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5.0
Titrate:
SSNL114 - Heavy Câble with thermal dilation


Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.02.114-A Page:
1/6

Organization (S): EDF/IMA/MN
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
V6.02.114 document

SSNL114 - Heavy Câble with thermal dilation

Summary:

This test validates the calculation of the cables subjected to gravity, with or without thermal dilation.

·
Analyze static
·
Elastic behavior
·
Great displacements
·
2 modelings: CABLE and POU_D_T_GD

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNL114 - Heavy Câble with thermal dilation


Date:
03/01/00
Author (S):
Key J.M. PROIX
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1
Problem of reference

1.1 Geometry

A cable length 2l0 at rest, in direction X, is subjected its actual weight (gravity in
direction - Z). It is embedded with the ends O and B, themselves distant of 2L.

Z
2L
O
X
O
C
2l0
B


Initially, 2l0 = 2L=325m

The surface of the section of the cable is worth: 2.2783E-04 m ²

1.2
Material properties

E = 5.70 E+10 Pa
= 0.3 (modeling B only)
ALPHA: 2.3 E-5 K1
RHO: 2.844230E+03 kg/m3

1.3
Boundary conditions and loadings

Embedding out of O and B

Gravity: (9.81, 0.0, 0.0, - 1.0)

The temperature in the cable varies according to time:

Moment: 0. T=0 temperature. °C

Moment: 1.Température T=39.26 °C

(The temperature of reference is worth: 0.°C)

One thus treats:

at moment 0, a cable subjected to its only actual weight
at moment 1, a heavy cable subjected to a thermal dilation.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

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Titrate:
SSNL114 - Heavy Câble with thermal dilation


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2
Reference solution

2.1
Method of calculation used for the reference solution

Analytical solution:

For an extensible cable (elastic), subjected to its actual weight, displacement is worth:

S G
X (S) = aArgsh
L

+ E 0 has
s2
G s2
L 2
2
0
G L
Z (S) = has 1 +
+
- 1+ have
-
0

a2
E 2
a2
E 2
l0 G
solution of the equation L has
= aArgsh
Al
F (A)

has +
=
E
0

With S X-coordinate curvilinear, ranging between - l0 and l0. One is interested here in the arrow in the center (point C):

L 2
G L 2
Z (C) = has - 1 + 0 have -
0
a2
E 2

l0 G
solution of the equation L has
= aArgsh
Al
F (A)

has +
=
E
0

The only difficulty in the calculation of this solution is the resolution of the equation L = F (A). This
resolution was numerically made (FORTRAN program using the routine of search of zero
of Aster ZEROFO).

Note:

In the case of thermal dilation, the solution is the same one as previously, while considering
that the initial length 2l0 is equal to its increased initial length 2L linear dilation:
L0 = L * (1+ALPHA * T)

2.2
Results of reference

·
Displacement in Z at the point C

2.3
Uncertainty on the solution

Semi solution - analytical: the numerical resolution of the equation L = F (A) gives a value to 10­3
near.

2.4 References
bibliographical

[1]
C.CONEIM “Sur the approximation of the equations of the statics of the overhead cables in
presence of electromagnetic fields of forces “. Thesis and note HI/3640-02 (Février
1981)

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
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Titrate:
SSNL114 - Heavy Câble with thermal dilation


Date:
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Author (S):
Key J.M. PROIX
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3 Modeling
With

3.1
Characteristics of modeling

elements CABLE

3.2
Characteristics of the grid

27 elements CABLE

3.3 Functionalities
tested

Commands
Keys
AFFE_MODELE AFFE
MODELISATION
CABLE
[U4.22.01]
STAT_NON_LINE COMP_ELAS
RELATION
:
CABLE [U4.32.01]
STAT_NON_LINE COMP_ELAS
DEFORMATION
GREEN [U4.32.01]

4
Results of modeling A

4.1 Values
tested

DZ (C)
Moment Not Identification Reference Aster %
(m)
diff
0. C
DZ ­ 6.352
­ 6.3536
0.025
1. C
DZ ­ 8.195
­ 8.1945
0.012

4.2 Parameters
of execution

Version: 5.1
Machine: SGI/ORIGIN 2000

Obstruction memory: 64 Mo
Time CPU To use: 6.5 seconds

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNL114 - Heavy Câble with thermal dilation


Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.02.114-A Page:
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5 Modeling
B

5.1
Characteristics of modeling

elements POU_D_T_GD

In order not to disturb the solution, the values of inertias of inflection are arbitrarily selected
small: for a section of surface 2.27830000000000128E-4, one poses IY=IZ= 1.0E-4

Let us announce however that values cannot be taken smaller without causing error
in the resolution.

5.2
Characteristics of the grid

27 elements POU_D_T_GD

5.3 Functionalities
tested

Commands
Keys
AFFE_MODELE AFFE
MODELISATION
POU_D_T_GD
[U4.22.01]
STAT_NON_LINE COMP_ELAS
RELATION
:
ELAS_POUTRE_GD
[U4.32.01]
STAT_NON_LINE COMP_ELAS
DEFORMATION
GREEN
[U4.32.01]

6
Results of modeling B

6.1 Values
tested

DZ (C)
Moment Not Identification
Reference Aster %
(m)
diff
0. C
DZ ­ 6.352
­ 6.3269
0.4
1. C
DZ ­ 8.195
­ 8.2109
0.2

6.2 Parameters
of execution

Version: 5.1
Machine: SGI/ORIGIN 2000

Obstruction memory: 64 Mo
Time CPU To use: 7.1 seconds

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNL114 - Heavy Câble with thermal dilation


Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.02.114-A Page:
6/6

7
Summary of the results

The results show that one can obtain the solution of the problem of the heavy cable with good
precision for the elements of cable (0.02%), and a precision acceptable for the elements
POU_D_T_GD (0.4%).

Indeed, this mechanical problem is difficult for the algorithm of resolution, because the solution cannot
to be obtained that with the assumption of great displacements. Convergence can be obtained only with
the geometrical matrix of rigidity.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

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