Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
1/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
Organization (S):
EDF-R & D/AMA
Data-processing manual of Description
D9.05 booklet: -
Document: D9.05.03
New architecture THM. Integration of
equilibrium equations
Summary:
In order to allow the development of rather general nonlinear laws of behavior in the module
THM of Code_Aster, it appeared necessary to completely separate the equilibrium equations and the relations
of behavior.
This document defines the principles of this separation, and described the specifications of under program
credits EQUTHM, integrating one or more equilibrium equations and calling the laws of behavior.
One supposes that the medium can be made up with more than one solid and of two components, each of these two
components being able to exist under two phases. Each one of these elements can or not exist, it thermal can
to be taken into account or not. The thermal equation not takes into account a formulation in entropy, but
in energy utilizing mass enthali of the components.
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
2/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
Count
matters
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
3/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
1
Variational writings of the equilibrium equations
1.1 Mechanics
One leaves the following differential writing:
Div
R
m
+
=
F
0
éq 1.1-1
We will further see we always adopt the decomposition
=
+
p
I
, where
indicate
the effective stress.
It is thus with the load of the module of integration of the equilibrium equations to make the sum:
=
+
p
I
.
One will then write a variational form of [éq 1.1-1] at time
T
+
.
()
+
+
+
+
+
=
+
=
+
+
+
p
I
R
U
m
ext.
AD
.
.
v
F
v
F
v
v
éq
1.1-2
1.2 Hydraulics
One leaves the following differential writing:
()
DM
dt
Div
+
=
M
0
éq
1.2-1
It is considered that there can be two components, and for each one D `them two phases.
More precisely, variables
m
1
1
, M
and
m
2
2
, M
refer each one to a component of mass
conservative.
One poses by principle:
m
m
m
m
m
m
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
2
2
1
2
2
=
+
=
+
=
+
=
+
;
;
M
M
M
M
M
M
What we will write:
m
m
component
component
phase
Nb phasedu
component
component
component
phase
Nb phasedu
component
=
=
M
M
In the applications, one could for example have:
2 components: air and water
2 phases for water
1 phase for the air
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
4/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
One would have then:
m and
1
1
1
1
M
: contribution of mass and liquid water flow
m and
1
2
1
2
M
: contribution of mass and vapor flow
m and
2
1
2
1
M
: contribution of mass and flow of dry air
m and
2
2
2
2
M
: non-existent
It is considered that there are two pressures. No assumption is made on what the pressures mean
p
p
1
2
and
, that will depend on the laws of behavior and the way which one will choose to write them: one
could for example choose:
p
p
Z
1
2
=
=
capillary pressure (p (gas) - p (fluid))
pressionde ga (vapor + air)
One will write then a variational form of [éq 1.2-1].
(
)
(
)
(
)
-
+
+
+
=
+
D m
m
dt
P
ext.
ext.
AD
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
M
M
M
M
.
.
éq
1.2-2
(
)
(
)
(
)
AD
ext.
ext.
P
dt
m
m
D
2
2
2
2
2
12
2
2
2
12
2
2
2
12
.
.
+
=
+
+
+
-
M
M
M
M
éq
1.2-3
After discretization by a teta method:
(
)
(
)
(
)
(
)
(
)
(
)
-
+
+
+
=
-
+
- -
+
+
+
+
+
+
+
-
-
-
-
m
m
T
m
m
T
T
P
ext.
ext.
AD
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
M
M
M
M
M
M
.
.
.
éq
1.2-4
(
)
(
)
(
)
(
)
(
)
(
)
-
+
+
+
=
-
+
- -
+
+
+
+
+
+
+
-
-
-
-
m
m
T
m
m
T
T
P
ext.
ext.
AD
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
2
2
1
M
M
M
M
M
M
.
.
.
éq
1.2-5
1.3 Thermics
We introduce the enthali of each phase of each component:
H
C
p
m
We note:
Np
C
the number of phases of the component C.
