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Code_Aster
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Version
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
10/12/02
Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
1/14
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Organization (S):
EDF-R & D/SINETICS













Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.120



FORMA05 - Thermomechanical adaptive mesh
on a fissured cylinder head



Summary:

In this case-test, it is a question of making sure of the not-regression of the TP n°2 associated Indicating courses the “
of error and adaptation of mesh; 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 cylinder head 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 mesh: 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 mesh
P
1
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 mesh is adapted jointly according to the same process
during a chained thermomechanical calculation. For the free adaptation of the mechanical mesh, 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
.
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
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O. BOITEAU
Key
:
V6.03.120-A
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
1
Problem of reference
1.1 Geometry
GM36
ECHANGE= (1000 W/m
2
°C, 350°C)
Y
X
3
10
3
8
4
GM37
ECHANGE= (5000 W/m
2
°C, 150°C)
GM33
OUTGOING FLOW
=-400 W/m
2
6
GM34
GM35
55
20
Appear 1.1-a: Diagram of the thermal loadings and geometry (modelings A and B)
Be reproduced 1.1-b: Isovaleurs of the thermal field on the initial thermal mesh (modelings A and B)
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
10/12/02
Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
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Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
It is about one “
cylinder head
” metal fissured (steel 16MND5, E= 210.10
3
Mpa, v= 0.2,
C
m
W
C
m
J
C
p
°
=
°
=
/
5
,
33
,
/
10
.
526
3
4
).
In two modelings (A and B), one carries out an isotropic transitory linear calculation thermal
(
THER_LINEAIRE
or
THER_NON_LINE
) in lumpée modeling (
PLAN_DIAG
) on a mesh
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 mesh in
TRIA6/SEG3
.

GM36
ECHANGE= (1000 W/m
2
°C, 350°C)
GM37
ECHANGE= (5000 W/m
2
°C, 150°C)
GM33
OUTGOING FLOW
=-400 W/m
2
GM35
GM39/GM40
DX=DY=0
GM34
PRES_REP= - 0.1N
Appear 1.1-c: Diagram of the mechanical thermo loadings and the geometry (modeling B)
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
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Key
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Appear 1.1-d: Decrease of the potential energy of deformation
during the process of adjustment free of the mesh (modeling B)
Appear 1.1-e: Deformation of the mechanical mesh (modeling B)

The various key areas of calculation are indicated:
GM38
for all the voluminal part in
SORTED
,
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.
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
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Author (S):
O. BOITEAU
Key
:
V6.03.120-A
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
1.2
Material properties
On all the structure (
GROUP_MA
GM38
), the characteristics material are applied
C
m
W
C
m
J
C
Mpa
E
p
°
=
°
=
==
/
5
.
33
/
10
526
2
.
0
210000
3
4

1.3
Boundary conditions and loadings
One can synthesize the decomposition of the loadings by area in the shape of the following table:
Geometrical areas
(
GROUP_NO/GROUP_MA
)
Loadings
GM33
FLUX_REP
FLUN = - 400 W/m
2
GM36 EXCHANGE
COEF_H = 1000 W/m
2
°C
TEMP_EXT = 350 °C
GM37 EXCHANGE
COEF_H = 5000 W/m
2
°C
TEMP_EXT = 150 °C
GM39/40 DDL_IMPO
DX = DY = 0.
GM34 PRES_REP
CLOSE = - 0.1 NR
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
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Key
:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
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 the operator
MACR_ADAP_MAIL
option
UNIFORM
.

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. 10
­ 5
J

2.3
Uncertainty on the solutions
They acts only of approximate solutions obtained on a “quasi-converged” mesh.

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 mesh; State of the art and
establishment in Code_Aster “.
http://www.code-aster.com/utilisation/formations,
2002.
[5]
O.BOITEAU. “FORMA04: Mechanical adaptive mesh on a beam in bending”.
[V6.03.119], 2002.
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Code_Aster
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
10/12/02
Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
7/14
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
3 Modeling
With
3.1
Characteristics of modeling
The mesh is carried out with elements of the type
TRIA3
. Calculation is made in linear thermics
stationary isotropic with the 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 one
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
(relative component 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, mesh 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
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Titrate:
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Appear 3.1-b: Decreases of the relative errors of the deformation energy
and of the average temperature compared with that of the total component
relative of the indicator (
ERTREL
)

