Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
1/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Organization (S):
EDF/AMA, AUSY France
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
V6.01.100 document
SSNA100 - Tube of Bree: Method Zarka-Rack
(ZAC)
Summary:
This test of nonlinear quasi-static mechanics consists in modelizing an infinite cylinder subjected to a pressure
intern and a variation in temperature in the thickness depending recurringly on time (tube of BREE).
behavior is elastoplastic with a criterion of Von Mises and a linear kinematic work hardening. One
validate the simplified method thus Zarka-Rack (ZAC) into axisymmetric for a radial loading in a case
of adaptation (
T=30°C) then in a case of accommodation (
T=120°C). This method is a postprocessing
realized by the control
POST_ZAC
[U4.83.21]. For more details see document [R7.06.01].
Two modelings make it possible to test the method in 2D and 3D:
·
in modeling a: the cylinder is modelized by axisymmetric elements 2D (QUAD8),
·
in modeling b: the cylinder is modelized in 3D (meshs HEXA20).
The results obtained by Code_Aster are very close to the reference solution.
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
2/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Z
p
R
R=10.
d=0.12
+
E
-
E
a=0.2
With
B
C
D
E
F
1.2
Material properties
E = 200.000 MPa
= 0.3
= 1.e-4 °C
1
T
ref.
= 0.
Elastoplastic relation between behavior and criterion of Von Mises and kinematic work hardening
linear:
MPa
MPa
.
200
.
18181
=
=
y
T
E
1.3
Boundary conditions and loadings
On AB: U
Z
= 0
Loading:
·
constant uniform pressure p = 2. MPa on CD.
·
linear temperature in the thickness and varying according to time:
)
(
)
2
(
)
(
)
(
)
(
2
)
(
T
F
T
T
T
D
R
R
R
E
E
=
-
-
=
with
T
E
1
3
5
7
9
11
13
T/2
…
0
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
3/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Elastoplastic calculation carried out with the Code Aster on twenty cycles in the case of adaptation
(T = 30°C).
Analytical solution in the case of accommodation with T = 120°C ([bib1]).
2.2
Results of reference
zz
lim
p
and
zz
lim
moy
in the case of adaptation (
p
zz
moy
,
moy
zz
,
p
zz
inf
,
inf
zz
,
p
zz
sup
,
sup
zz
in the case
of accommodation) statements at the points C (skin interns), E (average surface) and F (external skin).
2.3 References
bibliographical
[1]
Contract EDF SEPTEN NC 4158. Study relating to the behavior of the components of
nuclear jet engines. Laboratory of mechanics of the solids. Polytechnic school,
Palaiseau, June 1985.
[2]
S. TAHERI: “Method ZAC”. Note EDF/DER HI-71/6139 of June 14, 1989.
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
4/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
It is about an axisymmetric modeling.
Z
6 elements
R
N26
N3
N32
N33
N2
N4
N17
N19
M1
M2
M3
M4
M5
M6
N18
The loading and the boundary conditions are modelized by:
DDL_IMPO: (NODE: (N26 N3), DY: 0.)
TEMP_CALCULEE: temple
where temple is the higher definite positive function for the moments t=1 and 3 [§1.3]
PRES_REP: (GROUP_MA: L4, NEAR: 2.)
Two preliminary calculations are carried out:
·
an elastic design for the loadings min. and max. on a cycle (T
min
= 1 and T
max
= 3)
·
an optional elastoplastic calculation until the maximum loading before discharge (T
With
= 3)
3.2
Characteristics of the mesh
A number of nodes:
33
A number of meshs and type:
6 elements
QUAD8
3.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING
AXIS
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
SY
AFFE_CHAR_MECA
PRES_REP
TEMP_CALCULEE
GROUP_MA
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_CINE_LINE
MECA_STATIQUE
OPTION
SIEF_ELGA_DEPL
POST_ZAC
EVOL_ELAS
EVOL_NOLI
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
5/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
·
T = 30°C, case of adaptation.
The results of reference come from an elastoplastic calculation Aster on 20 cycles.
-
without elastoplastic semi-cycle given (
0
=0)
Identification Reference
ZAC - Aster %
difference
zz
lim
p
with the N32 node (skin interns)
1.7898 10
3
2.7142
10
3
+51.65%
zz
lim
moy
with the N32 node (skin interns)
86.55 72.27 16.50%
zz
lim
p
with the node N4 (external skin)
3.1031 10
3
3.8715
10
3
+24.76%
zz
lim
moy
with the node N4 (external skin)
114.03 128.35 +12.56%
-
with elastoplastic semi-cycle given (
0
_0)
Identification Reference
ZAC - Aster %
difference
zz
lim
p
with the N32 node (skin interns)
1.7898 10
3
1.7872
10
3
0.14%
zz
lim
moy
with the N32 node (skin interns)
86.55 89.09 +2.93%
zz
lim
p
with the node N4 (external skin)
3.1031 10
3
3.1053
10
3
+0.07%
zz
lim
moy
with the node N4 (external skin)
114.03 114.31 +0.24
%
·
T = 120°C, case of accommodation.
