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Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
1/10
Organization (S): EDF/AMA, AUSY France
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
V6.01.100 document
SSNA100 - Tube de Bree: Method Zarka-Rack
(ZAC)
Summary:
This test of nonlinear quasi-static mechanics consists in modelling 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 thus the simplified method Zarka-Casier (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 command 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 modelled by axisymmetric elements 2D (QUAD8),
· in modeling b: the cylinder is modelled in 3D (meshs HEXA20).
The results obtained by Code_Aster are very close to the reference solution.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
2/10
1
Problem of reference
1.1 Geometry
Z
D
+ E
E
a=0.2
p
B
With
- E
C
F
R
R=10.
d=0.12
1.2
Material properties
E = 200.000 MPa
= 0.3
= 1.e-4 °C1
Tréf = 0.
Elastoplastic relation between behavior and criterion of Von Mises and kinematic work hardening
linear:
T
E =
.
18181 MPa
y =
.
200 MPa
1.3
Boundary conditions and loadings
On AB: uz = 0
Loading:
· constant uniform pressure p = 2. MPa on CD.
· linear temperature in the thickness and varying according to time:
(
2 R - R)
T
(R) = -
(T) with (T) = (
) F (T)
D
E
E
2
E
T/2
T
0
1
3
5
7
9
11
13…
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
Elastoplastic calculation carried out with 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
p
moy
p
p
p
and
in the case of adaptation (
,
,
,
,
,
in the case
zz
zz
zz
zz
zz
zz
lim
zzlim
moy
moy
inf
inf
zz
sup
sup
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 engines. Laboratory of mechanics of the solids. Polytechnic school,
Palaiseau, June 1985.
[2]
S. TAHERI: “Method ZAC”. Note EDF/DER HI-71/6139 of 14 Juin 1989.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
It is about an axisymmetric modeling.
Z
N17
N33
N2
M1
M2
M3
M4
M5
M6
N26
N3
N18
N32
N4
N19
R
6 elements
The loading and the boundary conditions are modelled by:
DDL_IMPO: (NOEUD: (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, PRES: 2.)
Two preliminary calculations are carried out:
· an elastic design for the loadings min. and max. on a cycle (tmin = 1 and T
= 3)
max
· an optional elastoplastic calculation until the maximum loading before discharge (your = 3)
3.2
Characteristics of the grid
A number of nodes:
33
A number of meshs and type:
6 elements QUAD8
3.3 Functionalities
tested
Commands
AFFE_MODELE
AFFE
MODELISATION
AXIS
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
SY
AFFE_CHAR_MECA
PRES_REP
GROUP_MA
TEMP_CALCULEE
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_CINE_LINE
MECA_STATIQUE
OPTION
SIEF_ELGA_DEPL
POST_ZAC
EVOL_ELAS
EVOL_NOLI
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
5/10
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
p
with the N32 node (skin interns)
zz
1.7898 103 2.7142
103
+51.65%
lim
moy
with the N32 node (skin interns)
86.55 72.27 16.50%
zzlim
p
with the node N4 (external skin)
zz
3.1031 103 3.8715
103
+24.76%
lim
moy with the node N4 (external skin)
114.03 128.35 +12.56%
zzlim
-
with elastoplastic semi-cycle given (0_0)
Identification Reference
ZAC - Aster %
difference
p
with the N32 node (skin interns)
zz
1.7898 103 1.7872
103
0.14%
lim
moy
with the N32 node (skin interns)
86.55 89.09 +2.93%
zzlim
p with the node N4 (external skin)
zz
3.1031 103 3.1053
103
+0.07%
lim
moy with the node N4 (external skin)
114.03 114.31 +0.24
%
zzlim
· 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
p with the N32 node (skin interns)
zz
4.141 103
4.424 103
+6.83%
moy
with the N32 node (skin interns)
zzmoy
91.82 87.52 4.68%
p with the node N4 (external skin)
zz
9.59 103 9.75
103
+1.64%
moy
with the node N4 (external skin)
zzmoy
191.90 195.17 +1.70%
p with the node N18 (surf.moyenne)
zz
5.96 103 6.20
103
+4.06%
moy
with the node N18 (surf.moyenne)
zzmoy
319.18 320.45 +0.39%
p with the N32 node (skin interns)
zz
3.6363 103 3.6574
103
+0.58%
inf
with the N32 node (skin interns)
zzinf
472.72 474.66 +0.41%
p with the node N4 (external skin)
zz
3.6328 103 3.6098
103
0.63%
inf
with the node N4 (external skin)
zzinf
472.72 473.97 +0.26%
p with the N32 node (skin interns)
zz
3.6363 103
3.6604 103
+0.66%
sup
with the N32 node (skin interns)
zzsup
472.72 473.31 +0.12%
p with the node N4 (external skin)
zz
3.6328 103 3.6097
103
0.63%
sup
with the node N4 (external skin)
zzsup
472.72 473.18 +0.09%
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
6/10
-
with elastoplastic semi-cycle given (0_0)
Identification Reference
ZAC - Aster %
difference
p with the N32 node (skin interns)
zz
4.141 103 4.177
103
+0.89%
moy
with the N32 node (skin interns)
zzmoy
91.82 83.43 9.13%
p with the node N4 (external skin)
zz
9.59 103 9.51
103
0.87%
moy
with the node N4 (external skin)
zzmoy
191.90 190.39 0.79%
p with the node N18 (surf.moyenne)
zz
5.959 103 5.963
103
+0.08%
moy
with the node N18 (surf.moyenne)
zzmoy
319.18 313.5
1.78%
p with the N32 node (skin interns)
zz
3.6363 103
3.6574 103
+0.58%
inf
with the N32 node (skin interns)
zzinf
472.72 474.66 +0.41%
p
with the node N4 (external skin)
zz
3.6328 103 3.6098
103
0.63%
inf
with the node N4 (external skin)
zzinf
472.72 473.97 +0.26%
p with the N32 node (skin interns)
zz
3.6363 103
3.6604 103
+0.66%
sup
with the N32 node (skin interns)
zzsup
472.72 473.31 +0.12%
p with the node N4 (external skin)
zz
3.6328 103 3.6097
103
0.63%
sup
with the node N4 (external skin)
zzsup
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 a zone
adapted whereas the central zone (meshs m2 and m3) remains adapted.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
7/10
5 Modeling
B
5.1
Characteristics of modeling
Modeling 3D
Angle nets: 5°
Z
y
X
The loading and the boundary conditions are modelled 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, PRES: 2.)
