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Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
1/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
Organization (S):
EDF/MTI/MN, DeltaCAD
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.503
SSNL503 - Elastoplastic ruin of a bent pipe
thin
Summary:
This test consists in calculating the elastoplastic ruin of a thin bent pipe subjected to a bending in its plan
and with a pressure interns with basic effect. It makes it possible to validate modeling finite elements PIPE (SEG3
and SEG4) and TUYAU_6M (SEG3) in the quasi-static field in non-linear material.
The results obtained are compared with a numerical reference solution obtained with the computer code
(ABAQUS).
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
2/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
1,83
0.61m
M
0.407m
0.0104m
R= 0.61m
p
With
B
C
D
Z
X
y
1.2
Properties of material
The properties of material constituting the pipe are:
E
= 193. 10
9
AP
Young modulus
= 0.2642
Poisson's ratio
Stress
AP
Deformation
Plastic
p
2,72E+08
0.
3,46E+08
0.00473
3,79E+08
0.01264
4,04E+08
0.02836
4,24E+08
0.04910
5,28E+08
0.10500
5
4
3
2
1
0.02 0.04 0.06 0.08 0.10
(x10
8
AP)
=
E
+
p
1.3
Boundary conditions and loadings
-
C.L. : - Embedded Section A
- Rigid Section D (no deformation of the section)
-
Loading: one seeks the successive states of balance under the following loadings:
·
Stage a: 0 T < T
1
-
the pressure varies from 0 to 3.45 10
6
AP
-
The force (basic effect) at the point D varies from 0 to 4.0414 10
5
NR
-
the moment is null
·
Stage b: T
1
T < T
2
-
the pressure is constant and is worth 3.45 10
6
AP
-
the force (basic effect) at the point D is constant and is worth 4.0414 10
5
NR
-
the moment varies from 0 to 2.534 10
5
N.m
1.4 Conditions
initial
Without object.
Code_Aster
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Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
3/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution was obtained numerically with ABAQUS 5.5. The mesh used is
constituted of elements ELBOW31 to 2 nodes with 6 modes of Fourier. The discretization used is
following:
·
Part AB: 24 elements,
·
Part BC: 8 elements,
·
Part CD: 12 elements.
Integration in the section is as follows:
·
7 layers in the thickness,
·
18 sectors in the circumferential direction.
2.2
Results of reference
Moment limits = 253.4 10
3
N.m for a rotation around Z of 0.22 rad at point D.
2.3
Uncertainties on the solution
< 2%
2.4 References
bibliographical
[1]
ABAQUS/Standard Version 5.5: Example Problems Manual Volume 2, p 4.2.2-1.
Code_Aster
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Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
4/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
4
12
6
Modeling PIPE (SEG3)
D
C
B
With
X, U
y, v
X
y
Z, v
Z
Cutting for numerical integration
- A Number of layers: 7
- A Number of sectors: 18
Boundary conditions:
Not a:
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ
= 0
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
Not D:
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
3.2
Characteristics of the mesh
A number of nodes: 45
A number of meshs and type: 22 SEG3
3.3 Functionalities
tested
Controls Key word
factor Key word
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI, SY
AFFE_MODELE AFFE
MODELISATION=' TUYAU'
AFFE_CARA_ELEM ORIENTATION
CARA=' GENE_TUYAU'
AFFE_CHAR_MECA FORCE_TUYAU
NEAR
STAT_NON_LINE COMP_INCR
PILOTING
“VMIS_ISOT_LINE”
TUYAU_NCOU, TUYAU_NSEC
TYPE=' DDL_IMPO'
TEST_RESU RESU
PARA=' ETA_PILOTAGE'
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
5/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
DRZ
Identification Moments Reference
Aster %
difference
0.32
ETA_PILOTAGE
18.1.0 1.1699 16.99
0.34
ETA_PILOTAGE
18.5 1.0
1.1787
17.87
0.36
ETA_PILOTAGE
19.1.0 1.1869 18.69
0.38
ETA_PILOTAGE
19.5 1.0
1.1946
19.46
0.40
ETA_PILOTAGE
20.1.0 1.2020 20.20
4.2 Remarks
At the time of stage A, one gradually imposes the internal pressure and the effort due to the basic effect on
the interval of time 0<t<10. Then (stage B), one gradually imposes the bending moment on
the interval of time 10<t<20. To solve, one forces at the time of the stage B an increase in
rotation DRZ of 0.4 rad to the solution obtained at the time of stage A.
