Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 1/14
Organization (S): EDF/IMA/MN, SAMTECH SA
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
V6.01.301 document
SSNA301 - Fond of pressurized thick tank
Summary:
This test consists in analyzing until the ruin, the spherotoric bottom of a thick tank subjected to a pressure
intern by taking of account the elastoplastic behavior of material and the nonlinear behavior of
the structure.
Modeling is made with axisymmetric elements of type MEAXQU8.
One will test the taking into account here or not nongeometrical linearities and the use of one or two
assumptions material.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 2/14
1
Problem of reference
1.1 Geometry
With
L = 50 ''
B
1.2
Material properties
Elastoplastic material without work hardening
E = 3.E+07 MPa
= 0.3
y = 3.E+04 MPa
1.3
Boundary conditions and loadings
Not a: ux =0
Not b: uy =0.
The setting charges some (= pressure interns) following is applied:
p = 1.737 p0 (vicinity of the ruin) with p0 = 658.257 MPa (fine of the linear mode)
The load p is applied in 50 identical increments.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 3/14
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation finite element with the SAMCEF software Version 7.0 (Mecanl).
2.2
Reference solution
Variation of the tensions on the skins along the meridian section for an internal pressure
p0 [bib2]
Variation of the tensions on the skins along the meridian section in the vicinity of the ruin
for a pressure pmax interns [bib2]
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 4/14
Variation of the azimuth constraint on the higher skin along the meridian section
in the vicinity of the ruin for a pressure pmax interns. Geometrical linear calculation.
30
p
20
10
0
0,0
, 9
, 9
, 8
, 3
, 7
5,0
- 10
12
25
38
51
63
10
- 20
- 30
- 40
Meridian length
Variation of the azimuth constraint on the lower skin along the meridian section
in the vicinity of the ruin for a pressure pmax interns. Geometrical linear calculation.
30
p
20
10
0
0
8
0,
,
7
,
4
,
1
,
3
,
6
12
25
38
49
60
1,
10
- 10
- 20
Meridian length
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 5/14
Variation of the azimuth constraint on the skin higher along the meridian section than
vicinity of the ruin for a pressure interns pmax. Geometrical nonlinear calculation.
30
p
20
10
0
0
, 9
, 9
, 8
, 3
, 7
0,
12
25
38
51
63
4,9
- 10
10
- 20
- 30 node 1
node 73
node 137
Meridian length
Variation of the azimuth constraint on the lower skin along the meridian section
in the vicinity of the ruin for a pressure pmax interns. Geometrical nonlinear calculation.
30
p
20
10
0
0
8
0,
, 7
, 4
, 1
, 3
, 6
12
25
38
49
60
1,
10
- 10
- 20
node 1
node 27
node 57
node 87
node 137
Meridian length
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 6/14
Z
Meridian length
higher skin
Node
Position 1
There are 68 elements
(with nodes mediums)
and 137 nodes along
skin
skin
lower
Node
Position 137
Discretization used for the reference solution. Definition of the axes
Geometrical nonlinear calculation: pressure = pmax
Skin Length
meridian
Position node
(inch)
p
0.0 1
26.223
Higher 46.298
73 26.688
137.9 137
24.103
0.0 1
25.231
16.491 27
27.909
Lower 35.518
57 12.711
52.707 87
8.1652
134.76 137
25.103
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 7/14
Geometrical linear calculation: pressure = pmax
Skin Length
meridian
Position node
(inch)
p
0.0 1
26.2
Higher 45.1
71 30.7
138 137
24.0
0.0 1
25.231
22.833
37
29.899
Lower 32.981
53 16.127
52.707
87
13.756
134.76 137
25.008
Field of displacement (not A, lower skin)
Calculation… geometrical Longueur meridian Position
Pressure Displacement
UZ
(inch)
node
(inch)
Linear 0.0
1
0.5
pmax
0.100945
0.0
1
pmax
0.370468
Nonlinear
0.0
1
0.5 pmax
0.0990524
0.0
1
pmax
0.244347
2.3
Uncertainty on the solution
Uncertainty lower than 2% (linear mode), lower than 5% (elastoplastic mode).
