Code_Aster ®
Version
6.2
Titrate:
Note of use of the model of thin hull thermal

Date:
22/01/02
Author (S):
A. Mr. DONORE, F. VOLDOIRE Key
:
U2.03.03-A Page
: 1/6

Organization (S): EDF/AMA
Handbook of Utilization
U2.03 booklet: Thermomechanical
Document: U2.03.03

Note of use of the mean model of hull
thermics

Summary

Determination of the field of temperature in a mean structure subjected to various conditions
thermics can be done advantageously using the model of thin hull thermal describes in [R3.11.01].
The temperature is described by three scalar fields, noted TEMP, TEMP_INF, TEMP_SUP defined on
surface average (X) hull, which will have to be with a grid, and by a distribution in the thickness x3 given by
:
T (X, x3) = TEMP (X) P (X
(X
(X
1
3) + TEMP_INF (X) P2
3) + TEMP_SUP (X) P3 3)
the functions P
and being given. In this model, the curvature of the hull does not intervene.
1, P2
P3
One can treat the stationary situations, as well as the problems of evolution. The latter must however
to respect a limitation: it is necessary that the moments Tc characteristics of the evolution of the loadings
are such as:

T > C H2
C
33

with:

·
C: voluminal heat of material constitutive of the hull,
·
H: half thickness of the hull,
·
33: coefficient of transverse conductivity.

One gives here the description of the Aster commands useful for calculation, classified by chronological functionalities.
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-66/02/003/A

Code_Aster ®
Version
6.2
Titrate:
Note of use of the model of thin hull thermal

Date:
22/01/02
Author (S):
A. Mr. DONORE, F. VOLDOIRE Key
:
U2.03.03-A Page
: 2/6

1
Management of work: grid

The process of the most general grid of an unspecified surface in IR3 being the triangularisation,
one must thus constitute a grid by triangles of the average surface of the hull, plunged in
IR3. That can be done with IDEAS and procedure PRE_IDEAS for the conversion of the universal file
IDEAS [U4.13.01].
In the case of a plate or of a cylinder, one can use of Ali-Baba and procedure PRE_ALIBABA
for the conversion [U4.13.02], which generates a grid plunged in IR3.

Example:

PRE_ALIBABA (

PLAQUE
: /“OUI”

/
“NON”
[DEFAUT]





CYLINDRE:
(R: radius)




);

In the case of the cylinder the plane grid (X, Y) of Ali-Baba is transformed into a grid:

(X = R cos X, y = R sin X, Z = Y)
in IR3, where R is the radius.
R
R


y
Y
X/R
B
D
F
With
X
C
E
B
D
Z
F
0
X
With
C
E
Z
2R


The cylinder created by rolling up of the plate 2D is of axis z>0; the wall external with the cylinder
corresponds to the face 2D higher Z>0.

The equations of the thermics of hull being of command 2, one will be able to use to net:

·
triangles with 3 nodes (which will give P1 elements),
·
triangles with 6 nodes (for of P2).
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-66/02/003/A

Code_Aster ®
Version
6.2
Titrate:
Note of use of the model of thin hull thermal

Date:
22/01/02
Author (S):
A. Mr. DONORE, F. VOLDOIRE Key
:
U2.03.03-A Page
: 3/6

2
Modeling, characteristics, material, loadings

·
To describe for example the materials, the loadings…, one can use constants,
functions or of the tablecloths with operators DEFI_CONSTANTE, DEFI_FONCTION or
DEFI_NAPPE [U4.21.01, - .02, - .03].

·
To affect the finite elements on the grid, one uses operator AFFE_MODELE in the way
following:

MOD = AFFE_MODELE (
MAILLAGE:
my

[grid]







AFFE:
(
TOUT
:
“OUI”












PHENOMENE: “THERMIQUE”











MODELISATION: “COQUE”)






);

·
To assign the geometrical characteristics to the elements, in fact the thickness, one must
to use operator AFFE_CARA_ELEM [U4.24.01]:

= AFFE_CARA_ELEM will cara
(MODELE: MOD
[model]








COQUE:
(TOUT
:
“OUI”












EPAIS: thick







);

·
The definition of materials and their assignment with the grid are made in a usual way [U4.23.01 and
- .02].

·
The assignment of the thermal loadings is done using operators AFFE_CHAR_THER or
AFFE_CHAR_THER_F [U4.25.02]. The various key words usable are:

I TEMP_IMPO
: (/NOEUD
: lno
/
GROUP_NO
: lgno






I TEMP
:
T1
[R]
or
[function]







I TEMP_INF
: t2
[R]
or
[function]







I TEMP_SUP
: T3
[R]
or
[function]





);

One can thus choose the ddl which will have specified values.