We adopt the rule of summation of the dumb indices:
H
H
C
p
m
C
p
C
I
m
C
I
I
Np
C
M
M
=
=
1
H DM
dt
H DM
dt
C m
p
C
p
C m
I
C
I
I
Np
C
=
=
1
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
5/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
The equation of thermics (or energy) is written:
(
)
dQ
dt
H DM
dt
Div H
R
C m
p
C
p
C
p
m
C
p
C
p
m
'
.
+
+
+
= +
M
Q
MR. F
éq
1.3-1
One will then write a variational form of [éq 1.3-1] without injecting the hydraulic equilibrium equation there:
(
)
(
)
(
)
dQ
dt
H
DM
dt
H
R
H
T
C
p
m
C
p
C
p
m
C
p
C
p
C
p
m
C
p
ext.
ext.
AD
'
.
.
.
+
-
+
=
+
-
+
M
Q
MR. F
M
Q
éq 1.3-2
The discretization of [éq 1.3-2] by teta method leads to:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
Q
Q
T
H
T
H
H
m
m
H
m
m
T
T
T R
T
H
C
p
m
C
p
C
p
m
C
p
C
p
m
C m
p
C m
p
C
p
m
C m
p
C m
p
C
p
m
C
p
m
C
p
m
C
p
ext.
ext.
'
'
…
.
.
.
+
-
+
+
+
-
-
-
+
-
+
-
-
-
+
- -
+
+
+
-
+ -
-
=
+
+ -
+
-
+
+
-
+
-
M
Q
M
Q
M
F
M
F
M
Q
1
1
1
T
AD
éq 1.3-3
One notices in the equation [éq 1.3-3] a term of contribution of heat by the flow of fluid at the edge of
field:
(
)
H
C
p
m
C
p
ext.
ext.
M
Q
+
.
.
One will be able in makes consider that the conditions of heat flux define directly:
~
Q
M
Q
ext.
C
p
m
C
p
ext.
ext.
H
=
+
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
6/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
2 Laws
of
behavior
2.1 Mechanics
2.1.1 Writing
general
(
)
(
)
=
=
-
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
,
,
,
,
,
;
,
,
,
,
,
,
,
,
;
,
,
,
2
1
2
1
2
1
2
1
T
p
p
T
p
p
T
p
p
T
p
p
éq
2.1.1-1
2.1.2 Case of the effective stresses
In the case of the assumption of the effective stresses, this function will break up in the form:
scalar
one
is
effective
S
stress
tensor
is
:
p
p
I
+
=
(
)
(
)
=
=
+
+
+
+
-
-
-
-
+
+
+
+
-
-
-
-
,
;
,
,
,
,
;
,
,
,
T
T
T
T
éq
2.1.2-1
(
)
(
)
p
p
H
H
H
H
p p p p
p p p p
+
+
+
+
-
-
-
+
+
+
+
-
-
-
=
=
1
2
1
2
1
2
1
2
,
;
,
,
,
;
,
,
éq
2.1.2-2
It is noticed that in this decomposition:
·
the dependence compared to thermics was left in the effective stresses;
typically, it is thought that the laws on the effective stresses are written as in thermo
conventional mechanics:
(
)
=
-
-
+
+
+
+ +
-
- -
-
-
T
T
;
,
,
·
one distinguished the internal variables relating to the law from behavior on the stresses
effective, that one wrote
, the variables intern origin hydraulics which one has
written
H
and the variables intern thermal origin which one wrote
T
(see
following paragraphs).
2.1.3 Choice of the stresses
Because of rather frequent use of the assumption of the effective stresses, one decides that it
vector of the stresses for the mechanical part contains in all the cases the tensor of the stresses
effective
and the scalar
p
. In the general case where the assumption of the effective stresses is not
not retained, one will have simply:
0
=
p
.
It is thus with the load of the module of integration of the equilibrium equations to make the sum:
=
+
p
I
.
