Code_Aster
®
Version
5.0
Titrate:
SSNL114 - Heavy cable with thermal dilation
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.02.114-A
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
V6.02.114 document
SSNL114 - Heavy cable 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
Code_Aster
®
Version
5.0
Titrate:
SSNL114 - Heavy cable with thermal dilation
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.02.114-A
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
A cable length 2l
0
at rest, in direction X, its actual weight is subjected (gravity in
direction - Z). It is embedded with the ends O and B, themselves distant of 2L.
O
B
2L
Z
X
O
2l
0
C
Initially, 2l
0
= 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 AP
= 0.3 (modeling B only)
ALPHA: 2.3 E-5 K
1
RHO: 2.844230E+03 kg/m
3
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.
Code_Aster
®
Version
5.0
Titrate:
SSNL114 - Heavy cable with thermal dilation
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.02.114-A
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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:
()
()
X S
aArgsh its
G
E L
Z S
has
S
has
G
E
S
has
L
has
G
E
L
has
L aArgsh
G
E Al
F has
=
+
=
+
+
-
+
-
=
+
=
0
2
2
2
02
2
02
0
0
1
2
1
2
()
solution of the equation
With S X-coordinate curvilinear, ranging between -
L
0
and
L
0
. One is interested here in the arrow in the center (point C):
()
Z C
has has
L
has
G
E
L
has
L aArgsh
G
E Al
F has
()
= -
+
-
=
+
=
1
2
02
2
02
0
0
solution of the equation
The only difficulty in the calculation of this solution is the resolution of the equation
()
L
F has
=
. 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 2l
0
to its increased initial length 2L is equal linear dilation:
L
0
= 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 has
=
give a value to 10
3
near.
2.4 References
bibliographical
[1]
C.CONEIM “On 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 (February
1981)
Code_Aster
®
Version
5.0
Titrate:
SSNL114 - Heavy cable with thermal dilation
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.02.114-A
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
elements
CABLE
3.2
Characteristics of the mesh
27 elements
CABLE
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE AFFE
MODELING
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
(m)
Moment Not Identification Reference Aster %
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
Overall dimension memory: 64 Mo
Time CPU To use: 6.5 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNL114 - Heavy cable with thermal dilation
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.02.114-A
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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 bending 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 mesh
27 elements
POU_D_T_GD
5.3 Functionalities
tested
Controls
Keys
AFFE_MODELE AFFE
MODELING
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
(m)
Moment Not Identification
Reference Aster %
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
Overall dimension memory: 64 Mo
Time CPU To use: 7.1 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNL114 - Heavy cable with thermal dilation
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.02.114-A
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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.