Code_Aster ®
Version
3
Titrate:
HPLV100 - Parallélépipède whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
Document: V7.03.100
HPLV100 - Parallélépipède 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].
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A

Code_Aster ®
Version
3
Titrate:
HPLV100 - Parallélépipède whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C Page:
2/6
1
Problem of reference
1.1 Geometry
y
I
p
B
D
H
C
O
With
X
Z
H
I = 20. H = 10. O = (0. 0. 0.) With = (20. 0. 0.) D = (20. 5. 5.)
1.2
Material properties
Thermal conductivity: = 1.
1000.
Young modulus: E =
(T being the températur) E
800.­ T
Poisson's ratio: = 0.3
1.3
Boundary conditions and loadings
· Thermics
T
T ()
To = 0.,
= - 2.
X =
N

for
I
= + 2. for X = 0
= - 3. for y = H/2.
= + 3. for y = - H/2.
= - 4 for Z = H/2.
= + 4. for Z = - H/2.
N being the outgoing normal.
· Mechanics
:
ux (O) = uy (O) = uz (O) = 0.
ux (B) = ux (C) = uz (B) = 0.
· Pressure
:
p = 1.
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A

Code_Aster ®
Version
3
Titrate:
HPLV100 - Parallélépipède whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
T = ­ 2x ­ 3y ­ 4z + 40
1000
One thus has: E =
Emin = .138 Emax = 120
2x + 3y + 4z + 760
With
Ah
2
2
2

ux (X, y, Z) = p

2 [X + (y + Z)] + B xy + C xz + Dx ­ v
(y + Z)

4



B
x2
Ah
C H
2
2

uy (X, y, Z) = ­ Pa xy + y ­ Z +
+ C yz + Dy ­
X ­
Z


2

4
4


C
x2
C H
Ah
2
2

uz (X, y, Z) = ­ Pa xz + B yz + Z ­ y +
+ Dz +
y ­
X


2

4
4


With:
To = 0 002
.
, B = 0 003
.
, C = 0 004
.
, D = 0 7
. 6
2.2
Result of reference
Temperature at the point O and point D.
Displacement of point A.
2.3 Reference
bibliographical
[1]
S. ANDRIEUX “analytical Une solution to a linear problem of elasticity isotropic 3D with
Young modulus function of the variables of space [V4.90.01].
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A

Code_Aster ®
Version
3
Titrate:
HPLV100 - Parallélépipède whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
3D
3.2
Characteristics of the grid
A number of nodes: 141
A number of meshs and types: 16 HEXA20
3.3 Functionalities
tested
Commands
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 one took 250 points (E, T
I
I).
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A

Code_Aster ®
Version
3
Titrate:
HPLV100 - Parallélépipède whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C Page:
5/6
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 ux
+15.6
+15.60
0
uy
­ 0.57
­ 0.5701
0.02
uz
­ 0.77
­ 0.7700
0
D ux
+16.3
+16.30
0
uy
­ 1.785
­ 1.785
0
uz
­ 2.0075
­ 2.0075
0
4.2 Parameters
of execution
Version: 3.05.13
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
12 seconds
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A

Code_Aster ®
Version
3
Titrate:
HPLV100 - Parallélépipède whose Young modulus is a function
Date:
21/05/96
Author (S):
P. MIALON
Key:
V7.03.100-C Page:
6/6
5
Summary of the results
This problem requires a very fine discretization of the function E (T) to obtain the solution of
reference.
Handbook of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A

Outline document