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
7/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
2.2 Hydraulics
The hydraulic law of behavior will provide the following relations:
(
)
m
m
p p T
p p T m
p
p p
p T
T
p
p p
p T
T
this pde with Np
C
p
C
p
D
Q
D
Q
H
C
p
C
p
D
Q
H
m
C
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
-
+
=
=
,
,
,
; ,
,
,
,
,
,
,
,
,
,
,
,
;
,
,
,
,
,
,
,
,
;
_
_
1
2
1
2
1
1
2
2
1
1
2
2
1
M
M
M
M
F
(
)
H
H
H
p p T
p p T m m
+
+
+
+
+
+
-
-
-
-
-
-
=
,
,
,
; ,
,
,
,
,
,
_
1
2
1
2
1
2
éq 2.2-1
It is noticed that the field of gravity is a data of the hydraulic law of behavior by it
that the evolution of the vector of flow follows relations of the type:
[
]
M
F
=
- +
H
fl
fl
m
P
.
2.3 Thermics
The laws of behavior will provide:
(
)
(
)
(
)
Q
Q
p p T
p p T S
H
H
p p T
p p T S
this pde with Np
p p T
T
p p T
T
p p
C
p
m
C
p
m
D
Q
m
C
T
T
'
'
,
,
,
; ,
,
,
,
,
,
,
; ,
,
,
,
,
,
,
,
; ,
,
,
,
,
,
,
,
+
+
+
+
+
+
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
+
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
=
=
=
=
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
Q
Q
Q
(
)
(
)
T
T
p p T
T
With H
H
H
H
H
T
D
Q
m
m
m
m
m
+
+
-
-
-
-
-
-
-
-
-
-
-
=
,
; ,
,
,
,
,
,
,
,
1
2
1
1
1
2
2
1
2
2
éq 2.3-1
2.4
homogenized density
R
R
m
m
m
m
+
+
+
+
+
= +
+
+
+
0
1
1
1
2
2
1
2
2
éq
2.4-1
3 Efforts
generalized
It arises of what is written higher than the generalized stresses are:
,
;
,
,
;
,
,
;
,
,
;
,
,
;
',
p
m
m
m
m
m
H
m
H
m
H
m
H
Q
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
1
2
2
2
2
2
2
M
M
M
M
Q
The associated generalized deformations are:
()
U
U
,
;
,
;
,
; ,
p
p
p
p
T
T
1
1
2
2
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
8/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
4
Algorithm of resolution
4.1
Nonlinear algorithm of resolution of the equilibrium equations
In the general case of modeling (variable coefficients, desaturation, convection) the problem
variational presented above is nonlinear compared to the fields of displacement, pressure and
temperature. After discretization by finite elements, one obtains a nonlinear matric system.
stamp resolution contains moreover one nonsymmetrical term and is treated like such (not
symmetrization of this matrix to use methods of minimum). One uses in all the cases of
modeling the nonlinear solvor of Code_Aster
STAT_NON_LINE
resting on a method of
Newton-Raphson, described in [R5.03.01]. Its principle is as follows (the equations corresponding to
processing by dualisation of the boundary conditions are not indicated explicitly here).
The equilibrium equation thermo poro-mechanics at the moment
T
+
, knowing at the previous moment
(
)
U
-
-
-
,
P T
, as well as the possible internal variables is written:
(
)
()
(
)
F
P T
L T
G
P T
I
E
U
U
+
+
+
+
-
-
-
=
-
,
,
,
To find the solution of this nonlinear equation, a continuation is built:
·
initialized by a prediction which gives
(
) (
) (
)
U
U
U
0
0
0
0
0
0
,
,
,
,
,
P T
P T
P
T
=
+
- - -
:
(
)
(
)
() ()
DF
P
T
L T
L T
I
P
T
E
E
U
U
-
-
-
·
=
-
+
-
,
,
0
0
0
·
corrected by recursion giving
(
) (
) (
)
U
U
U
N
N
N
N
N
N
N
N
N
P
T
P T
P
T
+
+
+
+
+
+
=
+
1
1
1
1
1
1
,
,
,
,
,
:
(
)
(
)
()
(
)
DF
P
T
F
P T
L T
G
P T
I
N
N
N
I
N
N
N
E
·
= -
+
-
+
+
+
+
-
-
-
U
U
U
1
1
1
,
,
,
,
The following notations were adopted:
·
(
)
F
P T
I
U
,
contains the work of deformation, the contributions to the current moment of the terms
of hydraulic and thermal dissipation expressed within
- method, and of the variations
of fluid contribution of mass and entropy;
·
DF
I
appoint the tangent operator, who can not be brought up to date with each iteration in
(
)
U
N
N
N
P T
,
, according to a compromise cost calculation-speed of convergence; convergence is
checked by a test on the relative standard of the difference of reiterated successive (via the key word
INCO_GLOB_RELA
);
·
(
)
G
P T
U
-
-
-
,
contains the contributions to the previous moment of the terms of dissipation
hydraulics and thermics expressed within
- method, and of the variations of contribution of
mass fluid and of entropy;
·
()
L T
E
indicate the virtual work of the “dead” forces external and external contributions
hydraulics and of heat expressed by
- method.
