Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
1/14

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

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.101

SSLL101 - Tuyautery: Problem of HOVGAARD

Summary:

It is about a linear elastic test, in statics, of a noncoplanar three-dimensional piping comprising
elbows. There is a test in dynamics of same structure (SDLX02) [V2.05.002].

One tests elements POU_D_T, POU_C_T, TUYAU (SEG3 and SEG4) and TUYAU_6M (SEG3) by the intermediary
of five modelings, each elbow is represented by:

·
20 elements POU_D_T in modeling A,
·
2 elements POU_C_T in modeling B,
·
28 elements TUYAU (SEG3) in modeling C,
·
28 elements TUYAU_6M (SEG3) in modeling D,
·
28 elements TUYAU (SEG4) in modeling E.

The loadings are:

·
gravity,
·
thermal dilation,
·
nodal forces.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
2/14

1
Problem of reference

1.1 Geometry

Geometry, as well as the points of modeling are represented on the following figure:

0.
With
­ 1.828
­ 0.922
2.75
Z
0.922
B
=
­ 0.922
=
0.
4 5
=
3
6
=
7
=
With
8
9
10
B
3.69
11
2
12
y
13
=
14
=
=
15
=
1.96
=
X
1


lengths given in meters

·
diameter external of the pipe:
0.185 m
·
thickness of the pipe:
6.12 mm
·
radius of curvature of the elbows:
0.922 m
·
piping full of water


1.2
Material properties

E = 1.658 E+11 Pa

= 0.3

= 13404.10 kg/m3

= 0.1288 E4/C°

1.3
Boundary conditions and loadings

·
Items 1 and 15 embedded,
·
Loading:
1) Gravity according to ­ Z,
2) Uniform rise in temperature of 472.22 C°,
3) Forces
nodal.

Nodes
2
3
4 - 10
5 - 9
6 - 7 - 8
11
12 - 13
14
Fz (NR)
­
­
­ 327.654
­
­ 102.5145 ­ 222.687
­
­ 176.580
624.897 788.724
214.839
117.720
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
3/14

2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solutions adopted to check Code_Aster modelings are as follows:

· for modelings POUTRE: comparison with the codes: POUX, ADL and TITUS-T [bib1],
using a modeling of the beam type,
· for modelings TUYAUX: comparison with code ABAQUS, using one
modeling of the pipe type. The number of mode of Fourier (M) used during calculation of
reference is identical to that used during calculations with Code_Aster.

2.2
Results of reference

Case of
Displacement
Modeling Beam
Modeling
Modeling
Loading
at item 3
(LICE, ADL, TITUS)
Pipe: M=3
Pipe: M=6
(ABAQUS)
(ABAQUS)
Actual weight
DX ­ 0.1658E3
­ 0.16517E3
­ 0.16512E3
DY ­ 0.2040E4 ­ 0.13870E4
­ 0.13946E4
DZ ­ 0.8010E5 ­ 0.80376E5
­ 0.80369E5






DX ­ 0.1651E3
­ 0.16445E3
­ 0.16441E3
Nodal force
DY ­ 0.2080E4 ­ 0.14245E4
­ 0.14320E4
DZ ­ 0.9516E5 ­ 0.10047E4
­ 0.10047E4






DX ­ 6.1418E3
­ 6.3277E3
­ 6.3236E3
Dilation
DY ­ 13.090E3
­ 13.092E3 ­ 13.093E3
DZ 16.799E3
16.798E3 16.798E3

2.3
Uncertainty on the solution

2%

2.4 References
bibliographical

[1]
Mr. W. KELLOG Co. Design off Piping Systems. New York, 1956 - Problem n°5.9

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
4/14

3 Modeling
With

3.1
Characteristics of modeling

The curved elements are modelled by right elements.

A curved half element is modelled by 20 right elements.

2.75
=
=
N400
=
N500 N600
=
N300
N700
=
With
N800
N900
N1000
B
3.69
N1100
N200
N1200
y
N1300
=
N1400
=
=
N1500
=
1.96
=
X
N100


Lengths given in meters

3.2
Characteristics of the grid

A number of nodes: 93
A number of meshs and type: 92 POU_D_T

3.3 Functionalities
tested

Commands



AFFE_CHAR_MECA GRAVITY


TEMP_CALCULEE


“MECHANICAL” AFFE_MODELE “POU_D_T'
TOUT
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
5/14

4
Results of modeling A

4.1 Values
tested

Identification Displacement
Reference
beam
Aster %

Actual weight
N300 DX
­ 0.1658E3
­ 0.1658E3
0.0
DY ­ 0.2040E4
­ 0.2039E4
0.02
DZ ­ 0.8010E5
­ 0.8010E5
0.0






