Code_Aster ®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane Mur in stationary thermics

Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.02.100-B Page:
1/6

Organization (S): EDF/AMA

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
Document: V4.02.100

TPLL100 - Anisotropic plane Mur in thermics
stationary

Summary:

This test the purpose of which relates to it thermal linear stationary and transitory be to validate the anisotropy
Cartesian.

Two modelings are carried out:

· a first into voluminal,
· a second in plan.

The results obtained are in perfect agreement with the analytical values.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane Mur in stationary thermics

Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.02.100-B Page:
2/6

1
Problem of reference

1.1 Geometry


Z 0
J
I
Y 0
K
E
B
H
Z 1
D
X 1
Y
G 1
F
X
With
0
C


In the reference mark (X0, Y0, Z0), the points have as co-ordinates:

C (0.03; 0; 0)
D (0.07; 0.03; 0)
E (0.04; 0.07; 0)
F (0; 0.04; 0)
To (0.015; 0.02; 0)
B (0.055; 0.05; 0)
G (0.035; 0.035; 0)



FK = CH = DI = EJ = 0,05.Z0
(


,
CD X = rad

Z//Z
1)
0
1
4

1.2
Material properties

Anisotropic material, direction privileged along the axes of the reference mark (X1, Y1, Z1):

X = 1 W/°
m C
Y = 0.5 W/°
m C
Z = 2 W/°
m C
C = 2 J/M3

° C
p

1.3
Boundary conditions and loadings

face FEJK: Outgoing flow of 400 W/m2.

face CDIH: Entering flow of 400 W/m2.

face EDIJ: Outgoing flow of 1.200 W/m2.

face FCHK: Imposed temperature 100°C.

Others faces: condition of Neumann.

1.4 Conditions
initial

To make this stationary calculation, a transitory calculation is made for which the boundary conditions are
constants in time. This makes it possible to test elementary calculations of mass and rigidity
intervening in the first member as well as the second member.

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

Code_Aster ®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane Mur in stationary thermics

Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.02.100-B Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

Analytical solution.
Temperature varying linearly according to CD.

Isotherms parallel with faces CHKF and DIJE.

CD CH CF
:
locate



In

,
,

:
has

one
,
CD CH


CF

- (
2
2
T


X cos

+ Y
sin

)



X
X


T
= - -

y
()
cos

sin



X



Z
0





:
with
X = 1200 y = 400 = (X, 1CD) -
T (X)
X
=
X + T (A)

2
2
X cos + Y
sin
1
:

that is to say T (X) = -

1600 X + 20
.X = cos X - sin y
720

that is to say
O

if = (CD, Xo). =sin +
cos
720

that is to say
Y
X
Z
O

2.2
Results of reference

Temperature at the points A, B, G.

Flow following the directions Xo and Yo.

T (A) = 100
T (B) = 20
T (G) = 60
X = 720
Y
O
O = 1040

2.3 References
bibliographical

[1]
NR. RICHARD: Note technical HM-18/94/0011, “Développement of the thermal anisotropy
in the Aster software ".

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

Code_Aster ®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane Mur in stationary thermics

Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.02.100-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

diagram in time, forced on 1 to test the calculation of the second member.
4 elements 3D, HEXA8.

3.2
Characteristics of the grid

4 Hexa 8.

3.3 Functionalities
tested

Commands
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
--
ANGL_REP
--
MAILLE
AFFE_MODELE
AFFE
MODELISATION
“3D”
THER_LINEAIRE
TEMP_INIT
STATIONNAIRE
“OUI”
INCREMENT
LIST_INST
--
PARM_THETA
1.
--
CARA_ELEM
CALC_NO
--
OPTION
“FLUX_ELNO_TEMP”
CALC_CHAM_ELEM
--
CARA_ELEM
--
OPTION
“FLUX_ELNO_TEMP”
--
OPTION
“FLUX_ELGA_TEMP”

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
T (A) N7 *
100°
100°
0.
T (B) N2
20°C
20°C
0.
T (G) N13
60°C
60°C
0.
Xo
720.720 0.
Yo
1040 1040
0.

*: imposed temperature

4.2 Remarks

The analytical solution being of command 1 and the field represented by the discretization, the code finds,
with the round-off errors close, this solution.

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

Code_Aster ®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane Mur in stationary thermics

Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.02.100-B Page:
5/6

5 Modeling
B

5.1
Characteristics of modeling

Similar to the modeling A, but solved in 2D in plan CDEF.

5.2
Characteristics of the grid

4 QUAD 4.

5.3 Functionalities
tested

Commands
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
--
ANGL_REP
--
MAILLE
AFFE_MODELE
AFFE
MODELISATION
“PLAN”
THER_LINEAIRE
TEMP_INIT
STATIONNAIRE
“OUI”
INCREMENT
LIST_INST
--
PARM_THETA
1.
--
CARA_ELEM
CALC_NO
--
OPTION
“FLUX_ELNO_TEMP”
CALC_CHAM_ELEM
--
CARA_ELEM
--
OPTION
“FLUX_ELNO_TEMP”
--
OPTION
“FLUX_ELGA_TEMP”

6
Results of modeling B

6.1 Values
tested

Identification Reference
ASTER %
difference
T (A) N5 *
100°
100°
0.
T (B) N2
20°C
20°C
0.
T (G) N8
60°C
60°C
0.
Xo
720.720 0.
Yo
1040 1040
0.

*: imposed temperature

6.2 Remarks

The analytical solution being of command 1 and the field represented by the discretization, the code finds,
with the round-off errors close, this solution.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane Mur in stationary thermics

Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.02.100-B Page:
6/6

7
Summary of the results

Key word ANGL_REP introduced into command AFFE_CARA_ELEM is thus tested in 3D and plane 2D
on an anisotropic problem of thermics.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A

Outline document