4.3 Parameters
of execution
Version:
NEW 5.04.18
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 256 megabytes
Time CPU To use: 221.44 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
6/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
4
12
6
Modeling TUYAU_6M (SEG3)
D
C
B
With
X, U
y, v
X
y
Z, v
Z
Cutting for numerical integration
- A Number of layers: 7
- A Number of sectors: 18
Boundary conditions:
Not a:
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ
= 0
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,6)
UOm = VOm = WOm = 0 (m=2,6)
WI1 = WO1 = WO = 0
Not D:
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,6)
UOm = VOm = WOm = 0 (m=2,6)
WI1 = WO1 = WO = 0
5.2
Characteristics of the mesh
A number of nodes: 45
A number of meshs and type: 22 SEG3
5.3 Functionalities
tested
Controls Key word
factor
Key word
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI, SY
AFFE_MODELE AFFE
MODELISATION=' TUYAU_6M'
AFFE_CARA_ELEM ORIENTATION
CARA=' GENE_TUYAU'
AFFE_CHAR_MECA FORCE_TUYAU
NEAR
STAT_NON_LINE COMP_INCR
PILOTING
“VMIS_ISOT_LINE”
TUYAU_NCOU, TUYAU_NSEC
TYPE=' DDL_IMPO'
TEST_RESU RESU PARA=' ETA_PILOTAGE'
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
7/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
6
Results of modeling B
6.1 Values
tested
DRZ
Identification Moments Reference
Aster %
difference
0.32
ETA_PILOTAGE
18.1.0 1.0296 2.96
0.34
ETA_PILOTAGE
18.5 1.0
1.0379
3.79
0.36
ETA_PILOTAGE
19.1.0 1.0456 4.56
0.38
ETA_PILOTAGE
19.5 1.0
1.0528
5.28
0.40
ETA_PILOTAGE
20.1.0 1.0597 5.97
6.2 Remarks
At the time of stage A, one gradually imposes the internal pressure and the effort due to the basic effect on
the interval of time 0<t<10. Then (stage B), one gradually imposes the bending moment on
the interval of time 10<t<20. To solve, one forces at the time of the stage B an increase in
rotation DRZ of 0.4 rad to the solution obtained at the time of stage A.
6.3 Parameters
of execution
Version:
NEW 5.04.18
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 256 megabytes
Time CPU To use: 585.95 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
8/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
7 Modeling
C
7.1
Characteristics of modeling
4
12
6
Modeling PIPE (SEG4)
D
C
B
With
X, U
y, v
X
y
Z, v
Z
Cutting for numerical integration
- A Number of layers: 7
- A Number of sectors: 18
Boundary conditions:
Not a:
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ
= 0
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
Not D:
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
7.2
Characteristics of the mesh
A number of nodes: 67
A number of meshs and type: 22 SEG4
7.3 Functionalities
tested
Controls Key word
factor
Key word
CREA_MAILLAGE MODI_MAILLE
OPTION:“SEG3_4”
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI, SY
AFFE_MODELE AFFE
MODELISATION=' TUYAU'
AFFE_CARA_ELEM ORIENTATION CARA=' GENE_TUYAU'
AFFE_CHAR_MECA FORCE_TUYAU NEAR
STAT_NON_LINE COMP_INCR
PILOTING
“VMIS_ISOT_LINE”
TUYAU_NCOU, TUYAU_NSEC
TYPE=' DDL_IMPO'
TEST_RESU RESU PARA=' ETA_PILOTAGE'
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
9/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
8
Results of modeling C
8.1 Values
tested
DRZ
Identification Moments Reference
Aster %
difference
0.32
ETA_PILOTAGE
18.1.0 1.1681 16.81
0.34
ETA_PILOTAGE
18.5 1.0
1.1678
16.78
0.36
ETA_PILOTAGE
19.1.0 1.1758 17.58
0.38
ETA_PILOTAGE
19.5 1.0
1.1834
18.34
0.40
ETA_PILOTAGE
20.1.0 1.1905 19.05
8.2 Remarks
At the time of stage A, one gradually imposes the internal pressure and the effort due to the basic effect on
the interval of time 0<t<10. Then (stage B), one gradually imposes the bending moment on
the interval of time 10<t<20. To solve, one forces at the time of the stage B an increase in
rotation DRZ of 0.4 rad to the solution obtained at the time of stage A.
8.3 Parameters
of execution
Version:
NEW 5.04.20
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 256 megabytes
Time CPU To use: 427.64 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNL503 - Elastoplastic ruin of a thin bent pipe
Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V6.02.503-A
Page:
10/10
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A
9
Summary of the results
Rotation at the loose lead according to the moment
0,0E+00
5,0E+04
1,0E+05
1,5E+05
2,0E+05
2,5E+05
3,0E+05
3,5E+05
0,00
0,05
0,10
0,15
0,20
0,25
0,30
Rotation (Rad)
Moment (N.m)
PIPE (SEG4
TUYAU_6M (SEG3)
PIPE (SEG3)
The results obtained for modeling PIPE (SEG3 and SEG4) are rather far away from the solution
of reference, (error of 20%). On the other hand, they are better for modeling TUYAU_6M (error
from 6%).
The deformation of the transverse section in the elbow is represented better by modeling
TUYAU_6M, adapted better to the modeling of the thin pipes. In this modeling, them
displacements of the average surface of the pipe are broken up into Fourier series until command 6,
instead of 3 for modeling PIPE. The modeling of reference uses a decomposition in
Fourier series until command 6.