N300 DX
­ 0.1651E3
­ 0.1651E3
0.04
Nodal force
DY ­ 0.2080E4
­ 0.2080E4
­ 0.01
DZ ­ 0.9516E5
­ 0.9516E5
0.004






N300 DX
­ 6.1418E3
­ 6.1413E3
0.007
Dilation
DY ­ 13.090E3
­ 13.091E3 0.012
DZ 16.799E3
16.799E3 0.003

4.2 Notice

The differences between the Aster results and the reference solution beam are all lower than
0.04%

4.3 Parameters
of execution

Version: 5.6



Machine: Origin 2000



Obstruction memory:
16 Mo
Time CPU To use:
3 seconds

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
6/14

5 Modeling
B

5.1
Characteristics of modeling

The curved elements are modelled by elements “POU_C_T”.

2.75
=
=
N400
=
N500 N600
=
N300
N700
=
With
N800
N900
N1000
B
3.69
N1100
N200
N1200
y
N1300
=
N1400
=
=
N1500
=
1.96
=
X
N100


Lengths given in meters

5.2
Characteristics of the grid

A number of nodes: 15

A number of meshs and type:
10 POU_D_T
4
POU_C_T

5.3 Functionalities
tested

Commands



AFFE_CHAR_MECA GRAVITY


TEMP_CALCULEE


“MECHANICAL” AFFE_MODELE
“POU_D_T'
TOUT
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
7/14

6
Results of modeling B

6.1 Values
tested

Identification Displacement
Reference
beam Aster %

Actual weight
N300 DX
­ 0.1658E3
­ 0.1658E4
0.017
DY ­ 0.2040E4
­ 0.2053E5
0.65
DZ ­ 0.8010E5
­ 0.8010E6
­ 0.006






N300 DX
­ 0.1651E3
­ 0.1652E4
0.04
Nodal force
DY ­ 0.2080E4
­ 0.2080E5
0.02
DZ ­ 0.9516E5
­ 0.9516E6
0.002






N300 DX
­ 6.1418E3
­ 6.1404E3
­ 0.02
Dilation
DY ­ 13.090E3
­ 13.090E2 0.005
DZ 16.799E3
16.799E2
0.003

6.2 Notice

The differences between the Aster results and the results of reference beam are all lower than
0.02% except for DY in actual weight where the variation is 0.65%

6.3 Parameters
of execution

Version: 5.6



Machine: Origin 2000



Obstruction memory:
16 Mo
Time CPU To use:
3 seconds

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
8/14

7 Modeling
C

7.1
Characteristics of modeling

5
E
Modeling PIPE (SEG3)
D
4
Z
With
F
B
y
5
10
G
4
Boundary conditions: Points C and H
H
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0

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


7.2
Characteristics of the grid

A number of nodes:
57
A number of meshs and type:
28 SEG3

7.3 Functionalities
tested

Commands



AFFE_MODELE AFFE
MODELISATION=' TUYAU'

AFFE_CARA_ELEM
POUTRE:(SECTION:“CERCLE”)

ORIENTATION:(CARA:“GENE_TUYAU”
VALE: (X Y Z)
AFFE_CHAR_MECA GRAVITY


TEMP_CALCULEE


Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
9/14

8
Results of modeling C

8.1 Values
tested

Identification Displacement
Reference
pipe Aster %

(M = 3)
Actual weight
Not D DX
­ 0.16517E3
­ 0.1636E3
­ 0.93
DY
­ 0.13870E4
­ 0.1251E4
­ 9.80
DZ
­ 0.80376E5
­ 0.8018E5
­ 0.24






Not D DX
­ 0.16445E3
­ 0.1629E3
­ 0.94
Nodal force
DY
­ 0.14245E4
­ 0.1288E4
­ 9.61
DZ
­ 0.10047E4
­ 0.1003E4
­ 0.20






Not D DX
­ 6.3277E3
­ 6.4534E3
1.99
Dilation
DY
­ 13.092E3
­ 13.103E3
0.08
DZ
16.798E3
16.880 E3
0.49

8.2 Notice

The results obtained with Code_Aster are similar to those of ABAQUS by elements pipes
except for the displacement DY (actual weight and nodal force) where the variation is about 10%.

