Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
1/8

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
V4.05.301 document

TPLP301 - Square Plaque 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.

Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
2/8

1
Problem of reference

1.1 Geometry
Y
has = 1 m
D
C
I
H
Poin
Poi ts
T
X
Y
has
B
E
0,0
0. 1
5 0,0
0. 1
00
G
E
F
0,0
0. 1
5 0,0
0. 2
25
F
G
0,0
0. 1
5 0,0
0. 3
50
G
H
0,0
0. 2
5 0,0
0. 1
75
F
H
I
0,0
0. 2
5 0,0
1. 2
00
0,02 0,03
X
With
E
B
0,03 0,04
Tp = sin (X)


1.2
Properties of material


=
1. W/m.°C
Thermal conductivity

1.3
Boundary conditions and loadings

· side [AB]
imposed temperature Tp = sin (X),
· side [BC]
imposed temperature T0 = 0°,
· side [CD]
imposed temperature T0 = 0°,
· side [BA]
imposed temperature T0 = 0°.

1.4 Conditions
initial

Without object.

Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
3/8

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 have quadrilateral
element ", Int. J. num. Meth. Engng, flight 20, n°5, p 931-948, 1984.
Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
4/8

3 Modeling
With

3.1
Characteristics of modeling

COQUE (TRIA3)

y
0.5
n17 (D)
n153 (I)
Limiting conditions:
- dimensioned AE
T= sin (X)
n149 (H)
- dimensioned JD, DA T= 0°C
- dimensioned EJ:
= 0
n145 (G)
Not
X
y
Node
E
0.5
0.
n137
F
0.5
0.25
n141
n141 (F)
G
0.5
0.5
n145
H
0.5
0.75
n149
I
0.5
1.
n153
n1 (A)
n137 (E)
n1
n35
n69
n103
n137
X
n18
n52
n86
n120


3.2
Characteristics of the grid

A number of nodes:
153
A number of meshs and types: 256 TRIA3

3.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
COQUE

AFFE_CHAR_THER
TEMP_IMPO
TEMP_SUP, TEMP
TEMP_INF

AFFE_CARA_ELEM
COQUE

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/m3 °C.

The condition limits = 0. is implicit on the free edges.
Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
5/8

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster difference
tolerance
Temperature (°C)









E Noeud n137 skin inf.
1.0
1.00000
0.00% *
1%
E Noeud n137 skin moy.
1.0
1.00000
0.00% *
1%
E Noeud n137 skin sup.
1.0
1.00000
0.00% *
1%
F Noeud n141 skin inf.
0.45269
0.45379
0.24%
1%
F Noeud n141 skin moy.
0.45269
0.45379
0.24%
1%
F Noeud 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

Obstruction memory:
8 megawords
Time CPU To use: 2.36 seconds
Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
6/8

5 Modeling
B

5.1
Characteristics of modeling

PLAN (TRIA3)

y
0.5
n17 (D)
n153 (I)
Limiting conditions:
- dimensioned AE
T= sin (X)
n149 (H)
- dimensioned JD, DA T= 0°C
- dimensioned EJ:
= 0
n145 (G)
Not
X
y
Node
E
0.5
0.
n137
F
0.5
0.25
n141
n141 (F)
G
0.5
0.5
n145
H
0.5
0.75
n149
I
0.5
1.
n153
n1 (A)
n137 (E)
n1
n35
n69
n103
n137
X
n18
n52
n86
n120


5.2
Characteristics of the grid

A number of nodes:
153
A number of meshs and types: 256 TRIA3

5.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
PLAN
TOUT
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/m3 °C.

The condition limits = 0. is implicit on the free edges.
Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
7/8

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

Obstruction memory:
8 megawords
Time CPU To use: 2.05 seconds
Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Square TPLP301 Plaque with imposed temperature distributed sinusoïdalement Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.05.301-A Page:
8/8

7
Summary of the results

2 modelings carried out, COQUE 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.

Handbook of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A

Outline document