2.4 References
bibliographical
[1]
LARSEN, P.K., POPOV, E.P., Elastic-plastic analysis off thick-walled presses vessels with
sharp discontinuities, Trans. ASME Applied Mechanics, p 1016-1019, 1971
[2]
NYSSEN, C., Modélisation by finite elements of the nonlinear behavior of structures
aerospace, thesis of doctorate, Université of Liege, 1979
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 8/14
3 Modeling
With
3.1
Characteristics of modeling A
Nonlinear material + linear geometrical
3.2
Characteristics of the grid
A number of nodes:
2197
A number of meshs and types: 544 MEAXQU8 (diagram of integration 3 X 3) + 68 SEG3 (68 meshs on
the length (30 on the part with a radius of 100 '', 20 on the part with
a radius of 20 '' and 18 on the right part) and 8 on the thickness)
3.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU ECRO_LINE D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE COMP_INCR RELATION VMIS_ISOT_LINE
[U4.32.01]
DEFORMATION
PETIT
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 9/14
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster
% difference
SIZZ/p Peau sup Long. Merid=0. p=pmax
26.2
26.218
0.071
SIZZ/p Peau sup Long. Merid=45.1 p=pmax
30.7
30.531
0.553
SIZZ/p Peau sup Long. Merid=138 p=pmax
24.0
24.011
0.553
SIZZ/p Peau inf Long. Merid=0. p=pmax
25.231
25.229
0.553
SIZZ/p Peau inf Long. Merid=22.833
29.899 29.957 0.553
p=pmax
SIZZ/p Peau inf Long. Merid=32.981
16.127 16.294 0.553
p=pmax
SIZZ/p Peau inf Long. Merid=52.707
13.756 13.699 0.553
p=pmax
SIZZ/p Peau inf Long. Merid=134.76
25.008 25.012 0.553
p=pmax
DY node 2313 with p=0.5 pmax
0.100945
0.100946
0.002
DY node 2313 with pmax
0.370468
0.370470
0.001
4.2 Parameters
of execution
Version: 3.09
Machine: CRAY
System:
Obstruction memory:
16 Megawords
Time CPU To use:
360.52 seconds
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 10/14
5 Modeling
B
5.1
Characteristics of modeling B
Nonlinear material + nonlinear geometrical
5.2
Characteristics of the grid
A number of nodes:
2197
A number of meshs and types: 544 MEAXQU8 (diagram of integration 3 X 3) + 68 SEG3 (68 meshs on
the length (30 on the part with a radius of 100 '', 20 on the part with
a radius of 20 '' and 18 on the right part) and 8 on the thickness)
5.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU ECRO_LINE D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE COMP_INCR RELATION VMIS_ISOT_LINE
[U4.32.01]
DEFORMATION
PETIT_REAC
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 11/14
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster
% difference
SIZZ/p Peau sup Long. Merid=0. p=pmax
26.223
26.299
0.025
SIZZ/p Peau sup Long. Merid=45.298
26.688 27.156
1.756
p=pmax
SIZZ/p Peau sup Long. Merid=137.9 p=pmax
24.103
24.018
0.352
SIZZ/p Peau inf Long. Merid=0. p=pmax
25.231
25.236
0.021
SIZZ/p Peau inf Long. Merid=16.491
27.909 28.086 0.638
p=pmax
SIZZ/p Peau inf Long. Merid=35.518
12.711 13.095
3.026
p=pmax
SIZZ/p Peau inf Long. Merid=52.707
8.1652 8.426
3.196
p=pmax
SIZZ/p Peau inf Long. Merid=134.76
25.103 25.018 0.337
p=pmax
DY node 2313 with p=0.5 pmax
0.099052
0.099191
0.141
DY node 2313 with pmax
0.244347
0.246979
1.077
6.2 Parameters
of execution
Version: 3.09
Machine: CRAY
System:
Obstruction memory:
16 megawords
Time CPU To use:
456.41secondes
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 12/14
7 Modeling
C
7.1
Characteristics of modeling C
All the meshs have a nonlinear behavior material, except the 8x5 meshs of the part
lower of the structure (this part does not plasticize) which has a linear behavior material.
A geometrical linear analysis is carried out.
7.2
Characteristics of the grid
A number of nodes:
2197
A number of meshs and types: 544 MEAXQU8 (diagram of integration 3 X 3) + 68 SEG3 (68 meshs on
the length (30 on the part with a radius of 100 '', 20 on the part with
a radius of 20 '' and 18 on the right part) and 8 on the thickness)
7.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU ECRO_LINE D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE COMP_INCR RELATION VMIS_ISOT_LINE
[U4.32.01]
DEFORMATION
PETIT
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 13/14
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster
% difference
SIZZ/p Peau sup Long. Merid=0. p=pmax
26.2
26.218
0.071
SIZZ/p Peau sup Long. Merid=45.1 p=pmax
30.7
30.531
0.553
SIZZ/p Peau sup Long. Merid=138 p=pmax
24.0
24.011
0.553
SIZZ/p Peau inf Long. Merid=0. p=pmax
25.231
25.229
0.553
SIZZ/p Peau inf Long. Merid=22.833
29.899 29.957 0.553
p=pmax
SIZZ/p Peau inf Long. Merid=32.981
16.127 16.294 0.553
p=pmax
SIZZ/p Peau inf Long. Merid=52.707
13.756 13.699 0.553
p=pmax
SIZZ/p Peau inf Long. Merid=134.76
25.008 25.012 0.553
p=pmax
DY node 2313 with p=0.5 pmax
0.100945
0.100946
0.002
DY node 2313 with pmax
0.370468
0.370470
0.001
8.2 Parameters
of execution
Version: 3.09
Machine: CRAY
System:
Obstruction memory: 16 megawords
Time CPU To use:
196.02 seconds
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSNA301 Fond of pressurized thick tank
Date:
16/11/98
Author (S):
J.M. PROIX, L. LAMMERANT, J.P. DELSEMME
Key: V6.01.301-A Page: 14/14
9
Summary of the results
The results provided by Aster concerning modelings A and C are close to the reference
(variation < 0.6%). Moreover, one finds well the same results for modelings A and C; what
is normal because the lower part remains elastic.
For modeling B, variations of results between Code_Aster and reference (the SAMCEF software)
3.3% reach and come owing to the fact that nonthe geometrical linearities are treated in manner
different in Code_Aster (by command “PETIT_REAC”) and in the SAMCEF software.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/01/010/A
Outline document