8.3 Parameters
of execution

Version: 5.6


Machine: SGI-Origin2000 R12000


Obstruction memory: 16 Mo
Time CPU To use: 4,7 seconds

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
10/14

9 Modeling
D

9.1
Characteristics of modeling

5
E
Modeling TUYAU_6M (SEG3)
D
4
Z
With
F
B
y
5
10
G
4
Boundary conditions: Points C and H
H
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0

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


Lengths given in meters

9.2
Characteristics of the grid

A number of nodes:
57
A number of meshs and type:
28 SEG3

9.3 Functionalities
tested

Commands



AFFE_MODELE AFFE

MODELISATION=' TUYAU_6M'

AFFE_CARA_ELEM
POUTRE:(SECTION:“CERCLE”)

ORIENTATION:(CARA:“GENE_TUYAU”
VALE: (X Y Z)
AFFE_CHAR_MECA GRAVITY


TEMP_CALCULEE


Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
11/14

10 Results of modeling D

10.1 Values
tested

Identification Displacement
Reference
pipe Aster %

(M = 6)
Actual weight
Not D DX
­ 0.16512E3
­ 0.1636E3
­ 0.93
DY
­ 0.13946E4
­ 0.1258E4
­ 9.78
DZ
­ 0.80369E5
­ 0.8018E5
­ 0.24






Not D DX
­ 0.16441E3
0.1629E3
­ 0.94
Nodal force
DY
­ 0.14320E4
­ 0.1295E4
­ 9.58
DZ
­ 0.10047E4
­ 0.1003E4
­ 0.21






Not D DX
­ 6.3236E3
­ 6.4495E3
1.99
Dilation
DY
­ 13.093E3
­ 13.104E3
0.08
DZ
16.798E3
16.880E3
0.49

10.2 Notice

The results obtained with Code_Aster are similar to those of ABAQUS for elements pipes
except for the displacement DY (actual weight and nodal force) where the variation is about 10%.

10.3 Parameters
of execution

Version: 5.6


Machine: SGI-Origin2000 R12000


Obstruction memory: 16 Mo
Time CPU To use: 10,56 seconds

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
12/14

11 Modeling
E

11.1 Characteristics of modeling

5
E
Modeling PIPE (SEG4)
D
4
Z
With
F
B
y
5
10
G
4
Boundary conditions: Points C and H
H
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0

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


11.2 Characteristics of the grid

A number of nodes:
85
A number of meshs and type:
28 SEG4

11.3 Functionalities
tested

Commands


CREA_MAILLAGE MODI_MAILLE
OPTION:“SEG3_4”
AFFE_MODELE AFFE

MODELISATION=' TUYAU'
AFFE_CARA_ELEM
POUTRE:(SECTION:“CERCLE”)
ORIENTATION:(CARA:“GENE_TUYAU”
VALE: (X Y Z)
AFFE_CHAR_MECA GRAVITY

TEMP_CALCULEE

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
13/14

12 Results of modeling E

12.1 Values
tested

Identification Displacement
Reference
pipe Aster %

(M = 3)
Actual weight
Not D DX
­ 0.16517E3
­ 0.1648E3
­ 0.22
DY
­ 0.13870E4
0.1321E4
­ 4.73
DZ
­ 0.80376E5
­ 0.8024E5
­ 0.18






Not D DX
­ 0.16445E3
­ 0.1638E3
­ 0.37
Nodal force
DY
­ 0.14245E4
­ 0.1400E4
­ 1.74
DZ
­ 0.10047E4
­ 0.9997E5
­ 0.50






Not D DX
­ 6.3277E3
­ 6.329E3
0.02
Dilation
DY
­ 13.092E3
­ 13.105E3
0.10
DZ
16.798E3
16.843E3
0.27

12.2 Remarks

The grid in SEG4 is obtained starting from a grid SEG3 with command CREA_MAILLAGE,
MODI_MAILLE with option “SEG3_4”. It is important that the node medium of the SEG3 is well with
medium, Code_Aster checks this condition with a tolerance.

The results obtained with Code_Aster are similar to those of ABAQUS with elements pipes
except for displacement DY (actual weight and nodal force) or the variation is about 5% and 2%.

12.3 Parameters
of execution

Version: 5.6


Machine: SGI-Origin2000 R12000


Obstruction memory: 16 Mo
Time CPU To use: 7,62 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLL101 - Tuyautery: problem of HOVGAARD


Date:
29/10/01
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.01.101-C Page:
14/14

13 Summary of the results

Modeling beam:

The results are similar to the reference solution (modeling beam: average of results of
3 codes) as well for modeling A, where each elbow is discretized by 20 right elements,
POU_D_T, that for modeling B, where one uses the elements curves POU_C_T. One notes
simply, in this case, a variation a little more important in a value of displacement (0.65%).

Modeling pipe:

The Code_Aster results are similar to those of ABAQUS (for elements pipes), except for
displacement DY and for the loadings actual weight and nodal forces where the variation with the solution of
reference is more important with meshs SEG3 (10%) that with meshs SEG4 (5%).

The loading of dilation gives similar results.

This case-test makes it possible to test a noncoplanar piping.

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A

Outline document