Code_Aster ®
Version
7.4
Titrate:
Operator THER_NON_LINE_MO


Date:
20/01/05
Author (S):
C. Key DURAND
:
U4.54.03-D Page
: 1/6
Organization (S): EDF-R & D/AMA
Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.54.03
Operator THER_NON_LINE_MO

1 Goal

To calculate the nonlinear stationary thermal response with mobile loading.

This operator allows to solve the equation of stationary heat in a mobile reference frame related to
a loading and moving in a given direction and at a speed [R5.02.04].

Nonthe linearities of the problem come as well from the characteristics of material which depend
temperature, that boundary conditions of the radiation type.

The problems of this type can be dealt with with models using of the finite elements of
structure plans, axisymmetric and three-dimensional.

The concept produced by this operator is of evol_ther type as for an analysis by
THER_LINEAIRE [U4.54.01] or THER_NON_LINE [U4.54.02], but it contain one number
of command since a stationary calculation is carried out.

Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator THER_NON_LINE_MO


Date:
20/01/05
Author (S):
C. Key DURAND
:
U4.54.03-D Page
: 2/6

2 Syntax


temper [evol_ther] = THER_NON_LINE_MO

(
MODELE
=
Mo,
[model]



CHAM_MATER =
chmat,
[cham_mater]


EXCIT =_F (









CHARGE
=
tank,
[char_ther]






),



TEMP_INIT =_F (








EVOL_THER
=
temp,
[evol_ther]








NUME_INIT
=/nuini_evol, [I]
/
0,
[DEFAUT]







),



CONVERGENCE =_F (








CRIT_TEMP_RELA =/1.E-3,
[DEFAUT]
/
testr,
[R]








CRIT_ENTH_RELA =/1.E-2,
[DEFAUT]
/
testl,
[R]








ITER_GLOB_MAXI =/10,
[DEFAUT]
/
iterl,
[R]







),


SOLVEUR =_F (see document [U4.50.01])






),


TITER
=
titrate,
[l_Kn]

);

Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator THER_NON_LINE_MO


Date:
20/01/05
Author (S):
C. Key DURAND
:
U4.54.03-D Page
: 3/6

3 Operands

3.1 Operand
MODELE

MODELE = Mo

Name of the model whose elements are the subject of thermal calculation.

3.2 Operand
CHAM_MATER

CHAM_MATER = chmat

Name of the affected material field on the model.

3.3 Word
key
EXCIT

EXCIT
=

Key word factor allowing to define several loadings. For each occurrence of the key word
factor, one defines a time-constant load.

3.3.1 Operand
CHARGE



CHARGE = tank

Concept of the type charges produces by AFFE_CHAR_THER or AFFE_CHAR_THER_F
[U4.44.02].

Important remarks:

For each occurrence of the key word factor EXCIT the various concepts tank used
must be built on the same model Mo.

In addition, operator AFFE_CHAR_THER or AFFE_CHAR_THER_F must obligatorily
to inform under the key word factor CONVECTION a concept of the cham_no_DEPL_R type
defining the rate of travel of the field and product by AFFE_CHAM_NO.

It is necessary to take care to define boundary conditions coherent with the run of the part
(or of the loading, according to the selected reference frame) and the assumption of stationnarity:

If the solid is animated of a uniform translatory movement at constant speed, it is
equivalent to consider the field of temperature calculated:
· like a photograph at a given moment,
· or like a temporal succession of the card of temperature in a section
of fixed, orthogonal X-coordinate with the direction of run.
Mobile loading
v = scrolling speed
C.L temperature
Adiabatic C.L
imposed
time
T = 0
T = infinite

Thus, downstream under space (early in time), the boundary condition on the edge of
coin must impose the temperature of the coin before does not arrive the mobile loading.
Upstream in space (or late in time), a heat flux no one (adiabaticity)
the assumption of stationnarity guarantees.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator THER_NON_LINE_MO


Date:
20/01/05
Author (S):
C. Key DURAND
:
U4.54.03-D Page
: 4/6

3.4 Word
key
TEMP_INIT

TEMP_INIT = litps

Allows to define the initial field from which calculation in pointer under condition of
stationnarity is carried out.

