Code_Aster ®
Version
5.0
Titrate:
Circular TPLA300 Plaque subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.300-A Page:
1/6

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
V4.01.300 document

TPLA300 - Circular Plaque subjected to a source
of voluminal heat

Summary:


This test results from the validation independent of version 3 in linear stationary thermics.

The interest of this case test plane 2D is to validate a thermal element under various boundary conditions
(imposed temperature, heat source).

This case test includes/understands two modelings 2D, one axisymmetric, the other planes.

The results are compared with an analytical solution.

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Circular TPLA300 Plaque subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.300-A Page:
2/6

1
Problem of reference

1.1 Geometry
R=5.0
With
O
Q


1.2
Properties of material

= 0.04 W/m.°C thermal Conductivité

1.3
Boundary conditions and loadings

· voluminal heat source Q = 1W/m3,
· temperature imposed on surface outside (R = 5): T = 0°C.

1.4 Conditions
initial

Without object.

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Circular TPLA300 Plaque subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.300-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

Analytical solution:

T (R) = 6.25 (25 - r2)

2.2
Results of reference

Temperature for R = 0., 0.625, 1.25, 1.875, 2.5, 3.125, 3.75, 4.375, 5.

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 have quadrilateral
element ", Int. J. num. Meth. Engng, flight 20, n°5, p 931-948, 1984.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Circular TPLA300 Plaque subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.300-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

PLAN (QUAD4)

y
C
N17
N15
N13
N184
N168
N11
N151
Limiting conditions:
N9
N133
- dimensioned AB = 0
N7
N108
- dimensioned CA = 0
- dimensioned BC T = 0°C
N5
N3
B
N1
In N45 N116 N171 N207
X
N79 N146 N191 N217


3.2
Characteristics of the grid

A number of nodes:
217
A number of meshs and types: 192 QUAD4

3.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
PLAN
TOUT
AFFE_CHAR_THER
TEMP_IMPO
SOURCE

THER_LINEAIRE
EXCIT
CHARGE

RECU_CHAMP
NUME_ORDRE


Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Circular TPLA300 Plaque subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.300-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
tolerance
temperatures (°C)









R = 0.000 (N1)
156.25
156.07
- 0.114
1%
R = 0.625 (N3)
153.81
153.63
- 0.116
1%
R = 0.625 (N45)
153.81
153.63
- 0.116
1%
R = 1.250 (N5)
146.48
146.31
- 0.117
1%
R = 1.250 (N79)
146.48
146.31
- 0.117
1%
R = 1.875 (N7)
134.28
134.10
- 0.131
1%
R = 1.875 (N116)
134.28
134.10
- 0.131
1%
R = 2.500 (N9)
117.19
116.98
- 0.182
1%
R = 2.500 (N108)
117.19
116.82
- 0.313
1%
R = 2.500 (N146)
117.19
116.98
- 0.182
1%
R = 3.125 (N11)
95.21
95.04
- 0.178
1%
R = 3.125 (N133)
95.21
95.00
- 0.216
1%
R = 3.125 (N171)
95.21
95.04
- 0.178
1%
R = 3.750 (N13)
68.36
68.23
- 0.191
1%
R = 3.750 (N151)
68.36
68.21
- 0.214
1%
R = 3.750 (N191)
68.36
68.23
- 0.191
1%
R = 4.375 (N15)
36.62
36.55
- 0.194
1%
R = 4.375 (N168)
36.62
36.54
- 0.211
1%
R = 4.375 (N207)
36.62
36.55
- 0.194
1%
R = 5.000 (N17)
0.00 *
0.00
0.00
1%
R = 5.000 (N217)
0.00 *
0.00
0.00
1%
R = 5.000 (N184)
0.00 *
0.00
0.00
1%

* Limiting condition

4.2 Parameters
of execution

Version: 5.03


Machine: SGI - ORIGIN 2000 - R12000

Obstruction memory:
8 megawords
Time CPU To use: 1.98 seconds
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Circular TPLA300 Plaque subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.300-A Page:
6/6

5
Summary of the results

The results obtained are very satisfactory, the maximum change is 0.313%.

Among the points of observation, the most important variation is noted with the N108 node which belongs to
the element more deformed grid.

The grid used is that proposed in the reference. A radial grid with the same cutting and
with the same meshs should give better results.

This test made it possible to test the taking into account of a source term within meshs QUAD9 with one
modeling AXIS (AFFE_CHAR_THER associated with key word SOURCE).

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Outline document