Code_Aster ®
Version
7.0
Titrate:
HPLP300 - Plaque with Young modulus function of the temperature
Date:
13/10/04
Author (S):
Key J.M. PROIX
:
V7.02.300-A Page:
1/6

Organization (S): EDF-R & D/AMA
Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
Document: V7.02.300
HPLP300 - Plaque 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).


Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.0
Titrate:
HPLP300 - Plaque with Young modulus function of the temperature
Date:
13/10/04
Author (S):
Key J.M. PROIX
:
V7.02.300-A Page:
2/6


1
Problem of reference

1.1 Geometry

Y,

v

D

B

pressure Po

C1

H = 10
X,

O
C
U

B1

With

H

1.2
Material properties

Thermal conductivity: = 1

10000
Young modulus: E =
, T = temperature
8000 - T

Poisson's ratio: v = 0 3
.

1.3
Boundary conditions and loadings

1.3.1 Thermics

T (0) = 40


T
= - 4 on edge X = H/2
N


T
= +4 on edge X = - H/2
N
Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.0
Titrate:
HPLP300 - Plaque with Young modulus function of the temperature
Date:
13/10/04
Author (S):
Key J.M. PROIX
:
V7.02.300-A Page:
3/6



T
= - 3 on edge y = H/2
N


T
= +3 on edge y = - H/2
N

1.3.2 Mechanics

· Not O blocked (U = v = O)
· Displacement following X blocked 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:


C
CH
2
2

U = V
- p Bxy + (X - y) + Dx +
y




2
4

B
CH
2
2

v = V
- p
(y - X) + Cxy + Dy - y




2
4

1 - v
where B = 0.003 C = 0.004 D = 0.76 p =
Po
v

· The field of deformations is given by:

=
vp By Cx D
xx = yy = -
(+ +) xy = 0.

· The stress field is given by:


E
1000
vp
v
=
0 004
.
X 0 003
.
y 0 7
. 6
p
Po
xx = yy =
= -
(
+
+
) = -
= -

1 - v
800 - T1 v
1 - v
Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.0
Titrate:
HPLP300 - Plaque with Young modulus function of the temperature
Date:
13/10/04
Author (S):
Key J.M. PROIX
:
V7.02.300-A Page:
4/6


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 constraints.

y, v

B
D

C1
X, U
O

C

With
B1



Cutting: 4 X 4 elements

Limiting conditions:

· out of O, U = v = O
· out of B, U = O

Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.0
Titrate:
HPLP300 - Plaque with Young modulus function of the temperature
Date:
13/10/04
Author (S):
Key J.M. PROIX
:
V7.02.300-A Page:
5/6


3.2
Characteristics of the grid

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

Commands




DEFI_FONCTION
“TEMP”

DEFI_MATERIAU ELAS_FO



THER
“MECHANICAL” AFFE_MODELE
“2D”
TOUT

`THERMIQUE
“2D”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


PRES_REP
GROUP_MA
TEMP_CALCULEE
AFE_CHAR_THER TEMP_IMPO
GROUP_NO


FLUX_REP
GROUP_MA
POST_RELEVE “TEMP”
“EXTRACTION”

“DEPL”

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.].
Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.0
Titrate:
HPLP300 - Plaque with Young modulus function of the temperature
Date:
13/10/04
Author (S):
Key J.M. PROIX
:
V7.02.300-A Page:
6/6


5
Summary of the results

The results obtained with Code_Aster are in concord with the analytical solution.

Handbook of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
HT-66/04/005/A

Outline document