With convergence with the iteration
N
+
1
, an updating of the fields is operated
(
) (
)
U
U
+
+
+
+
+
+
=
,
,
P
T
P
T
N
N
N
1
1
1
.
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
9/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
In the version present of algorithm THM, we decided to gather all the terms y
included/understood those due to the following forces and those of time less:
While posing:
(
)
(
) (
)
-
= -
-
-
-
-
R
P T
F
P T
G
P T
I
N
N
N
I
N
N
N
U
U
U
,
,
,
, therefore
DF
DR.
I
I
=
one has finally:
(
)
(
)
()
DF
P
T
R
P T
L T
I
N
N
N
I
N
N
N
E
·
= -
+
+
+
+
+
U
U
1
1
1
,
,
,
The general algorithm of balance will be written then, for a pitch of time:
Initializations:
Calculation of
()
L T
E
+
(option
CHAR_MECA
)
Calculation of
(
)
DF
I
P
T
U
-
-
-
,
(option
RIGI_MECA-TANG
)
Calculation of
(
)
U
0
0
0
,
P
T
by:
(
)
(
)
() ()
DF
P
T
L T
L T
I
P
T
E
E
U
U
-
-
-
·
=
-
+
-
,
,
0
0
0
Iterations of balance of Newton N
If option
FULL_MECA
:
Calculation of
(
)
DF
I
P T
N
N
N
U
+
+
+
,
,
and
(
)
-
+
+
+
R
P T
I
N
N
N
U
,
,
:
update stamps tangent:
(
)
DF
DF
I
I
P T
N
N
N
=
+
+
+
U,
,
If option
RAPH_MECA
Calculation of
(
)
-
+
+
+
R
P T
I
N
N
N
U
,
,
Calculation of
(
)
U
N
N
N
P
T
+
+
+
1
1
1
,
,
by:
(
)
(
) ()
DF
P
T
R
P T
L T
I
N
N
N
I
N
N
N
E
·
= -
+
+
+
+
+
+
+
+
U
U
1
1
1
,
,
,
,
Updating:
(
) (
)
(
)
U
U
U
N
N
N
N
N
N
N
N
N
P
T
P T
P
T
+
+
+
+
+
+
+
+
+
+
+
+
=
+
1
1
1
1
1
1
,
,
,
,
,
,
IF test convergence OK
fine Newton: no next time
If not
N = n+1
4.2
Loop on the elements, the points of Gauss
As in all the codes of finite elements, the terms are calculated by loop on the elements and
loop on the points of gauss:
(
)
(
)
(
)
(
)
R
P T
W R
P T
DF
W DF
I
N
N
N
G
el
G
el
I
N
N
N
G
el
I
P T
G
el
G
el
I
P T
G
el
N
N
N
N
N
N
U
U
U
U
+
+
+
+
+
+
=
=
+
+
+
+
+
+
,
,
,
,
,
,
,
,
Code_Aster
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New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
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C. CHAVANT
Key
:
D9.05.03-A
Page
:
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Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
Let us note:
{}
X
el
the vector of the nodal unknown factors, on a finite element el
{}
3
node
2
node
1
node
example
by
=
T
p
p
W
v
U
T
p
p
W
v
U
T
p
p
W
v
U
X
el
2
1
2
1
2
1
In this paragraph, to simplify the presentation, we suppose that we deal with one
supporting finite element of the ddl of displacement, two ddl of pressure and a ddl of temperature.