3.4.1 Operand
EVOL_THER



EVOL_THER = temp

Name of the structure of data of the evol_ther type whose the field is extracted from
temperature from which the solution with the problem is calculated.

3.4.2 Operand
NUME_INIT




NUME_INIT =/nuini_evol
/
0
[DEFAUT]

Sequence number of the field to be extracted from this structure of data.

Note:

For this type of calculation, there is no initial condition to define (it is defined with one
boundary condition on an edge of the field defined by the model). But, one can
nevertheless to carry out stationary calculation starting from a field of temperature already calculated
as solution of the problem for part of the load only. That can be useful
if the application of the totality of the loading makes convergence difficult. One
can then connect several resolutions with a loading which evolves/moves
gradually and to take as reiterated first of a calculation running the solution of calculation
precedent. Concretely, one uses key word TEMP_INIT then to define the field of
temperature with which one wants to initialize current calculation.

3.5 Word
key
CONVERGENCE


CONVERGENCE =

Allows to define the values associated with the criteria with convergence:

3.5.1 Operand
CRIT_TEMP_RELA




CRIT_TEMP_RELA =/1.e-3
/
testr

The algorithm continues the iterations as long as the relative variation of reiterated is higher than
testr.



where
indicate the value of the temperature to node I for the nth iteration.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator THER_NON_LINE_MO


Date:
20/01/05
Author (S):
C. Key DURAND
:
U4.54.03-D Page
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3.5.2 Operand
CRIT_ENTH_RELA




CRIT_ENTH_RELA =/1.e-2
/
testl

The algorithm continues the iterations as long as the relative variation of reiterated is higher than
testl.



where
indicate the value of the enthalpy to the nth iteration at the iième point of Gauss.

3.5.3 Operand
ITER_GLOB_MAXI




ITER_GLOB_MAXI =/10
/
iterl

The algorithm continues the external iterations as long as the iteration count external is
lower than iterl.

3.6 Word
key
SOLVEUR


SOLVEUR =

This key word factor is optional: it makes it possible to choose another solvor of resolution of system.

This operand is common to the whole of the total commands [U4.50.01].

3.7 Operand
TITER

TITER = title

Titrate that one wants to give to the result stored in temp structure of data of the evol_ther type
[U4.03.01].

4 Modeling

The problems of nonlinear thermics in pointer and under condition of stationnarity can
to be treated with models using the finite elements 3D or plane 2D described in the documents
[U3.23.01] and [U3.24.01].
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator THER_NON_LINE_MO


Date:
20/01/05
Author (S):
C. Key DURAND
:
U4.54.03-D Page
: 6/6

5 Examples

One presents below the principal commands used to carry out a calculation of thermics
non-linear in pointer and under condition of stationnarity.

conduc =
DEFI_FONCTION (
NOM_PARA
=
“TEMP”,
VALE =
(


20.0,
95.0,

500.0, 325.0,
1000.0, 700.0
),
PROL_DROIT =
“CONSTANT”,
PROL_GAUCHE=
“CONSTANT”,








)

enthal =
DEFI_FONCTION
(
NOM_PARA
=
“TEMP”,
VALE =
(



0.0, 0.0,

500.0, 1.40E9,

510.0, 3.50E9,
1200.0, 4.70E9
),
PROL_DROIT =
“LINEAIRE”,
PROL_GAUCHE=
“LINEAIRE”,








)

chechmate =
DEFI_MATERIAU
(THER_NL=
_F (LAMBDA =
conduc,
BETA =
enthal
),)


chavi = AFFE_CHAM_NO
(MAILLAGE = mall,
SIZE = “DEPL_R”,
AFFE =_F (ALL = “YES”,
NOM_CMP = (“DX”, “DY”),
VALE_R = (1.0, 0.0))

tank = AFFE_CHAR_THER
(
MODELE =
model,
FLUX_REP =_F (GROUP_MA = penny,
FLUN = 5.E6),
CONVECTION =_F (SPEED =
chavi)
)

temple
=
THER_NON_LINE_MO
(
MODELE
=
model,
CHAM_MATER =
chmat,
EXCIT
=_F (CHARGE =
tank
),








)


FIN ()


Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

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