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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
1/10
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: V6.03.119



FORMA04 - Mechanical adaptive mesh on one
beam in bending



Summary:

In this case-test, it is a question of making sure of the not-regression of the TP n°1 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”.

In fact, one “abuses” an elastic design on a metal beam in bending in forced modeling
plane. One makes it converge uniformly via the tool of refinement-déraffinement LOBSTER
®
encapsulated in
MACR_ADAP_MAIL
, then freely by coupling the process with a card of space errors (exhumed via
CALC_ELEM
“ERRE_ELGA_NORE”
or
“ERRE_ELEM_NOZ1”
) localized on each finite element.

From a data-processing validation point of view, this case test of course makes it possible to test the not-regression of
different coupling calculations from card of errors/procedure of refinement-déraffinement in mechanics, but
also options the “pre one and postprocessings” of these calculations (smoothing of the stresses to the nodes, passage
of an error by element with an error with the nodes by element).

Each modeling is associated a question of the TP and one retranscribed “substantial” marrow of it
elements of correction. Entirety of the text of the TP being available on Internet site
http://www.code-aster.com/utilisation/formations
.
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
2/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
1
Problem of reference
1.1 Geometry
Appear Deformed 1.1-a: of the mesh
X
10
GM12
PRES_REP=0.1 NR
1 1
GM13
DX=0
DY=0
Y
100
GM10
GM14
Appear 1.1-b: Diagram of the thermal loadings and geometry
It is about a metal beam (steel 16MND5,
E
= 210.10
3
Mpa,
= 0.2) in bending. Calculation
rubber band (
MECA_STATIQUE
or
STAT_NON_LINE
) in modeling forced plane (
C_PLAN
).
Mesh in
TRIA3/SEG2
(modeling A) and
TRIA6/SEG3
(modelings B and C).
The various key areas of calculation are indicated:
GM14
for all the voluminal part in
SORTED
,
GM13
for embedding (
DDL_IMPO DX=DY=0
for all the points (X=0, Y=0… 10)),
GM12
for
pressure distributed (
PRES_REP=0.1N
for all the points (X=50… 100, Y=10)) and
GM10
(mesh-point
M1=N2
at the point (X=100, Y=0) on the level of which one will measure the arrow).

1.2
Material properties
On all the structure (
GROUP_MA GM14
), the characteristics material are applied
2
.
0
210000
=
=
Mpa
E
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Code_Aster
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Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
3/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
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
GM13
DDL_IMPO
DX = 0, DY = 0
GM12
PRES_REP
= 0.1 NR


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 arrow and the potential energy of deformation is
in fact an approximate solution obtained after a series of four uniform refinements (on
even mesh but in
TRIA6
).
This procedure of uniform refinement can be controlled by a loop
PYTHON
and the operator
MACR_ADAP_MAIL
option
UNIFORM
. The first two modelings are precisely one
illustration of this functionality.

2.2
Result of reference
Potential energy of deformation = 0.102242 J
Arrow
= ­ 0.0614777 m

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 “Run 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.
[4]
O. BOITEAU “FORMA05: Thermomechanical adaptive mesh on a fissured cylinder head”.
[V6.03.120], 2002.
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
4/10
Manual of Validation
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 elasticity with
the operator
STAT_NON_LINE
.
One calculates the cards of space errors of the indicator of Zhu-Zienkiewicz version 1
(
ERRE_ELEM_NOZ1
) and of the indicator in pure residue (
ERRE_ELGA_NORE
). Beforehand it is necessary to have
smoothed the stress field of the points of Gauss to the nodes (
SIEF_ELNO_ELGA
) and, for post-
to treat the card of error (via GIBI), it is necessary to transform it of one
CHAM_ELEM
by element with one
CHAM_ELEM
with the nodes by element. One determines also the value of the arrow (
POST_RELEVE_T
) and of energy
potential of deformation (
POST_ELEM
).
The whole is placed in a loop PYTHON allowing the installation of a procedure of
uniform refinement in
nb_calc
=4 levels (via
MACR_ADAP_MAIL
option
UNIFORME=' RAFFINEMENT'
).
One can thus note the convergence of the values of arrow and energy, the increase of theirs
errors relative compared to the errors provided by the indicators (they same into relative and on
all the structure), variations of the indices of effectiveness of the indicators and their 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 error in residue (component absolute
ERREST
)
on the initial mesh.
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
5/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Appear 3.1-b: Decreases of the relative errors of the deformation energy
and of the arrow compared with those of the relative total component of the indicators.