Let us note
{}
G
el
the vector of the deformations generalized at the point of gauss G of the element el
For example:
{}
()
G
el
p
p
p
p
T
T
=
U
U
1
1
2
2
We note
{}
G
el
the vector of stresses generalized for the point of Gauss G of the element el
Code_Aster
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New architecture THM. Integration of the equilibrium equations
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Key
:
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:
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For example, and always in the most complete case:
{}
G
el
p
m
m
m
m
m
H
m
H
m
H
m
H
Q
=
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
1
2
2
2
2
2
2
M
M
M
M
Q
'
The routines finite elements calculate the matrix:
[]
B
G
el
defined by:
{}
[]
{}
G
el
G
el
B
X
=
Code_Aster
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New architecture THM. Integration of the equilibrium equations
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Key
:
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:
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D9.05 booklet: -
HT-66/05/003/A
The algorithm will become then:
Initializations:
Calculation of
()
L T
E
+
(option
CHAR_MECA
)
Calculation of
(
)
DF
I
P
T
U
-
-
-
,
(option
RIGI_MECA-TANG
)
Calculation of
(
)
U
0
0
0
,
P
T
by:
(
)
(
)
() ()
DF
P
T
L T
L T
I
P
T
E
E
U
U
-
-
-
·
=
-
+
-
,
,
0
0
0
Iterations of balance of Newton N
Loop elements el
Loop points of gauss G
calculation
[]
B
G
el
calculation
{}
[]
{}
G
el
G
el
B
X
-
-
=
and
{}
[]
{}
G
el
N
G
el
N
B
X
+
+
=
Calculation
+
N
el
G
,
(
)
-
+
+
+
R
P T
I G
el
N
N
N
U
,
,
and
(
)
DF
G
el
I
P T
N
N
N
U
+
+
+
,
,
(according to options) from:
{} {} {} {}
[]
G
el
G
el
N
G
el
G
el
N
G
el
B
-
+
-
+
,
,
,
,
Calculation of
(
)
U
N
N
N
P
T
+
+
+
1
1
1
,
,
by:
(
)
(
) ()
DF
P
T
R
P T
L T
I
N
N
N
I
N
N
N
E
·
= -
+
+
+
+
+
+
+
+
U
U
1
1
1
,
,
,
,
Updating:
(
) (
)
(
)
U
U
U
N
N
N
N
N
N
N
N
N
P
T
P T
P
T
+
+
+
+
+
+
+
+
+
+
+
+
=
+
1
1
1
1
1
1
,
,
,
,
,
,
IF test convergence OK
fine Newton: no next time
If not
N = n+1
4.3
Vectors and matrices according to options': routine
EQUTHM
The framed central part of the algorithm presented Ci above is carried out by a generic routine
EQUTHM. We give in appendix a chart of the call of this routine.
This routine is parameterized according to the equations present (mechanics, hydraulics with 1 or
2 pressures, thermics). The work carried out by this routine is parameterized by the option.
The term
(
)
-
R
P T
I
N
N
N
U
,
will be calculated by the options
RAPH_MECA
and
FULL_MECA
. This term includes them
following forces of volume: it will be considered that the following forces will be integrated into the options
RAPH_MECA
,
FULL_MECA
and
RIGI_MECA_TANG
. If the user data
do not comprise forces of volume, the vector
F
m
+
will be simply null.
The presentations made in the two following paragraphs are made in the most general case where
there is an equation of mechanics, two equations of hydraulics and an equation of thermics.
routine EQUTHM will calculate or not the various terms according to description that one will make him
equations present.
The indices G and el from now on are omitted, but it is clear that what is described applies to each point
of gauss of each element.
