Code_Aster
®
Version
5.0
Titrate:
Orthotropic Square TPLP02
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.002-A
Page:
1/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
V4.05.002 document
TPLP02 - Orthotropic square
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It is about a problem plane 2D represented by only one modeling (plane).
The functionalities tested are the use of plane thermal elements, of an orthotropic material, three
limiting types of conditions:
- convection
-
linear variation of the outside air temperatures,
- flow
imposed.
The results are compared with an analytical solution (VPCS).
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Square TPLP02
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.002-A
Page:
2/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
X
Y
has
O
Cubic of edge = 0.2 m has
Center cube = (0., 0.)
1.2
Properties of material
X
= 1.0 W/m.°C
thermal conductivity along axis X
y
= 0.75 W/m.°C
thermal conductivity along the axis y
1.3
Boundary conditions and loadings
·
density flux:
y
= 60 W/m ˛
face y =
-
0.1 (entering flow)
y
= - 60 W/m ˛
face y = 0.1 (outgoing flow)
·
convection on the faces X =
-
0.1 and X = 0.1: H = 15 W/m ˛ °C,
·
linear variation of the outside air temperatures:
- T
ext.
= 30 - 80y face X =
-
0.1,
- T
ext.
= 15 - 80y face X = 0.1.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Square TPLP02
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.002-A
Page:
3/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card TPLP02/89 of guide VPCS
Analytical solution.
T (X, y, Z) = ax + by + D = - 45x - 80y + 22.5
Figure 0.1
Figure 0.2
Not T (°C)
O
22.5
With
35.0
B
26.0
C
10.0
D
19.0
E
30.5
F
18.0
G
14.5
H
27.0
X
= 45 W/m ˛ = constant
y
= 60 W/m ˛ = constant
X
Y
O
E
D
C
B
With
D
H
F
G
2.2
Results of reference
Temperature at the points located on the figure above.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Guide validation of the software packages of structural analysis. French company of
Mechanics, AFNOR 1990 ISBN 2-12-486611-7
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Square TPLP02
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.002-A
Page:
4/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (QUAD4)
m6
m5
X
Limiting conditions:
- dimensioned AB
y
= 60 W/m ˛
- dimensioned CD
y
= - 60 W/m ˛
- dimensioned BC H = 15 W/m ˛ °C
T
ext.
= 15-80y
- dimensioned AD H = 15 W/m ˛ °C
T
ext.
= 30-80y
E
D
C
B
With
H
F
G
y
O
N11
N6
N1
N66
N56
N121
N116
N111
m1
m10
m91
m100
m45
N61
m56
m50
m60
m41
m51
m96 m95
3.2
Characteristics of the mesh
A number of nodes:
121
A number of meshs and types: 100 QUAD4
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
SOLID MASS
DEFI_FONCTION
NOM_PARA: “X”
NOM_PARA: “Y”
AFFE_CHAR_THER_F
EXCHANGE
FLUX_REP
THER_LINEAIRE
EXCIT
CARA_ELEM
CALC_CHAM_ELEM
CARA_ELEM
FLUX_ELNO_TEMP
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Square TPLP02
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.002-A
Page:
5/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster difference
tolerance
Temperature °C
T (O) 22.5
22.5
0.0
1%
T (A) 35.0
35.0
0.0
1%
T (B) 26.0
26.0
0.0
1%
T (C) 10.0
10.0
0.0
1%
T (D) 19.0
19.0
0.0
1%
T (E) 30.5
30.5
0.0
1%
T (F) 18.0
18.0
0.0
1%
T (G) 14.5
14.5
0.0
1%
T (H) 27.0
27.0
0.0
1%
Flow
W/m ˛
X
(A)
45.0 45.0 0.0 1%
X
(H)
45.0 45.0 0.0 1%
X
(D)
45.0 45.0 0.0 1%
X
(B)
45.0 45.0 0.0 1%
X
(F)
45.0 45.0 0.0 1%
X
(C)
45.0 45.0 0.0 1%
y
(A)
60.0 60.0 0.0 1%
y
(E)
60.0 60.0 0.0 1%
y
(B)
60.0 60.0 0.0 1%
y
(D)
60.0 60.0 0.0 1%
y
(G)
60.0 60.0 0.0 1%
y
(C)
60.0 60.0 0.0 1%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.40 seconds
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Square TPLP02
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.002-A
Page:
6/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
5
Summary of the results
The results obtained are excellent. The computed values by Aster are identical to the values of
reference. That is “a normally awaited” result since the field solution which is linear
belongs to the space of interpolation of the element tested.
This test made it possible to test the following controls:
·
DEFI_FONCTION
associated the operand
NOM_PARA
, allowing to define a variation of
outside air temperature according to the X-coordinate or of the ordinate,
·
DEFI_MATERIAU
associated the key word
THER_ORTH
,
allowing to define the characteristics
of an orthotropic material,
·
AFFE_CARA_ELEM
associated the key word
SOLID MASS
,
allowing to define the axes of orthotropism.