3.2
Characteristics of the mesh
Initially: 61
TRIA3
, 15
SEG2
, 48 nodes
After a uniform refinement: 244
TRIA3
, 30
SEG2
, 156 nodes
After two uniform refinements: 976
TRIA3
, 60
SEG2
, 555 nodes
After three uniform refinements: 3904
TRIA3
, 120
SEG2
, 2085 nodes
After four uniform refinements: 15616
TRIA3
, 240
SEG2
, 8073 nodes

3.3 Functionalities
tested
Controls
DEFI_MATERIAU ELAS
LIRE_MAILLAGE INFORMATION
VERI_MAIL
MACR_INFO_MAIL QUALITY
INTERPENETRATION
CUT
CONNEXITY
DEFI_GROUP CREA_GROUP_NO
MECHANICAL AFFE_MODELE C_PLAN
AFFE_MATERIAU
AFFE_CHAR_MECA DDL_IMPO
PRES_REP
STAT_NON_LINE COMP_INCR=' ELAS'
CALC_ELEM “SIEF_ELNO_ELGA” “ERRE_ELEM_NOZ1”
“ERRE_ELGA_NORE”
“ERRE_ELNO_ELGA”
IMPR_RESU FORMAT=' CASTEM'
POST_ELEM ENER_POT
POST_RELEVE_T OPERATION=
“EXTRACTION”
IMPR_TABLE
MACR_ADAP_MAIL UNIFORME=
“REFINEMENT”
INTERPENETRATION QUALITY
CUT
CONNEXITY
Various PYTHON
Loop
Structure of control
Passage SD
ASTER - > PYTHON
Passage
SD
PYTHON - > ASTER
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
6/10
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 out of arrow and potential energy of deformation by
report/ratio with the reference solutions (cf [§2.2]). And this, on the initial mesh and after four refinements
uniforms. Tests having to be multi-platforms, the relative tolerance, which is on the errors
initial 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)
39.406851%
idem
10
­ 6
% ­ 1.26
10
­ 12
~ 0%
ERREEN0 eren0
E
p
(4)
0.274116%
idem
10
­ 4
% 1.5
10
­ 12
~ 0%
ERREEN4 eren4
Arrow (0)
39.244715%
idem
10
­ 6
% 1.09
10
­ 13
~ 0%
ERREFL0 erfl0
Arrow (4)
0.270896%
idem
10
­ 4
% ­ 2.25
10
­ 13
~ 0%
ERREFL4 erfl4

4.2
What it was necessary to retain of this part of the TP…
MACR_INFO_MAIL
is thus complementary to
LIRE_MAILLAGE
(
VERI_MAIL
and
INFORMATION)
and
POST_ELEM
. Their combined “efforts” can thus allow:
·
to check the agreement of the mesh with the initial geometry (in mass, dimension, in
surface and in volume),
·
to list them
GROUP_MA
and
GROUP_NO,
primordial for a good modeling of CLs,
·
to diagnose possible problems (symmetrization or connexity, elements of outline
still present in the model, taken into CL account on surfaces or lines of
bad dimensions, interpenetration of elements),
·
to strictly evaluate the quality of the mesh from a point of view finite element.
K
K
K
H
H
T
K
=
the possible close relation of 1
For example, an empirical criterion could be:
·
at least 50% of EFs with a quality standard in lower part of 1.5,
·
at least 90%, in lower part of 2.
The sequence “mechanical thermo operators/
“UNIFORM” MACR_ADAP_MAIL OPTION”
allows to make converge properly, automatically and easily a mesh. It is necessary
however to take guard with the number of generated DDL which can quickly become prohibitory!
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
7/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
5 Modeling
B
5.1
Characteristics of modeling
Identical to modeling A, but in
TRIA6
.
5.2
Characteristics of the mesh
Initially: 61
TRIA6
, 15
SEG3
, 156 nodes
After a uniform refinement: 244
TRIA6
, 30
SEG3
, 555 nodes
After two uniform refinements: 976
TRIA6
, 60
SEG3
, 2085 nodes
After three uniform refinements: 3904
TRIA6
, 120
SEG3
, 8073 nodes
After four uniform refinements: 15616
TRIA6
, 240
SEG3
, 31761 nodes
5.3 Functionalities
tested
Identical to modeling A.

6
Results of modeling B
6.1 Values
tested
One tests the values of the relative errors out of arrow and potential energy of deformation by
report/ratio with the reference solutions (cf [§2.2]). And this, on the initial mesh and after four refinements
uniforms. Tests having to be multi-platforms, the relative tolerance, which is on the errors
initial 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
référenc
E
Tolerance relative Variation
(in %)
Variable
ASTER
Variable
PYTHON
E
p
(0)
0.125637%
idem
10
­ 6
% ­ 2.65
10
­ 12
~ 0%
ERREEN0 eren0
E
p
(4)
7.015631 10
­ 4
%
idem 10
­ 4
% 4.71
10
­ 13
~ 0%
ERREEN4 eren4
Arrow (0)
0.106929%
idem
10
­ 6
% 1.6
10
­ 12
~ 0%
ERREFL0 erfl0
Arrow (4)
1.546674 10
­ 4
%
idem
10
­ 4
% ­ 3.33
10
­ 13
~ 0%
ERREFL4 erfl4
6.2
What it was necessary to retain of this part of the TP…
The elements P
1
are disadvised in mechanics. The good practice is rather: P
1
lumpé in
thermics and P
2
(possibly under-integrated) in mechanics (not artificially not to privilege
the thermal component of the field of deformation and to try to avoid oscillations spatio-
temporal of the field of temperature and its violation of the principle of the maximum).
The choice of the type of finite element premium on the quality of the meshs on which are pressed this
element.
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
8/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
7 Modeling
C
7.1
Characteristics of modeling
Identical to modeling A with the following amendments:
·
mesh in
TRIA6
,
·
free refinement-déraffinement (
MACR_ADAP_MAIL
option
LIBRE=' RAFF_DERA'
) controlled by
the component
NUEST
of
ERRE_ELGA_NORE
(relative component of the indicator in residue).
With like criteria
CRIT_RAFF_PE=CRIT_DERA_PE
=0.2 (one refines 20% of the elements them
worse and one déraffine 20% of best).

