Code_Aster
®
Version
7.0
Titrate:
HPLP300 - Plate with Young modulus function of the temperature
Date:
13/10/04
Author (S):
J.M. PROIX
Key
:
V7.02.300-A
Page:
1/6
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
Document: V7.02.300
HPLP300 - Plate with Young modulus function of
the temperature
Summary:
This elastic thermo test makes it possible to compare the solution obtained by Code_Aster with an analytical solution,
when the Young modulus varies in a nonlinear way compared to the temperature.
This test is deduced from the test 3D HPLV100 describes in [V7.03.100] (parallelepiped whose Young modulus is
function of the temperature).
Code_Aster
®
Version
7.0
Titrate:
HPLP300 - Plate with Young modulus function of the temperature
Date:
13/10/04
Author (S):
J.M. PROIX
Key
:
V7.02.300-A
Page:
2/6
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
1.2
Material properties
Thermal conductivity:
=
1
Young modulus:
E
T
=
-
10000
8000
, T = temperature
Poisson's ratio:
v
=
0 3
.
1.3
Boundary conditions and loadings
1.3.1 Thermics
T (0) = 40
T
N
= -
4
on edge X = H/2
T
N
= +
4
on edge X = - H/2
H = 10
Y,
v
D
pressure Po
X,
U
C
H
With
C1
O
B1
B
Code_Aster
®
Version
7.0
Titrate:
HPLP300 - Plate with Young modulus function of the temperature
Date:
13/10/04
Author (S):
J.M. PROIX
Key
:
V7.02.300-A
Page:
3/6
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A
T
N
= -
3
on edge y = H/2
T
N
= +
3
on edge y = - H/2
1.3.2 Mechanics
·
Not O locked (U = v = O)
·
Displacement following X locked out of B
·
Uniform pressure Po being exerted normally on contour: Po = 1.
2
Reference solution
2.1
Method of calculation used for the reference solution
·
The field of temperature is given by:
T = - 4X - 3Y + 40
·
The field of displacements is given by:
(
)
U
Vp Bxy C X
y
Dx CH y
= -
+
-
+
+
2
4
2
2
(
)
v
Vp B y
X
Cxy Dy CH y
= -
-
+
+
-
2
4
2
2
where B = 0.003 C = 0.004 D = 0.76
p
v
v Po
= -
1
·
The field of deformations is given by:
(
)
=
=
= -
+
+
xx
yy
vp By Cx D
xy
=
0.
·
The stress field is given by:
(
)
=
=
= - = - - -
+
+
= - - = -
xx
yy
E
v
T
vp
v
X
y
v
v p
Po
1
1000
800
1
0 004
0 003
0 76
1
.
.
.
Code_Aster
®
Version
7.0
Titrate:
HPLP300 - Plate with Young modulus function of the temperature
Date:
13/10/04
Author (S):
J.M. PROIX
Key
:
V7.02.300-A
Page:
4/6
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A
2.2
Results of reference
Temperature at the points O, A, B, C, D, B1, C1
Displacements at the points A, B, C, D, B1, C1
2.3
Uncertainty on the solution
Analytical solution.
3 Modeling
With
3.1
Characteristics of modeling
It is about a modeling in plane stresses.
Cutting: 4 X 4 elements
Limiting conditions:
·
out of O, U = v = O
·
out of B, U = O
y, v
B
D
C
X, U
O
B1
With
C1
Code_Aster
®
Version
7.0
Titrate:
HPLP300 - Plate with Young modulus function of the temperature
Date:
13/10/04
Author (S):
J.M. PROIX
Key
:
V7.02.300-A
Page:
5/6
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A
3.2
Characteristics of the mesh
A number of nodes: 65
A number of meshs and type: 16
QUAD8
Name of the nodes
O = N38
With = N1
B = N23
C = N16
D = N3
B1 = N9
C1 = N30
3.3 Functionalities
tested
Controls
DEFI_FONCTION
“TEMP”
DEFI_MATERIAU ELAS_FO
THER
“MECHANICAL” AFFE_MODELE
`THERMAL
“2D”
“2D”
ALL
ALL
AFFE_CHAR_MECA DDL_IMPO
PRES_REP
TEMP_CALCULEE
GROUP_NO
GROUP_MA
AFE_CHAR_THER TEMP_IMPO
FLUX_REP
GROUP_NO
GROUP_MA
POST_RELEVE “TEMP”
“DEPL”
“EXTRACTION”
4
Results of modeling A
4.1 Values
tested
Localization
Type of value
Reference
Aster
% difference
Not A
T
75.
75.
0.
Not B
T
25.
25.
0.
Not C
T
20.
20.
0.
Not D
T
5.
5.
0.
Not B1
T
55.
55.
0.
Not C1
T
60.
60.
0.
Not O
T
40.
40.
0.
Not A
U
2.68975
2.64249
- 1.75
v
2.55
2.55502
0.197
Not B
U
0.
1.13 10
- 17
1.3
10
- 17
v
- 2.65125
- 2.68625
- 1.32
Not C
U
- 2.695
- 2.694997
- 1.21 10
- 4
Not D
U
- 2.7002
- 2.74751
- 1.749
v
- 2.695
- 2.69503
9.67 10
- 4
Not B1
U
0.0700
0.0699585
- 0.059
v
2.59875
2.63376
1.347
Not C1
U
2.625
2.62501
4.73 10
- 4
4.2 Remarks
It is necessary to discretize finely the function E (T) to obtain satisfactory results. One has
taken for this test 160 points of discretization, for the interval of temperatures [5., 75.].
Code_Aster
®
Version
7.0
Titrate:
HPLP300 - Plate with Young modulus function of the temperature
Date:
13/10/04
Author (S):
J.M. PROIX
Key
:
V7.02.300-A
Page:
6/6
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A
5
Summary of the results
The results obtained with Code_Aster are in concord with the analytical solution.