I EXCHANGE
:
(
/
TOUT
:
“OUI”
/
MAILLE
:
lma
/
GROUP_MA

:
lgma





I COEF_H_INF
:
hinf [R]
or
[function]
TEMP_EXT_INF
:
tinf [R]
or
[function]





I COEF_H_SUP
:
hsup [R]
or
[function]
TEMP_EXT_SUP
:
tsup [R]
or
[function]




);

One thus gives the coefficients of exchange and the outside temperatures on the walls
higher and lower. It should be noted that the coefficients of exchange also intervene in
the expression of “rigidity” in the equations, and not only (as for the temperatures
external) in the second members.
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-66/02/003/A

Code_Aster ®
Version
6.2
Titrate:
Note of use of the model of thin hull thermal

Date:
22/01/02
Author (S):
A. Mr. DONORE, F. VOLDOIRE Key
:
U2.03.03-A Page
: 4/6

Note:

The model considered here neglects the curvature of the hull. However [R1.03.01.] if the thickness
hull is not weak enough compared to the average radius of curvature, it is preferable
to correct the values of the coefficients of exchange, or else one makes an error on
temperature about:

hinf - hsup
thick
*
hinf + hsup
radius

The correction is as follows:

COEF_H_INF: the value hinf multiplied by (1 - thick X courbure_moyenne).
COEF_H_SUP: the value hsup multiplied by (1 + thick X courbure_moyenne),

·
For the plates, that does not take place to be.
·
For the cylinders, the correction will be respectively:

(1 + thick/radius), (1 - thick/radius).

I FLUX_REP
: (
/
TOUT
:
“OUI”
/
MAILLE
:
lma
/
GROUP_MA
: lgma






I FLUX_INF
: finf [R]
or
[function]







I FLUX_SUP
: fsup [R]
or
[function]





)

One thus provides the values of the flows imposed on the 2 faces of the hull.

Note:

As for the coefficients of exchange (see above), one can be brought to correct them
flow in higher or lower wall by:
(thick 1±. courbure_moyenne).

Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-66/02/003/A

Code_Aster ®
Version
6.2
Titrate:
Note of use of the model of thin hull thermal

Date:
22/01/02
Author (S):
A. Mr. DONORE, F. VOLDOIRE Key
:
U2.03.03-A Page
: 5/6

3
TOTAL command: elementary calculation, assembly,
resolution

One can be useful oneself of total command THER_LINEAIRE for a stationary calculation [U4.33.02].

temp =
THER_LINEAIRE

(MODELE: MOD









CHAM_MATER
:
chechmate











TEMP_INIT
: (STATIONNAIRE: “yes”)









EXCIT:
(CHARGE: cht













FONC_MULT: coeff
[function]












)









CARA_ELEM: will cara








);

Or one can use the core operators:

mel =
CALC_MATR_ELEM
(
OPTION
:
“RIGI_THER”
[U4.41.01]









MODELE
: MOD
,









CHAM_MATER
:
chechmate
,









CARA_ELEM
: will cara,









CHARGE
: cht








);

vel =
CALC_VECT_ELEM
(
OPTION
:
“CHAR_THER”
[U4.41.02]









MODELE
: MOD
,









CHAM_MATER
:
chechmate
,









CARA_ELEM
: will cara,









CHARGE
: cht








);

naked
= NUME_DDL
(MATR_RIGI
: mel

); [U4.42.01]

my =

ASSE_MATRICE
(MATR_ELEM
: mel




[U4.42.02]









NUME_DDL
: naked








);

vecas =
ASSE_VECTEUR
(VECT_ELEM
: vel




[U4.42.03]









NUME_DDL
: naked








);

&ma
=
FACT_LDLT
(MATR_ASSE
: my
); [U4.51.01]

temper = RESO_LDLT

(MATR_FACT
: my,




[U4.51.02]









CHAM_NO
:
vecas







);

If one wishes to solve a problem of evolution, one will be able to use a decomposition on
space clean modes [R1.03.01].

One must initially build the matrix of “mass”, then to solve the problem with the eigenvalues
associated. For that one uses the succession of the operators (with the concepts created previously
described: mel, naked, my).
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-66/02/003/A

Code_Aster ®
Version
6.2
Titrate:
Note of use of the model of thin hull thermal

Date:
22/01/02
Author (S):
A. Mr. DONORE, F. VOLDOIRE Key
:
U2.03.03-A Page
: 6/6

melma =
CALC_MATR_ELEM
(
OPTION
:
“MASS_THER”
[U4.41.01]









MODELE
: MOD
,









CHAM_MATER
:
chechmate
,









CARA_ELEM
: will cara,









CHARGE
: cht








);

mama =
ASSE_MATRICE
(
MATR_ELEM
:
melma
[U4.42.02]









NUME_DDL
: naked
,








);

modeth = MODE_ITER_INV

(
MATR_A
:
my
,
[U4.52.01]









MATR_B
: mama,









CALC_FREQ: (LIST_FREQ: l_f)








);

4
Post processing of calculation

The calculation of the heat flows in the structure can be done using the following operator:

flu = CALC_CHAM_ELEM
(
MODELE
:
MOD










CHARGE
:
cht










TEMPE
: temper









CARA_ELEM
: will cara









CHAM_MATER
:
chechmate









OPTION
: /“FLUX_ELNO_TEMP”













/“FLUX_ELGA_TEMP”








);

Option 'FLUX_ELNO_TEMP' makes it possible to calculate flows with the nodes of each element by
interpolation (the concept result is well a field with the elements).

Option “FLUX_ELGA_TEMP” makes it possible to calculate flows at the points of GAUSS of each element.

5
Impressions of results

Procedure IMPR_RESU will be used:

IMPR_RESU
(MODELE
: MOD






RESU
:
(
CHAM_GD: nom_cham)




);

nom_cham, indicating a concept of the type: temperature, flow… (field with the nodes or field with
elements).

Example:

IMPR_RESU
(MODELE
: MOD

RESU:
(CHAM_GD: temper),
RESU
:
(CHAM_GD
:
flu)




);
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-66/02/003/A

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