7.2
Characteristics of the mesh
Initially: 61
TRIA6
, 15
SEG3
, 156 nodes
After a free refinement: 107
TRIA6
, 19
SEG3,
256 nodes
After two free refinements: 212
TRIA6
, 26
SEG3
, 479 nodes
After three free refinements: 404
TRIA6
, 33
SEG3
, 879 nodes
After four free refinements: 786
TRIA6
, 39
SEG3
, 1671 nodes

7.3 Functionalities
tested
Identical to modeling A with like only different line
MACR_ADAP_MAIL LIBRE=
“RAFF_DERA”
INTERPENETRATION QUALITY
CUT
CONNEXITY
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
9/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
8
Results of modeling C
8.1 Values
tested
One tests the values of the relative errors out of arrow and potential energy of deformation by
report/ratio with the reference solutions (cf [§2.2]). And this, on the initial mesh and after four refinements
uniforms. Tests having to be multi-platforms, the relative tolerance, which is on the errors
initial 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
référenc
E
Toléranc
E
Relative variation
(in %)
Variable
ASTER
Variable
PYTHON
E
p
(0)
0.125637%
idem
10
­ 6
% ­ 2.65
10
­ 12
~ 0%
ERREEN0 eren0
E
p
(4)
1.245370 10
­ 2
%
idem 10
­ 4
% ­ 2.27
10
­ 12
~ 0%
ERREEN4 eren4
Arrow (0)
0.106929%
idem
10
­ 6
% 1.6
10
­ 12
~ 0%
ERREFL0 erfl0
Arrow (4)
1.074923 10
­ 2
%
idem
10
­ 4
% ­ 2.34
10
­ 12
~ 0%
ERREFL4 erfl4
8.2
What it was necessary to retain of this part of the TP…
The sequence “
mechanical thermo operators/
“FREE” MACR_ADAP_MAIL OPTION
converge optimalement the mesh makes it possible to make.
The quality of the elements is impacted little by the process of refinement/déraffinement. Count
held of the choices operated in LOBSTER
®
, it can even improve in 3D!
The type of indicator and its mode of standardization affect great the final mesh.
Taking into account the type of standardization adopted for the indicators in mechanics,
2
,
0
2
)
(
)
(
100
)
(
K
H
rel
K
K
K
+
×
=
(in %)
On problems with singularities (embedding, discontinuity of curvature, re-entering corner,
fissure….), it is to better use the absolute component of these indicators. Because as for “our
good old woman fixed beam “:
0
)
(
K
rel
%
when
K
H
,
0
(close to embedding)
100
)
(
K
rel
%
when
0
,
0
K
H
(close to the arrow)
and this, independently of the true values of the absolute indicator
)
(K
!
This does not call at all into question the great utility of these indicators. It is just necessary to take account of
these elements to refine its diagnosis and “to possibly juggle” with these two components
to refine in the areas of interest.
The problem does not arise in thermics, because the indicator in residue for the thermal problem
is standardized differently. One can however “juggle” with the components of the indicator
thermics and of the limiting, “fictitious” conditions or not, to direct the construction of a mesh
refined or déraffiné by areas (cf [§6.3] [R4.10.03] and modeling A, _ TP21 _, of [V6.03.120]).
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Code_Aster
®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive mesh on a beam in bending
Date:
22/11/02
Author (S):
O. BOITEAU
Key
:
V6.03.119-A
Page:
10/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
9
Summary of the results
In this case-test, it is a question of making sure of the not-regression of the TP n°1 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 design on a metal beam in bending in modeling
plane stress. One makes it converge uniformly via the tool of refinement-déraffinement
LOBSTER
®
encapsulated in
MACR_ADAP_MAIL
, then freely by coupling the process with a card
errors space (exhumed via
CALC_ELEM
+
“ERRE_ELGA_NORE”
or
“ERRE_ELEM_NOZ1”
)
located on each finite element.
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…,
·
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 in mechanics,
but also options the “pre one and postprocessings” of these calculations (smoothing of the stresses with
nodes, passage of an error per element with an error with the 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
.