3.2
Characteristics of the mesh
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
Controls
DEFI_MATERIAU THER
LIRE_MAILLAGE INFORMATION
VERI_MAIL
MACR_INFO_MAIL QUALITY
INTERPENETRATION
CUT
CONNEXITY
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'
QUALITY
NTERPENETRATION
CUT
CONNEXITY
Various PYTHON
Loop
Structure of control
Passage SD
ASTER - > PYTHON
Passage
SD
PYTHON - > ASTER
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Code_Aster
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Version
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
10/12/02
Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
9/14
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
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 mesh 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: 10
­ 4
%.
These tests are carried out on variables PYTHON (via
TEST_FONCTION
) inserted beforehand
in functions ASTER (via
FORMULATE
).
Identification Values
Code_Aster
Values
of
reference
Tolerance relative Variation
(in %)
Variable
ASTER
Variable
PYTHON
E
p
(0)
0.491819%
idem
10
­ 6
% 1.1010
­ 11
~ 0%
ERREEN0 eren0
E
p
(4)
0.016287%
idem
10
­ 4
% 3.05
10
­ 12
~ 0%
ERREEN4 eren4
T (0)
0.921819%
idem
10
­ 6
% 2.42
10
­ 12
~ 0%
ERRETM0 ertm0
T (4)
0.208827%
idem
10
­ 4
% ­ 6.65
10
­ 13
~ 0%
ERRETM4 ertm4

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 areas where the resolution of the initial problem stumbles (fissure, corners, multi-material,
embedding, shock…). It is thus necessary to begin a process of adjustment (
UNIFORM
or
FREE
), with
a mesh refined already a little “with the hand” close to the areas of discontinuities (materials,
geometrical…).
MACR_ADAP_MAIL
do not have process of regularization, therefore a bad initial mesh
will produce, even coupled to an indicator, probably a bad adapted mesh!
As in mechanics, the thermal sequence “operators/
MACR_ADAP_MAIL OPTION
“FREE””
converge optimalement the mesh makes it possible to make.
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 mesh refined or déraffiné by
areas (cf [§6.3] [R4.10.03]).
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FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
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Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
5 Modeling
B
5.1
Characteristics of modeling
Thermal mesh (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 the nodes (
FLUX_ELNO_TEMP
and
SIEF_ELNO_ELGA
) and,
post-to treat the card of error (via GIBI), it should be transformed of one
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 the component
ERTREL
of
ERTH_ELEM_TEMP
(relative component of the indicator in
residue) for the thermal mesh,
·
by the component
NUEST
of
ERRE_ELGA_NORE
(relative component of the indicator in
residue) for the mechanical mesh.
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 mesh
on the mechanical mesh (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 mesh
Thermal mesh
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 mesh
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
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
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Key
:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
5.3 Functionalities
tested
Controls
DEFI_MATERIAU THER
ELAS
LIRE_MAILLAGE
DEFI_GROUP CREA_GROUP_NO
THERMAL AFFE_MODELE
PLAN_DIAG
MECHANICS
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'
QUALITY
INTERPENETRATION
CUT
CONNEXITY
Various PYTHON
Loop
Structure of control
Passage SD
ASTER - > PYTHON
Passage
SD
PYTHON - > ASTER
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
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O. BOITEAU
Key
:
V6.03.120-A
Page:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
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 mesh 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: 10
­ 4
%.
These tests are carried out on variables PYTHON (via
TEST_FONCTION
) inserted beforehand
in functions ASTER (via
FORMULATE
).
Identification Values
Code_Aster
Values
of
reference
Tolerance relative Variation
(in %)
Variable
ASTER
Variable
PYTHON
E
p
(0)
10.077761% idem 10
­ 6
% 4.79
­ 12
~ 0%
ERREEN0 eren0
E
p
(2)
0.459330%
idem
10
­ 4
% ­ 1.03
10
­ 12
~ 0%
ERREEN2 eren2

6.2
What it was necessary to retain of this part of the TP…
Into thermomechanical, various strategies of adaptation of mesh are offered to the user:
·
to adapt the mesh 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 mesh
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 elements P
1
lumpés in
thermics and P
2
in mechanics, that resulted in using two mesh (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 mesh, one can easily decline one of
quatres first strategies via the option
MAJ_CHAMP
of
MACR_ADAP_MAIL
. That allows, all in
adapting the mesh according to a thermal criterion (resp. mechanics), to update the field
complementary, mechanical (resp. thermics), on the new adapted mesh.
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Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
10/12/02
Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
13/14
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
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 mesh; State of the art and establishment in
Code_Aster “of the formation “Analyzes static non-linear with Code_Aster”.
In fact, one “abuses” an elastic thermo calculation on a metal cylinder head 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 mesh
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
mesh P
1
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 mesh is adapted jointly according to the same one
process during a chained thermomechanical calculation. For the free adaptation of the mesh
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 mesh. On standard cases, but
also on pathological cases and for chainings of calculations,
·
to detail the various parameter settings of the 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,
mesh 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-control, interactivity…). Official case-tests being gauged for
to function in batch, some of these aspects “were thus commentarisés” in the file
of control.
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
stresses 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
.
background image
Code_Aster
®
Version
6.0
Titrate:
FORMA05 - Thermomechanical adaptive mesh on a fissured cylinder head
Date:
10/12/02
Author (S):
O. BOITEAU
Key
:
V6.03.120-A
Page:
14/14
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A


























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