Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
Document: V3.05.101
SSLX101 - Tuyau right modelled in hulls
and in beams
Summary:
The purpose of this test is to validate the connection hull-beam. The pipe is embedded at an end, and subjected to 4
successive efforts (traction and 3 moments) on the other end. A half of the pipe is with a grid in hulls,
the other is with a grid in beams. Embedding and the connection between the hull part and the beam are carried out by
a connection hull-beam, allowing in particular to transmit to the hull only the torque efforts of
beam type, without generating secondary stresses.
The reference solution is analytical (RDM). The variation with the numerical solution (from 3 to 5%) is explained by
fact that the grid in hulls actually consists of element plans (facets). The geometry of the pipe is
thus itself approximate. The solution obtained makes it possible to check that connection enters the elements of
hull and the element of beam is correct.
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 2/8
1
Problem of reference
1.1 Geometry
Right pipe length 80m, modelled in hulls between 0 and 40m, and in beams between 40 and 80m.
External radius: 2m, thickness: 0.1m.
The axis of the pipe is in the Oxy plan, tilted of 30 degrees compared to OX.
y
x1
P2
P1
X
Z
1.2
Material properties
E = 2.1011 Pa
= 0.3
1.3
Boundary conditions and loadings
Embedding “of beam type” in X = y = 0, realized by a connection hull-beam between the C1 edge of
hull and a P1 point (located out of O). It is this point which is blocked.
4 unit loading cases applied to the point P2 (80 * cos30, 80 * sin30, 0)
Fx1=1N traction following the axis Ox1, is Fx = cos30.Fx and Fy = sin30.Fx1
Torque Mx1 = 1Nm around Ox1, is MX = cos30.Mx1 and My = sin30.Mx1
Bending moment My1= 1Nm around Oy1 is Mx= - sin30.My1 and My = cos30.My1
Bending moment around OZ, is Mz=1Nm
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution for each of the 4 cases of loading:
In theory of beams, within the framework of the assumptions of Euler-Bernouilli, the solution of the problem of
reference is that of a right beam subjected to efforts and moments at an end and embedded
at the other end:
X
Traction: U
= F
E
X
X
X
1
1 ES
1
X
Torsion: X = M X
E X
1
1 GJ
1
M there X
Inflection around OY: =
. E
1
y
y
1
I.E.(internal excitation)
1
y1
M
Inflection around O
Z X
Z: Z =
.
.ez
EIz
2.2
Results of reference
Traction:
L
ux
=
1 (P2)
Fx1 ESL
thus
ux (P2) = Fx
.cos ()
30
1 ES
L
uy (P2) = Fx
sin ()
30
1 ES
Torsion:
L
X
=
1 (P2)
Mx1 GJ
thus
L
X (P2) =
MX
cos ()
30
1 GJ
L
y (P2) =
MX
sin ()
30
1 GJ
Inflection around: OY
1
L
y =
M y
1
1 I.E.(internal excitation) y1
thus X =
- y. if (
N
)
30
1
y =
y
(
cos
)
30
1
L2
and
Z
U =
- My1 2EIy1
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 4/8
Inflection around: OZ
L
Z =
Mz EIz
L2
and
uy = Mz
1
2EIz
thus
ux =
uy sin ()
30
1
uy = uy cos ()
30
1
Note:
The use of the connection hulls beams for embedding and the loadings allows
to remain within the framework of the assumption of Euler-Bernouilli (cf [R3.03.06]). The analytical solution
the preceding one is thus well the reference solution of the problem.
2.3
Uncertainty on the solution
Analytical solution.
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 5/8
3 Modeling
With
3.1
Characteristics of modeling
1 mesh POI1 (modeling DIS_TR), 1280 meshs QUAD4 (modeling DKT), 4 meshs SEG2
(POU_D_E). 32 meshs SEG2 on each edge of the hull.
3.2
Characteristics of the grid
A number of nodes: 4416
A number of meshs and types: 1 POI1, 4 SEG2, 1280 QUAD4
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
MODELISATION
DKT
[U4.22.01]
POU_DE
DIS_TR
AFFE_CARA_ELEM
COQUE
[U4.24.01]
POUTRE
DISCRET
AFFE_CHAR_MECA
LIAISON_ELEM
COQUE_POU
[U4.25.01]
MACRO_ELAS_MULT
[U4.31.03]
4
Results of modeling A
4.1 Values
tested
Displacements and rotations at the P2 point (to be multiplied by 1.E-10 m).
Loading case
Identification
Reference
Aster %
difference
Traction DX
2.8273 2.7942
1.2
Traction DY
1.6324 1.6132
1.2
Torsion DRX
1.93195
1.8713 3.1
Torsion DRY
1.1154
1.0804 3.1
Inflection Y
DZ
68.64
64.88
5.5
Inflection Y
DRX
0.858
0.827
3.7
Inflection Y
DRY
1.4861
1.4319
3.7
Inflection Z
DX
34.32
32.44
5.5
Inflection Z
DY
59.44
56.19
5.5
Inflection Z
DRZ
1.716
1.653
3.7
4.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000
System:
Obstruction memory: 128 Mo
Time CPU To use:
11 seconds
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 6/8
5 Modeling
B
5.1
Characteristics of modeling
The beam part is modelled by pipe sections. The hull part is modelled in DKT.
5.2
Characteristics of the grid
A number of nodes: 4420
A number of meshs and types:
· 1 mesh POI1 (modeling DIS_TR),
· 1344 meshs QUAD4 (modeling DKT), 32 meshs SEG2 on each edge of the hull
· 4 meshs SEG3 (TUYAU)
5.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
MODELISATION
DKT
[U4.22.01]
POU_DE
DIS_TR
AFFE_CARA_ELEM
COQUE
[U4.24.01]
POUTRE
DISCRET
AFFE_CHAR_MECA
LIAISON_ELEM
COQUE_TUYAU
[U4.25.01]
MACRO_ELAS_MULT
[U4.31.03]
6
Results of modeling A
6.1 Values
tested
Displacements and rotations at the P2 point (to be multiplied by 1.E-10 m).
Loading case
Identification
Reference
Aster %
difference
Traction DX
2.8273 2.7942
1.2
Traction DY
1.6324 1.6132
1.2
Torsion DRX
1.93195
1.8713 3.1
Torsion DRY
1.1154
1.0804 3.1
Inflection Y
DZ
68.64
64.92
5.4
Inflection Y
DRX
0.858
0.827
3.7
Inflection Y
DRY
1.4861
1.4325
3.7
Inflection Z
DX
34.32
32.40
5.6
Inflection Z
DY
59.44
56.11
5.6
Inflection Z
DRZ
1.716
1.652
3.7
6.2 Parameters
of execution
Version: 5.1
Machine: SGI/ORIGIN 2000
System:
Obstruction memory: 128 Mo
Time CPU To use:
15 seconds
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 7/8
7
Summary of the results
The reference solution is analytical (RDM). The variation with the numerical solution (from 3 to 5%)
be explained by the fact that the grid in hulls actually consists of plane elements (facets).
geometry of the pipe is thus itself approximate. The solution obtained makes it possible to check that it
connection between the elements of hull and the element of beam is correct.
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLX101 - Tuyau right modelled in hulls and beams
Date:
05/02/00
Author (S):
J.M. PROIX
Key: V3.05.101-A Page: 8/8
Intentionally white left page.
Handbook deValidation
V3.05 booklet: Linear statics of the assembled structures
HI-75/01/010/A
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