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4.3.1 Residue or nodal force: options
RAPH_MECA
and
FULL_MECA
One will distribute the terms of the variational formulation according to the following principle:
If
* gel
indicate a virtual field of deformation,
()
(
)
*
,
,
,
,
,
G
el T
=
v
v
1
1
2
2
calculated
starting from a vector of displacement nodal virtual:
{}
X
el
*
(
)
()
*
.
,
,
G
el T
I G
el
R
P T
R
R
R
R
R
R
R
R
U
v
v
+
+
+
=
+
+
+ +
+ +
+
1
2
3 1
4
1
5
2
6
2
7
8
One has then:
Index R
associated
1
+
+
+
+
-
+
+
+
+
m
m
m
m
m
F
2
2
12
2
1
1
1
v
2
+
+
+
p
I
()
v
3
-
-
+
+
+
+
-
-
m
m
m
m
1
1
1
2
1
1
1
2
1
4
(
)
(
)
(
)
T
T
M
M
M
M
1
1
1
2
1
1
1
2
1
+
+
-
-
+
+ -
+
1
5
-
-
+
+
+
+
-
-
m
m
m
m
2
1
2
2
2
1
2
2
2
6
(
)
(
)
(
)
T
T
M
M
M
M
2
1
2
2
2
1
2
2
1
+
+
-
-
+
+ -
+
2
7
(
)
(
) (
)
(
)
(
) (
)
(
)
(
) (
)
(
)
(
) (
)
(
)
(
)
Q
Q
H
H
m
m
H
H
m
m
H
H
m
m
H
H
m
m
T
T
m
m
m
m
m
m
m
m
m
'
'
.
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
+
+
+
-
-
-
-
+ -
-
+
+ -
-
+ -
-
+
+ -
-
-
+
+
+
-
-
+
+
+
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
1
2
1
2
2
2
2
2
2
2
2
1
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
M
M
M
M
F
M
M
M
M
(
)
2
2
-
.
F
m
8
(
)
(
)
(
)
-
+
+
+
+
+
- -
+
+
+
+
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
-
-
T H
H
H
H
T H
H
H
H
m
m
m
m
m
m
m
m
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
2
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
2
1
M
M
M
M
Q
M
M
M
M
Q
From there one will define the vector nodal residue
{}
V
G
el
such as:
{}
{}
(
)
X
R
P T
el T
G
el T
I G
el
*
*
.
.
,
V
U
G
el
=
+
+
+
{}
V
G
el
will be calculated by:
{}
[]
{}
V
B
G
el
=
G
el T
R
.
Code_Aster
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Version
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Titrate:
New architecture THM. Integration of the equilibrium equations
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Key
:
D9.05.03-A
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D9.05 booklet: -
HT-66/05/003/A
4.3.2 Loading: options
CHAR_MECA
This chapter is here only for memory because the routine
EQUTHM
will not deal with these terms.
One will distribute the terms of the variational formulation according to the following principle:
()
()
*
.
G
el T
E G
el
L T
L
L
L
L
L
L
L
L
+
=
+
+
+ +
+ +
+
1
2
3 1
4
5
2
6
2
7
8
v
v
Index
L
element type associated with
1
F
ext.
+
edge
v
3
(
)
T
ext.
ext.
M
M
1
1
1
2
+
edge
1
5
(
)
T
ext.
ext.
M
M
2
1
2
2
+
edge
2
7
(
)
(
)
(
)
tR
T
H
H
T H
H
ext.
m
ext.
m
ext.
m
ext.
m
ext.
-
+
+
-
+
Q
M
M
M
M
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
2
= -
T
ext.
~
Q
volume
edge
4.3.3 Tangent operator: options
FULL_MECA
,
RIGI_MECA_TANG
Notice on the matric notations:
In what follows, if
X
indicate a vector of components
X
I
and
Y
a vector of components
Y
J
,
X
Y
a matrix will indicate of which the element
(
)
line I column J
: ,
:
is
X
Y
I
J
.
