Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
1/8
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
V4.05.301 document
TPLP301 - Square plate with imposed temperature
distributed sinusoïdalement
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It is about a problem plane 2D represented by two modelings, one planes, the second hull.
The functionalities tested are as follows:
·
plane thermal element,
·
thermal element hull,
·
limiting conditions: sinusoidal distribution of the imposed temperature
The results are compared with an analytical solution.
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
2/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
C
has = 1 m
has
Y
X
With
B
T
p
= sin (
X)
Points
X
Y
B
0,01 0,01
E
0,01 0,02
F
0,01 0,03
G
0,02 0,01
H
0,02 0,02
0,02 0,03
0,03 0,04
F
E
G
I
H
Points
X
Y
E
0.5 0.00
F
0.5 0.25
G
0.5 0.50
H
0.5 0.75
I
0.5 1.00
D
1.2
Properties of material
=
1. W/m.°C
Thermal conductivity
1.3
Boundary conditions and loadings
·
side [AB]
imposed temperature T
p
= sin (
X),
·
side [BC]
imposed temperature T
0
= 0°,
·
side [CD]
imposed temperature T
0
= 0°,
·
side [BA]
imposed temperature T
0
= 0°.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
3/8
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
Analytical solution:
T (X, y) = sinh [
(1.0 there)] sin (
X)/sinh (
)
2.2
Results of reference
Temperature at the points E, F, G, H, I
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
W.K. Liu, T. Belytschko, “Efficient linear and nonlinear heat conduction with has quadrilateral
element ", Int. J. num. Meth. Engng, flight 20, n°5, p 931-948, 1984.
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
4/8
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
HULL (TRIA3)
n17 (D)
n1 (A)
n137 (E)
X
y
Limiting conditions:
- dimensioned AE
T= sin (
X)
- dimensioned JD, DA T= 0°C
- dimensioned EJ:
= 0
Not
X
y
Node
E
0.5
0.
n137
F
0.5
0.25
n141
G
0.5
0.5
n145
H
0.5
0.75
n149
I
0.5
1.
n153
0.5
n141 (F)
n145 (G)
n149 (H)
n153 (I)
n1
n35
n69
n103
n137
n18
n52
n86
n120
3.2
Characteristics of the mesh
A number of nodes:
153
A number of meshs and types: 256 TRIA3
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
HULL
AFFE_CHAR_THER
TEMP_IMPO
TEMP_SUP, TEMP
TEMP_INF
AFFE_CARA_ELEM
HULL
THER_LINEAIRE
CARA_ELEM
EXCIT
RECU_CHAMP
NUME_ORDRE
3.4 Remarks
The imposed temperature, distributed sinusoïdalement on AE, entered node by node.
The data of voluminal heat CP is obligatory for Code_Aster (although without influence
in this simulation). One takes CP = 1. J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
5/8
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)
E Node n137 skin inf.
1.0
1.00000
0.00% *
1%
E Node n137 skin moy.
1.0
1.00000
0.00% *
1%
E Node n137 skin sup.
1.0
1.00000
0.00% *
1%
F Node n141 skin inf.
0.45269
0.45379
0.24%
1%
F Node n141 skin moy.
0.45269
0.45379
0.24%
1%
F Node n141 skin sup.
0.45269
0.45379
0.24%
1%
G Node n145: skin inf.
0.19927
0.20019
0.46%
1%
G Node n145: skin moy.
0.19927
0.20019
0.46%
1%
G Node n145: skin sup.
0.19927
0.20019
0.46%
1%
H Node n149: skin inf.
0.07522
0.07569
0.63%
1%
H Node n149: skin moy.
0.07522
0.07569
0.63%
1%
H Node n149: skin sup.
0.07522
0.07569
0.63%
1%
I Node n153: skin inf.
0.0
0.00000
-
2.E17 *
1.E4
I Node n153: skin moy.
0.0
0.00000
2.E17 *
1.E4
I Node n153: skin sup.
0.0
0.00000
1.E17 *
1.E4
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.36 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
6/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
PLAN (TRIA3)
n17 (D)
n1 (A)
n137 (E)
X
y
Limiting conditions:
- dimensioned AE
T= sin (
X)
- dimensioned JD, DA T= 0°C
- dimensioned EJ:
= 0
Not
X
y
Node
E
0.5
0.
n137
F
0.5
0.25
n141
G
0.5
0.5
n145
H
0.5
0.75
n149
I
0.5
1.
n153
0.5
n141 (F)
n145 (G)
n149 (H)
n153 (I)
n1
n35
n69
n103
n137
n18
n52
n86
n120
5.2
Characteristics of the mesh
A number of nodes:
153
A number of meshs and types: 256 TRIA3
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
AFFE_CHAR_THER
TEMP_IMPO
THER_LINEAIRE
EXCIT
CHARGE
5.4 Remarks
The data of voluminal heat CP is obligatory for Code_Aster (although without influence
in this simulation). One takes CP = 1. J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
7/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster difference
tolerance
Temperature (°C)
E: Node n137
1.0
1.00000
0.00% *
1%
F: Node n141
0.45269
0.45379
0.24%
1%
G: Node n145
0.19927
0.20019
0.46%
1%
H: Node n149
0.07522
0.07569
0.63%
1%
I: Node n153
0.0
0.00000
-
1.E17 *
1.E4
6.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.05 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLP301 Plates square with imposed temperature distributed sinusoïdalement
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.301-A
Page:
8/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
7
Summary of the results
2 modelings carried out, HULL and PLAN with meshs TRIA3 give results
satisfactory, the maximum change obtained is 0.63%. Results found for two modelings
are identical. The interest of this test is to compare the results obtained with an analytical solution.