Two preliminary calculations are carried out:
· an elastic design for the loadings min. and max. on a cycle (tmin = 1 and T
= 3)
max
· an optional elastoplastic calculation until the maximum loading before discharge (your = 3)
5.2
Characteristics of the grid
A number of nodes:
793
A number of meshs and type:
120 elements HEXA20
5.3 Functionalities
tested
Commands
AFFE_MODELE
AFFE
MODELISATION
AXIS
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
SY
AFFE_CHAR_MECA
PRES_REP
GROUP_MA
TEMP_CALCULEE
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_CINE_LINE
MECA_STATIQUE
OPTION
SIEF_ELGA_DEPL
POST_ZAC
EVOL_ELAS
EVOL_NOLI
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
8/10
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
p
at the point C (skin interns)
zz
1.7898 103 2.7151
103
51.700
lim
p
at the point F (external skin)
zz
3.1031 103 3.8794
103
25.014
lim
-
with elastoplastic semi-cycle given (0_0)
Identification Reference
ZAC - Aster %
difference
p
at the point C (skin interns)
zz
1.7898 103 1.7911
103
0.075
lim
p at the point F (external skin)
zz
3.1031 103 3.1133
103
0.327
lim
· 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
p at the point C (skin interns)
zz
4.141 103 4.4393
103
7.203
moy
at the point C (skin interns)
zzmoy
91.82 8.782E+01
4.345
p at the point F (external skin)
zz
9.59 103 9.766
103
1.803
moy
at the point F (external skin)
zzmoy
191.90 1.9537E+02
1.803
p at the point C (skin interns)
zz
3.6363 103 3.6299
103
0.176
inf
at the point C (skin interns)
zzinf
472.72 4.7328E+02
0.117
p at the point F (external skin)
zz
3.6328 103 3.6401
103
0.202
inf
at the point F (external skin)
zzinf
472.72 4.7367E+02
0.200
p at the point C (skin interns)
zz
3.6363 103 3.632
103
0.119
sup
at the point C (skin interns)
zzsup
472.72 4.7205E+02
0.142
p at the point F (external skin)
zz
3.6328 103 3.6405
103
0.212
sup
at the point F (external skin)
zzsup
472.72 4.7323E+02
0.106
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
9/10
-
with elastoplastic semi-cycle given (0_0)
Identification Reference
ZAC - Aster %
difference
p at the point C (skin interns)
zz
4.141 103 4.1905
103
1.195
moy
at the point C (skin interns)
zzmoy
9.182 10+1 8.305
10+1
9.552
p at the point F (external skin)
zz
9.59 103 9.5225
103
0.741
moy
at the point F (external skin)
zzmoy
1.9190 10+2 1.9031
10+2
0.832
p
at the point C (skin interns)
zz
3.6363 103 3.6299
103
0.176
inf
at the point C (skin interns)
zzinf
4.7272 10+2 4.732810+2
0.117
p
at the point F (external skin)
zz
3.6328 103 3.64041
103
0.202
inf
at the point F (external skin)
zzinf
4.7272 10+2 4.7367
10+2
0.200
p at the point C (skin interns)
zz
3.6363 103 3.632
103
0.119
sup
at the point C (skin interns)
zzsup
4.7272 10+2 4.720510+2
0.142
p at the point F (external skin)
zz
3.6328 103 3.6405
103
0.212
sup
at the point F (external skin)
zzsup
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 a zone
adapted whereas the central zone (meshs m2 and m3) remains adapted.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Code_Aster ®
Version
5.4
Titrate:
SSNA100 - Tube de Bree: Zarka method - Rack (ZAC)
Date:
13/09/02
Author (S):
S. TAHERI, J. Mr. PROIX, Key Mr. BONNAMY
:
V6.01.100-A Page:
10/10
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 the numerical COCAINE or solutions obtained with programmed method ZAC
in the INCA code.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
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