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Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
1/10

Organization (S): EDF/MTI/MN, DeltaCAD

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.503

SSNL503 - Elastoplastic Ruine of a bent pipe
thin

Summary:

This test consists in calculating the elastoplastic ruin of a thin bent pipe subjected to an inflection in its plan
and with a pressure interns with basic effect. It makes it possible to validate modeling finite elements TUYAU (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).
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
2/10

1
Problem of reference

1.1 Geometry
With
0.407m
1,83
y
p
0.0104m
B
X
R= 0.61m
C
D
M
Z
0.61m


1.2
Properties of material

The properties of material constituting the pipe are:

E = 193. 109 Pa
Young modulus
= 0.2642
Poisson's ratio

Constraint
Deformation
(x108 Pa)
5
Pa
Plastic p
4
2,72E+08
0.
3
3,46E+08
0.00473
3,79E+08
0.01264
2
4,04E+08
0.02836
1
4,24E+08
0.04910
5,28E+08
0.10500
0.02 0.04 0.06 0.08 0.10
= +
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 < T1
-
the pressure varies from 0 to 3.45 106 Pa
-
The force (basic effect) at the point D varies from 0 to 4.0414 105 NR
-
the moment is null
·
Stage b: T1 T < t2
-
the pressure is constant and is worth 3.45 106 Pa
-
the force (basic effect) at the point D is constant and is worth 4.0414 105 NR
-
the moment varies from 0 to 2.534 105 N.m

1.4 Conditions
initial

Without object.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
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Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
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2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solution was obtained numerically with ABAQUS 5.5. The grid 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 = 253.4 103 N.m for a rotation around Z of 0.22 rad to 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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
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Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
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3 Modeling
With

3.1
Characteristics of modeling

Modeling PIPE (SEG3)
y, v
y
With
Cutting for numerical integration
- A Number of layers: 7
- A Number of sectors: 18
12
Boundary conditions:
Not a:
B
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0

- DDL of Coque: UIm = VIm = Wim = 0 (m=2,3)
6
D
X, U
C
UOm = VOm = WOm = 0 (m=2,3)
Z, v
WI1 = WO1 = WO = 0
4

Not D:
Z
X
- DDL of Coque: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0


3.2
Characteristics of the grid

A number of nodes: 45
A number of meshs and type: 22 SEG3

3.3 Functionalities
tested
Commands Key word
factor Word-key
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
PRES
STAT_NON_LINE COMP_INCR
“VMIS_ISOT_LINE”

TUYAU_NCOU, TUYAU_NSEC
PILOTAGE
TYPE=' DDL_IMPO'
TEST_RESU RESU
PARA=' ETA_PILOTAGE'
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

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Version
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Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
5/10

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

Obstruction memory: 256 megabytes
Time CPU To use: 221.44 seconds
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
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5 Modeling
B

5.1
Characteristics of modeling

Modeling TUYAU_6M (SEG3)
y, v
y
With
Cutting for numerical integration
- A Number of layers: 7
- A Number of sectors: 18
12
Boundary conditions:
Not a:
B
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0

- DDL of Coque: UIm = VIm = Wim = 0 (m=2,6)
6
D
X, U
C
UOm = VOm = WOm = 0 (m=2,6)
Z, v
WI1 = WO1 = WO = 0
4

Not D:
Z
X
- DDL of Coque: UIm = VIm = Wim = 0 (m=2,6)
UOm = VOm = WOm = 0 (m=2,6)
WI1 = WO1 = WO = 0


5.2
Characteristics of the grid

A number of nodes: 45
A number of meshs and type: 22 SEG3

5.3 Functionalities
tested

Commands 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
PRES
STAT_NON_LINE COMP_INCR
“VMIS_ISOT_LINE”

TUYAU_NCOU, TUYAU_NSEC
PILOTAGE
TYPE=' DDL_IMPO'
TEST_RESU RESU PARA=' ETA_PILOTAGE'
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
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Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
7/10

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

Obstruction memory: 256 megabytes
Time CPU To use: 585.95 seconds
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
8/10

7 Modeling
C

7.1
Characteristics of modeling

Modeling PIPE (SEG4)
y, v
y
With
Cutting for numerical integration
- A Number of layers: 7
- A Number of sectors: 18
12
Boundary conditions:
Not a:
B
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0

- DDL of Coque: UIm = VIm = Wim = 0 (m=2,3)
6
D
X, U
C
UOm = VOm = WOm = 0 (m=2,3)
Z, v
WI1 = WO1 = WO = 0
4

Not D:
Z
X
- DDL of Coque: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0


7.2
Characteristics of the grid

A number of nodes: 67
A number of meshs and type: 22 SEG4

7.3 Functionalities
tested

Commands 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 “VMIS_ISOT_LINE”

TUYAU_NCOU, TUYAU_NSEC
PILOTAGE
TYPE=' DDL_IMPO'
TEST_RESU RESU PARA=' ETA_PILOTAGE'
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
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Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
9/10

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

Obstruction memory: 256 megabytes
Time CPU To use: 427.64 seconds
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNL503 - Elastoplastic Ruine of a thin bent pipe

Date:
29/10/01
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.02.503-A Page:
10/10

9
Summary of the results

Rotation at the loose lead according to the moment
3,5E+05
Moment (N.m)
3,0E+05
2,5E+05
2,0E+05
TUYAU (SEG4
TUYAU_6M (SEG3)
1,5E+05
TUYAU (SEG3)
1,0E+05
5,0E+04
Rotation (Rad)
0,0E+00
0,00
0,05
0,10
0,15
0,20
0,25
0,30

The results obtained for modeling TUYAU (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 TUYAU. The modeling of reference uses a decomposition in
Fourier series until command 6.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/01/010/A

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