Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
1/10
Organization (S): EDF-R & D/SINETICS
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.119
FORMA04 - Mechanical adaptive Maillage on one
beam in inflection
Summary:
In this case-test, it is a question of making sure of the not-regression of the TP n°1 associated the courses “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”.
In fact, one “abuses” an elastic design on a metal beam in inflection in forced modeling
plane. One makes it converge uniformly via the tool of refinement-déraffinement HOMARD® 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 constraints 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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
2/10
1
Problem of reference
1.1 Geometry
Appear 1.1-a: Déformée of the grid
GM12
PRES_REP=0.1 NR
Y
10
1 1
GM14
GM13
GM10
X
DX=0
DY=0
100
Appear 1.1-b: Schéma of the thermal loadings and geometry
It is about a metal beam (steel 16MND5, E = 210.103 Mpa, = 0.2) in inflection. Calculation
rubber band (MECA_STATIQUE or STAT_NON_LINE) in modeling forced plane (C_PLAN).
Grids in TRIA3/SEG2 (modeling A) and TRIA6/SEG3 (modelings B and C).
The various key zones of calculation are indicated: GM14 for all the voluminal part in TRIA,
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
To all structure (GROUP_MA GM14), one applies the characteristics material
E = 210000 Mpa
= 2
.
0
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
3/10
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)
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 grid but in TRIA6).
This procedure of uniform refinement can be controlled by a loop PYTHON and the operator
MACR_ADAP_MAIL option UNIFORME. 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” grid.
2.4 References
bibliographical
[1]
X. DESROCHES “Estimateurs of error of Zhu-Zienkiewicz in elasticity 2D”. [R4.10.01],
1994.
[2]
X. DESROCHES “Estimateur of error in residue”. [R4.10.02], 2000.
[3]
O. BOITEAU “Cours 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.
[4]
O. BOITEAU “FORMA05: Thermomechanical adaptive grid on a fissured bolt”.
[V6.03.120], 2002.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
The grid is carried out with elements of the type TRIA3. Calculation is made in linear elasticity with
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 nodes (SIEF_ELNO_ELGA) and, for post-
to treat the card of error (via GIBI), it is necessary to transform it of a CHAM_ELEM by element with a CHAM_ELEM
with the nodes by element. One determines also the value of the arrow (POST_RELEVE_T) and 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, 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 error in residue (component absolute ERREST)
on the initial grid.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
5/10
Appear 3.1-b: Décroissances 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 grid
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
Commands
DEFI_MATERIAU ELAS
LIRE_MAILLAGE INFORMATION
VERI_MAIL
MACR_INFO_MAIL QUALITY
INTERPENETRATION
TAILLE
CONNEXITE
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=
INTERPENETRATION QUALITY
“RAFFINEMENT”
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
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
6/10
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 grid 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: 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)
39.406851%
idem
106% 1.26
1012
ERREEN0 eren0
~ 0%
Ep (4)
0.274116%
idem
104% 1.5
1012
ERREEN4 eren4
~ 0%
Arrow (0)
39.244715%
idem
106% 1.09
1013
ERREFL0 erfl0
~ 0%
Arrow (4)
0.270896%
idem
104% 2.25
1013
ERREFL4 erfl4
~ 0%
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 INFO) and
POST_ELEM. Their combined “efforts” can thus allow:
· to check the agreement of the grid with the initial geometry (in mass, dimension, in
surface and in volume),
· to list the GROUP_MA and GROUP_NO, paramount 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 grid from a point of view finite element.
HK
K
T =
the possible close relation of 1
H
K
K
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/MACR_ADAP_MAIL OPTION “UNIFORME””
allows to make converge properly, automatically and easily a grid. It is necessary
however to take guard with the number of generated DDL which can quickly become prohibitory!
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
7/10
5 Modeling
B
5.1
Characteristics of modeling
Identical to modeling A, but in TRIA6.
5.2
Characteristics of the grid
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 grid 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: 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
référenc
E
Ep (0)
0.125637%
idem
106% 2.65
1012 ERREEN0 eren0
~ 0%
Ep (4)
7.015631 10 4%
idem 104% 4.71
1013
ERREEN4 eren4
~ 0%
Arrow (0)
0.106929%
idem
106% 1.6
1012
ERREFL0 erfl0
~ 0%
Arrow (4) 1.546674 10 4%
idem
104% 3.33
1013 ERREFL4 erfl4
~ 0%
6.2
What it was necessary to retain of this part of the TP…
The P1 elements are disadvised in mechanics. The good practice is rather: P1 lumpé in
thermics and P2 (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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
8/10
7 Modeling
C
7.1
Characteristics of modeling
Identical to modeling A with the following modifications:
· grid in TRIA6,
· free refinement-déraffinement (MACR_ADAP_MAIL option LIBRE=' RAFF_DERA') controlled by
component NUEST of ERRE_ELGA_NORE (component relative of the indicator in residue).
With as 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 grid
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=
INTERPENETRATION QUALITY
“RAFF_DERA”
TAILLE
CONNEXITE
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
9/10
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 grid 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: 104%.
These tests are carried out on variables PYTHON (via TEST_FONCTION) inserted beforehand
in functions ASTER (via FORMULE).
Identification Valeurs Valeurs Toléranc Ecart relative Variable Variable
Code_Aster
of
E
(in %)
ASTER PYTHON
référenc
E
Ep (0)
0.125637%
idem
106% 2.65
1012 ERREEN0 eren0
~ 0%
Ep (4)
1.245370 10 2%
idem 104% 2.27
1012 ERREEN4 eren4
~ 0%
Arrow (0)
0.106929%
idem
106% 1.6
1012
ERREFL0 erfl0
~ 0%
Arrow (4) 1.074923 10 2%
idem
104% 2.34
1012 ERREFL4 erfl4
~ 0%
8.2
What it was necessary to retain of this part of the TP…
The sequence “
mechanical thermo operators/MACR_ADAP_MAIL OPTION “LIBRE”
”
converge optimalement the grid 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 HOMARD®, it can even improve in 3D!
The type of indicator and its mode of standardization affect great the final grid.
Taking into account the type of standardization adopted for the indicators in mechanics,
(K)
(K) =100×
(in %)
rel
2
2
(K) + H 0, K
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 “:
(K)
% when
(close to embedding)
H
rel
0
0, K
(K)
% when
(close to the arrow)
H
0
rel
100
0, K
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 zones 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 grid
refined or déraffiné by zones (cf [§6.3] [R4.10.03] and modeling A, _ TP21 _, of [V6.03.120]).
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Code_Aster ®
Version
6.3
Titrate:
FORMA04 - Mechanical adaptive Maillage on a beam in inflection
Date:
22/11/02
Author (S):
O. BOITEAU Key
:
V6.03.119-A Page:
10/10
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 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 design on a metal beam in inflection in modeling
plane constraint. One makes it converge uniformly via the tool of refinement-déraffinement
HOMARD® 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 grid. On standard cases, but
also on pathological cases…,
· 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 in mechanics,
but also options the “pre one and postprocessings” of these calculations (smoothing of the constraints 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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-23/02/017/A
Outline document