Code_Aster
®
Version
3
Titrate:
HPLV100 - Parallelepiped whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C
Page:
1/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
Document: V7.03.100
HPLV100 - Parallelepiped of which the Young modulus
is a function of the temperature
Summary
This elastic thermo calculation compares the solution provided by Code_Aster with an analytical solution when it
Young modulus varies in a nonlinear way compared to the temperature.
Modeling does not have anything physics and is described in [V7.90.01].
Code_Aster
®
Version
3
Titrate:
HPLV100 - Parallelepiped whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C
Page:
2/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
1
Problem of reference
1.1 Geometry
y
I
Z
C
O
B
X
H
D
With
H
I = 20. H = 10. O = (0. 0. 0.) With = (20. 0. 0.) D = (20. 5. 5.)
p
1.2
Material properties
Thermal conductivity:
= 1.
Young modulus:
(
)
E
T
T
=
1000
800
.
.
being the temperature
Poisson's ratio:
= 0.3
1.3
Boundary conditions and loadings
·
Thermics
()
T WITH
T
N
X
X
y
H
y
H
Z
H
H
N
=
= -
=
=
= -
=
= +
-
= -
=
= +
-
0
2
2
3
2
3
2
4
2
4
2
.,
.
.
/.
.
.
/.
.
for
I
for
0
for
for
for
for
being the outgoing normal.
+.
=
=
/
Z =
/.
·
Mechanics
:
()
()
()
()
()
()
U O
U O
U O
U B
u.a.
U B
X
y
Z
X
X
Z
=
=
=
=
=
=
0
0
.
.
·
Pressure
:
p
=
1.
Code_Aster
®
Version
3
Titrate:
HPLV100 - Parallelepiped whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C
Page:
3/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
2
Reference solution
2.1
Method of calculation used for the reference solution
(
)
(
)
[
]
()
(
)
(
)
T
X
y
Z
E
X
y
Z
E
E
U X y Z
p With X
y
Z
B xy C xz Dx v Ah y Z
U X y Z
p With xy B y
Z
X
C yz Dy Ah X C H Z
U X y Z
p With xz B
X
y
Z
=
+
=
+
+
+
=
=
=
+
+
+
+
+
+
=
+
+
+
+
=
+
2
.
,
,
,
min
max
3
4
40
1000
2
3
4
760
138
120
2
4
2
4
4
2
2
2
2
2
2
One thus has:
yz C Z
y
X
Dz C H y Ah X
With
B
C
D
+
+
+
+
=
=
=
=
2
4
4
0 002
0 003
0 004
0 76
2
2
2
.
,
.
,
.
,
.
With:
2.2
Result of reference
Temperature at the point O and point D.
Displacement of point A.
2.3 Reference
bibliographical
[1]
S. ANDRIEUX “an analytical solution to a linear problem of elasticity isotropic 3D with
Young modulus function of the variables of space [V4.90.01].
Code_Aster
®
Version
3
Titrate:
HPLV100 - Parallelepiped whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C
Page:
4/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
3 Modeling
With
3.1
Characteristics of modeling
3D
3.2
Characteristics of the mesh
A number of nodes: 141
A number of meshs and types: 16 HEXA20
3.3 Functionalities
tested
Controls
Keys
DEFI_FONCTION
[U4.21.02]
DEFI_MATERIAU
ELAS_FO
[U4.23.01]
3.4 Remarks
It is necessary to envisage a great number of points of discretization of the curve
()
E T
for
to obtain the desired precision. Here 250 points were taken
(
)
E T
I
I
,
.
Code_Aster
®
Version
3
Titrate:
HPLV100 - Parallelepiped whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C
Page:
5/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
0 T
+40.
+40.00
0
D T
35.
35.00
0
With U
X
+15.6
+15.60
0
U
y
0.57
0.5701
0.02
U
Z
0.77
0.7700
0
D U
X
+16.3
+16.30
0
U
y
1.785
1.785
0
U
Z
2.0075
2.0075
0
4.2 Parameters
of execution
Version: 3.05.13
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
12 seconds
Code_Aster
®
Version
3
Titrate:
HPLV100 - Parallelepiped whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C
Page:
6/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
5
Summary of the results
This problem requires a very fine discretization of the function
()
E T
to obtain the solution of
reference.