Code_Aster
®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow roll
Date:
19/10/01
Author (S):
I. DEBOST
Key
:
V7.01.101-A
Page:
1/6
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A
Organization (S):
EDF/MTI/MN
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of the structures
axisymmetric
V7.01.101 document
HPLA101 - Elastic thermo hollow roll.
Derived compared to a variation from field
Summary
The purpose of this test is to test calculations of derived from the temperature, displacements and the stresses by
report/ratio with a variation of field (variation of the radius interns tube), under thermal dilation.
The analytical solution of reference for the mechanical thermo fields is described in the document
[V7.90.03]. The derivative are calculated by Mathematica. One has the results for modeling
following:
·
axisymmetric 2D: isoparametric finite elements axisymmetric QUAD8.
Code_Aster
®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow roll
Date:
19/10/01
Author (S):
I. DEBOST
Key
:
V7.01.101-A
Page:
2/6
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A
1
Problem of reference
1.1 Geometry
Z
R
R
E
R
I
F
B
D
With
C
R
Z
J
H
+
Interior radius
R
I
= 19.5 mm
External radius
R
E
= 20.5 mm
Not F
R = 20.0 mm
Thickness
H = 1.0 mm
Height
L = 10.0 mm
1.2
Properties of material
The material is homogeneous isotropic, thermoelastic linear, the initial state is virgin. Coefficients
thermo elasticity are:
E
NR mm
C
=
=
=
=
=
°
-
-
2 10
0 3
1
0
10
5
2
5
1
.
/
.
(expansion factor).
1.3
Boundary conditions and loadings
Thermal dilation:
()
(
) (
)
(
)
T R
T
T
T
T
T R R H
ref.
E
I
E
I
-
=
+
+
+
-
0 5
2
.
.
/
with:
T
C
T
C
T
C
E
I
ref.
=
°
= -
°
=
°
0 5
0 5
0
.
,
.
,
.
where
()
(
)
(
)
T R
T
T
R R
H
T
T
I
E
E
I
=
+
+ -
-
1
2
These fields of temperature are calculated with
THER_LINEAIRE
, using a stationary calculation on
the same mesh, but with a plane model in order to have a solution refines in the thickness.
Vertical displacements are locked on all the structure.
Code_Aster
®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow roll
Date:
19/10/01
Author (S):
I. DEBOST
Key
:
V7.01.101-A
Page:
3/6
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
To refer to the document [V7.90.03].
The analytical results of reference are:
·
temperatures,
·
displacements,
·
axial stress.
One deduces the derivative from it from the temperature, displacements and axial stresses by report/ratio
with a variation of
R
I
(with Mathematica) in the thickness of the cylinder.
Code_Aster
®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow roll
Date:
19/10/01
Author (S):
I. DEBOST
Key
:
V7.01.101-A
Page:
4/6
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Finite elements 2D axisymmetric
J
C
F
With
X
B
0
10
D
19.5
20.5
The discretized geometry is represented above:
Edge
group_no
BC BC
DA DA
LOW AB
CD HIGH
3.2
Characteristics of the mesh
The mesh is regular: 4 elements in the height, 8 in the thickness.
A number of nodes: 121
A number of meshs and type: 32 QUAD8
3.3 Functionalities
tested
Controls
AFFE_MODELE AFFE
MODELING
“AXIS”
AFFE_CHAR_MECA TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
SENSITIVITY
CALC_THETA
THETA_BANDE
OPTION: “TAPE”
THER_LINEAIRE SENSITIVITY
CALC_ELEM SENSITIVITY
CALC_NO OPTION
:
“DETE_NOEU_DLTE”
“DEDE_NOEU_DLDE”
“DESI_NOEU_DLSI”
Code_Aster
®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow roll
Date:
19/10/01
Author (S):
I. DEBOST
Key
:
V7.01.101-A
Page:
5/6
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Precision
Aster
% difference
Derived from
T
compared to
R
I
in
With (N120): 1
10
3
1
1.07
10
12
F (N69):
0.5
10
3
0.5 1.78
10
13
Derived from DX compared to
R
I
in a:
8.2804 10
6
10
3
8.2792
10
6
4.05
10
5
F:
1.1902 10
6
10
3
1.1903
10
6
2.46
10
4
Derived from Siyy compared to
R
I
out of F:
1.42491
10
3
1.42493
2.70
10
4
4.2 Remarks
Good results.
The derivative of the stresses compared to a variation of field in the area close to the radius
intern are very sensitive to the refinement of the mesh.
4.3 Parameters
of execution
Version: 5.04.20
Machine: SGI 02000 claster
Overall dimension memory: 64 Mo
Time CPU To use: 6.94 seconds
Code_Aster
®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow roll
Date:
19/10/01
Author (S):
I. DEBOST
Key
:
V7.01.101-A
Page:
6/6
Manual of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A
5
Summary of the results
One obtains good results for the derivative eulériennes of the temperature and displacements
compared to a variation of field. For the derivative of the stresses, one needs a very fine mesh
radially.