To calculate the tangent operator
DF
I
, the following quantities will be calculated:
[
]
DRDE
=
DR1U DR1E DR1P1 DR1GP1
DR1P2 DR1GP2
DR1T DR1GT
DR2U DR. 2nd DR2P1 DR2GP1
DR2P2 DR2GP2
DR2T DR2GT
DR3U DR. 3rd DR3P1 DR3GP1
DR3P2 DR3GP2
DR3T DR3GT
DR4U DR. 4th DR4P1 DR4GP1
DR4P2 DR4GP2
DR4T DR4GT
DR5U DR. 5th DR5P1 DR5GP1
DR5P2 DR5GP2
DR5T DR5GT
DR6U DR. 6th DR6P1 DR6GP1
DR6P2 DR6GP2
DR6T DR6GT
DR7U DR. 7th DR7P1 DR7GP1
DR7P2 DR7GP2
DR7T DR7GT
DR8U DR. 8th DR8P1 DR8GP1
DR8P2 DR8GP2
DR8T DR8GT
Code_Aster
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Titrate:
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Where one noted:
T
F
DRiGT
T
F
DRiT
p
F
DRiGP
p
F
DRiGP
p
F
DRiP
p
F
DRiP
F
DRiE
U
F
DRiU
I
I
I
I
I
I
I
I
=
=
=
=
=
=
=
=
2
1
2
1
2
1
2
1
Code_Aster
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Version
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Titrate:
New architecture THM. Integration of the equilibrium equations
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22/06/05
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C. CHAVANT
Key
:
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:
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Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
To make these calculations one considers that the laws of behavior will provide, for the options
corresponding, all the derivative following:
[
]
DSDE
U
U
U
M
U
M
=
p
p
p
p
T
T
p
p
p
p
T
T
m
m
m
p
m
p
m
p
m
p
m
T
m
T
p
p
p
p
p
p
p
p
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
M
M
M
M
M
M
U
U
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
2
2
1
2
p
p
p
p
T
T
H
H
H
p
H
p
H
p
H
p
H
T
H
T
m
m
m
p
m
p
m
p
m
p
m
T
m
m
m
m
m
m
m
m
m
1
2
1
2
1
2
1
2
1
1
2
1
1
2
2
1
2
2
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
2
2
1
2
2
1
2
1
2
2
1
2
1
2
1
1
2
1
1
2
1
T
p
p
p
p
T
T
H
H
H
p
H
p
H
p
H
p
H
T
H
T
m
m
m
p
m
p
m
p
m
m
m
m
m
m
m
m
M
U
M
M
M
M
M
M
M
U
U
2
2
1
2
2
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
2
1
2
2
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
2
1
2
2
1
2
1
2
2
2
2
2
2
m
p
m
T
m
T
p
p
p
p
T
T
H
H
H
p
H
p
H
p
H
p
H
T
H
T
m
m
m
m
m
m
m
m
m
m
m
M
U
M
M
M
M
M
M
M
U
U
p
m
p
m
p
m
p
m
T
m
T
p
p
p
p
T
T
H
H
H
p
H
p
H
p
H
p
H
T
H
m
m
m
m
m
m
m
m
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
M
U
M
M
M
M
M
M
M
U
T
Q
Q
Q
p
Q
p
Q
p
Q
p
Q
T
Q
T
p
p
p
p
T
T
'
'
'
'
'
'
'
'
U
Q
U
Q
Q
Q
Q
Q
Q
Q
1
1
2
2
1
1
2
2
Code_Aster
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Version
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Titrate:
New architecture THM. Integration of the equilibrium equations
Date
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:
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:
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D9.05 booklet: -
HT-66/05/003/A
In fact, in these expressions, the derivative compared to U are all null, but we keep
the writing taking into account the definition of the matrices
[]
B
G
el
that we adopted.