The results of reference come from an analytical solution given in [bib1]
-
without elastoplastic semi-cycle given (
0
=0)
Identification Reference
ZAC - Aster %
difference
zz
moy
p
with the N32 node (skin interns)
4.141 10
3
4.424 10
3
+6.83%
zz
moy
with the N32 node (skin interns)
91.82 87.52 4.68%
zz
moy
p
with the node N4 (external skin)
9.59 10
3
9.75
10
3
+1.64%
zz
moy
with the node N4 (external skin)
191.90 195.17 +1.70%
zz
moy
p
with the node N18 (surf.moyenne)
5.96 10
3
6.20
10
3
+4.06%
zz
moy
with the node N18 (surf.moyenne)
319.18 320.45 +0.39%
zz
inf
p
with the N32 node (skin interns)
3.6363 10
3
3.6574
10
3
+0.58%
zz
inf
with the N32 node (skin interns)
472.72 474.66 +0.41%
zz
inf
p
with the node N4 (external skin)
3.6328 10
3
3.6098
10
3
0.63%
zz
inf
with the node N4 (external skin)
472.72 473.97 +0.26%
zz
sup
p
with the N32 node (skin interns)
3.6363 10
3
3.6604 10
3
+0.66%
zz
sup
with the N32 node (skin interns)
472.72 473.31 +0.12%
zz
sup
p
with the node N4 (external skin)
3.6328 10
3
3.6097
10
3
0.63%
zz
sup
with the node N4 (external skin)
472.72 473.18 +0.09%
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
6/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
-
with elastoplastic semi-cycle given (
0
_0)
Identification Reference
ZAC - Aster %
difference
zz
moy
p
with the N32 node (skin interns)
4.141 10
3
4.177
10
3
+0.89%
zz
moy
with the N32 node (skin interns)
91.82 83.43 9.13%
zz
moy
p
with the node N4 (external skin)
9.59 10
3
9.51
10
3
0.87%
zz
moy
with the node N4 (external skin)
191.90 190.39 0.79%
zz
moy
p
with the node N18 (surf.moyenne)
5.959 10
3
5.963
10
3
+0.08%
zz
moy
with the node N18 (surf.moyenne)
319.18 313.5
1.78%
zz
inf
p
with the N32 node (skin interns)
3.6363 10
3
3.6574 10
3
+0.58%
zz
inf
with the N32 node (skin interns)
472.72 474.66 +0.41%
zz
inf
p
with the node N4 (external skin)
3.6328 10
3
3.6098
10
3
0.63%
zz
inf
with the node N4 (external skin)
472.72 473.97 +0.26%
zz
sup
p
with the N32 node (skin interns)
3.6363 10
3
3.6604 10
3
+0.66%
zz
sup
with the N32 node (skin interns)
472.72 473.31 +0.12%
zz
sup
p
with the node N4 (external skin)
3.6328 10
3
3.6097
10
3
0.63%
zz
sup
with the node N4 (external skin)
472.72 473.18 +0.09%
4.2 Remarks
In the case of accommodation (T=120°C), the M1 meshs, m2, M5 and M6 form an area
adapted whereas the central area (meshs m2 and m3) remains adapted.
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
7/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
Modeling 3D
Angle nets: 5°
The loading and the boundary conditions are modelized by:
DDL_IMPO: (GROUP_NO: facemoy,
DZ: 0.)
face0
DY: 0)
FACE_IMPO: (GROUP_MA: face10
DNOR: 0)
TEMP_CALCULEE: temple
where temple is the higher definite positive function for the moments t=1 and 3 [§1.3]
PRES_REP: (GROUP_MA: facepres, NEAR: 2.)
Two preliminary calculations are carried out:
·
an elastic design for the loadings min. and max. on a cycle (T
min
= 1 and T
max
= 3)
·
an optional elastoplastic calculation until the maximum loading before discharge (T
With
= 3)
5.2
Characteristics of the mesh
A number of nodes:
793
A number of meshs and type:
120 elements
HEXA20
5.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING
AXIS
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
SY
AFFE_CHAR_MECA
PRES_REP
TEMP_CALCULEE
GROUP_MA
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_CINE_LINE
MECA_STATIQUE
OPTION
SIEF_ELGA_DEPL
POST_ZAC
EVOL_ELAS
EVOL_NOLI
Z
X
y
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
8/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
·
T = 30°C, case of adaptation.
