHAMP).
Nevertheless, if one wishes to work only with one grid, one can easily decline one of
quatres first strategies via option MAJ_CHAMP of MACR_ADAP_MAIL. That allows, all in
adapting the grid according to a thermal criterion (resp. mechanics), to update the field
complementary, mechanical (resp. thermics), on the new adapted grid.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
13/14
7
Summary of the results
In this case-test, it is a question of making sure of the not-regression of the TP n°2 associated the courses
“Indicating of error and adaptation of grid; State of the art and establishment in
Code_Aster “of the formation “non-linear static Analyze with Code_Aster”.
In fact, one “abuses” an elastic thermo calculation on a metal bolt fissured in
plane forced modeling (for the mechanical part) and lumpé (for the thermal part).
In accordance with the “good practices” of quality type of the studies, one uses two grids
distinct: linear in thermics and quadratic in mechanics.
One first of all carries out (modeling A) the thermal calculation on which one makes converge freely it
P1 grid with a coupling card of indicator of space errors (CALC_ELEM +
“ERTH_ELEM_TEMP”)/refinement-déraffinement (MACR_ADAP_MAIL “RAFF_DERA”).
In the second modeling (B), the two grids are adapted jointly according to the same one
process during a chained thermomechanical calculation. For the free adaptation of the grid
mechanics, one has recourse to the indicator in pure residue “ERRE_ELGA_NORE”.
The objectives of this TP are multiple, it acts:
· to familiarize and put into practice the two dual problems: calculation of card
of indicator of error and strategies of adaptation of grid. On standard cases, but
also on pathological cases and for chainings of calculations,
· to detail the various parameter settings of accused operators (CALC_ELEM,
MACR_ADAP_MAIL) and related operators who can appear particularly
interesting for these problems (INFO_MAILLAGE,
MACR_INFO_MAIL,
PROJ_CHAMP…),
· to hammer consultings of “good practice” for the quality of the studies and the use of
tools already available on the subject. One is interested only in the aspects geometry with a grid,
grid itself and standard of finite elements. One is not delayed here on the problems of
no time, of calibration of numerical parameters and on the aspects sensitivity opposite
data,
· to illustrate the formidable potentialities and facilitated which allows the coupling “language
ASTER/PYTHON “in the command file of a study (test, loops, display, calculation,
personal macro-command, interactivity…). Official case-tests being gauged for
to function in batch, some of these aspects “were thus commentarisés” in the file
of command.
From a data-processing validation point of view, this case test of course makes it possible to test the not-regression of
various couplings calculations of card of errors/procedure of refinement-déraffinement into thermo
mechanics, but also options the “pre one and postprocessings” of these calculations (smoothing of
constraints and of the heat fluxes to the nodes, passage of an error per element with an error with
nodes by element).
Each modeling is associated a question of the TP and one retranscribed the “substantial one”
marrow of the elements of correction. Entirety of the text of the TP being available on Internet site
http://www.code-aster.com/utilisation/formations.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive Maillage on a fissured bolt Date:
10/12/02
Author (S):
O. BOITEAU Key
:
V6.03.120-A Page:
14/14
Intentionally white left page.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Outline document