The results of reference come from an elastoplastic calculation Aster on 20 cycles.
-
without elastoplastic semi-cycle given (
0
=0)
Identification Reference
ZAC - Aster %
difference
zz
lim
p
at the point C (skin interns)
1.7898 10
3
2.7151
10
3
51.700
zz
lim
p
at the point F (external skin)
3.1031 10
3
3.8794
10
3
25.014
-
with elastoplastic semi-cycle given (
0
_0)
Identification Reference
ZAC - Aster %
difference
zz
lim
p
at the point C (skin interns)
1.7898 10
3
1.7911
10
3
0.075
zz
lim
p
at the point F (external skin)
3.1031 10
3
3.1133
10
3
0.327
·
T = 120°C, case of accommodation.
The results of reference come from an analytical solution given in [bib1]
-
without elastoplastic semi-cycle given (
0
=0)
Identification Reference
ZAC - Aster %
difference
zz
moy
p
at the point C (skin interns)
4.141 10
3
4.4393
10
3
7.203
zz
moy
at the point C (skin interns)
91.82 8.782E+01
4.345
zz
moy
p
at the point F (external skin)
9.59 10
3
9.766
10
3
1.803
zz
moy
at the point F (external skin)
191.90 1.9537E+02
1.803
zz
inf
p
at the point C (skin interns)
3.6363 10
3
3.6299
10
3
0.176
zz
inf
at the point C (skin interns)
472.72 4.7328E+02
0.117
zz
inf
p
at the point F (external skin)
3.6328 10
3
3.6401
10
3
0.202
zz
inf
at the point F (external skin)
472.72 4.7367E+02
0.200
zz
sup
p
at the point C (skin interns)
3.6363 10
3
3.632
10
3
0.119
zz
sup
at the point C (skin interns)
472.72 4.7205E+02
0.142
zz
sup
p
at the point F (external skin)
3.6328 10
3
3.6405
10
3
0.212
zz
sup
at the point F (external skin)
472.72 4.7323E+02
0.106
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
9/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
-
with elastoplastic semi-cycle given (
0
_0)
Identification Reference
ZAC - Aster %
difference
zz
moy
p
at the point C (skin interns)
4.141 10
3
4.1905
10
3
1.195
zz
moy
at the point C (skin interns)
9.182 10
+1
8.305
10
+1
9.552
zz
moy
p
at the point F (external skin)
9.59 10
3
9.5225
10
3
0.741
zz
moy
at the point F (external skin)
1.9190 10
+2
1.9031
10
+2
0.832
zz
inf
p
at the point C (skin interns)
3.6363 10
3
3.6299
10
3
0.176
zz
inf
at the point C (skin interns)
4.7272 10
+2
4.732810
+2
0.117
zz
inf
p
at the point F (external skin)
3.6328 10
3
3.64041
10
3
0.202
zz
inf
at the point F (external skin)
4.7272 10
+2
4.7367
10
+2
0.200
zz
sup
p
at the point C (skin interns)
3.6363 10
3
3.632
10
3
0.119
zz
sup
at the point C (skin interns)
4.7272 10
+2
4.720510
+2
0.142
zz
sup
p
at the point F (external skin)
3.6328 10
3
3.6405
10
3
0.212
zz
sup
at the point F (external skin)
4.7272 10
+2
4.7323
10
+2
0.106
6.2 Remarks
In the case of accommodation (T=120°C), the M1 meshs, m2, M5 and M6 form an area
adapted whereas the central area (meshs m2 and m3) remains adapted.
Code_Aster
®
Version
5.4
Titrate:
SSNA100 - Tube of Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX,
Mr. BONNAMY
Key
:
V6.01.100-A
Page:
10/10
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
7
Summary of the results
It appears at the end of this test that the results obtained are in concord with the solutions of
reference. However, in the case of the adaptation (T=30°C) projection starting from an initial state
corresponding to the preliminary calculation of an elastoplastic semi-cycle is necessary to approach
accurately solutions. Contrary, the case of accommodation (T=120°C) has already results
correctly approximate starting from an initial state no one.
One will find in [bib1] and [bib2] of other results relating to this test like incremental calculation
realized with COCAINE or numerical solutions obtained with programmed method ZAC
in the INCA code.