The call to the laws of behavior will provide the pieces of the matrix
[
]
DSDE
according to the equations
present:
[
]
[
]
[
]
[
]
DMECDE
DMECP1
DMECP
DMECDT
=
=
=
=
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
T
T
T
T
;
;
1
1
1
1
2
2
2
2
2
[
]
[
]
[
]
DP11DE
M
DP11P1
M
M
DP11P2
M
M
=
=
=
m
H
m
p
m
p
p
p
H
p
H
p
m
p
m
p
p
p
H
p
H
p
m
m
m
m
m
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
;
;
[
]
=
DP11DT
M
M
m
T
m
T
T
T
H
T
H
T
m
m
1
1
1
1
1
1
1
1
1
1
1
1
[
]
[
]
[
]
DP12DE
M
DP12P1
M
M
DP12P2
M
M
=
=
=
m
H
m
p
m
p
p
p
H
p
H
p
m
p
m
p
p
p
H
p
H
p
m
m
m
m
m
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
;
;
[
]
=
DP12DT
M
M
m
T
m
T
T
T
H
T
H
T
m
m
1
2
1
2
1
2
1
2
1
2
1
2
[
]
[
]
[
]
DP21DE
M
DP21P1
M
M
DP21P2
M
M
=
=
=
m
H
m
p
m
p
p
p
H
p
H
p
m
p
m
p
p
p
H
p
H
p
m
m
m
m
m
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
;
;
[
]
=
DP21DT
M
M
m
T
m
T
T
T
H
T
H
T
m
m
2
1
2
1
2
1
2
1
2
1
2
1
[
]
[
]
[
]
DP22DE
M
DP22P1
M
M
DP22P2
M
M
=
=
=
m
H
m
p
m
p
p
p
H
p
H
p
m
p
m
p
p
p
H
p
H
p
m
m
m
m
m
2
2
2
2
2
2
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
;
;
[
]
=
DP22DT
M
M
m
T
m
T
T
T
H
T
H
T
m
m
2
2
2
2
2
2
2
2
2
2
2
2
[
]
[
]
[
]
[
]
=
=
=
=
T
T
T
Q
T
Q
p
p
p
Q
p
Q
p
p
p
Q
p
Q
Q
Q
Q
DTDT
Q
Q
DTDP2
Q
Q
DTDP1
Q
DTDE
'
'
'
'
;
'
'
;
'
2
2
2
2
1
1
1
1
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
18/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
In addition, by deriving the expression from the residue compared to the stresses, one defines:
[
]
=
Q
M
M
M
M
Q
M
M
M
M
Q
M
M
M
M
Q
M
M
M
M
Q
M
M
M
M
Q
M
M
M
M
Q
M
M
M
M
Q
M
M
M
M
DRDS
8
8
2
2
8
2
2
8
2
2
8
1
2
8
12
8
1
2
8
2
1
8
2
1
8
2
1
8
1
1
8
1
1
8
1
1
8
8
8
7
7
2
2
7
2
2
7
2
2
7
1
2
7
12
7
1
2
7
2
1
7
2
1
7
2
1
7
1
1
7
1
1
7
1
1
7
7
7
6
6
2
2
6
2
2
6
2
2
6
1
2
6
12
6
1
2
6
2
1
6
2
1
6
2
1
6
1
1
6
1
1
6
1
1
6
6
6
5
5
2
2
5
2
2
5
2
2
5
1
2
5
12
5
1
2
5
2
1
2
1
5
2
1
5
1
1
5
1
1
5
1
1
5
5
5
4
4
2
2
4
2
2
4
2
2
4
1
2
4
12
4
1
2
4
2
1
4
2
1
4
2
1
4
1
1
4
1
1
4
1
1
4
4
4
3
3
2
2
3
2
2
3
2
2
3
1
2
3
12
3
1
2
3
2
1
3
2
1
3
2
1
3
1
1
3
1
1
3
1
1
3
3
3
2
2
2
2
2
2
2
2
2
2
2
1
2
2
12
2
1
2
2
2
1
2
2
1
2
2
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
1
2
2
1
2
2
1
1
2
1
12
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
'
'
'
'
'
'
'
'
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
v
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
R
Q
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
H
R
R
m
R
R
R
m
m
m
m
p
m
m
m
m
p
m
m
m
m
p
m
m
m
m
p
m
m
m
m
p
m
m
m
m
p
m
m
m
m
p
m
m
m
m
p
All these quantities not being inevitably calculated, one will note:
[
]
[
]
=
=
+
+
+
+
+
+
+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
;
m
p
R
R
m
R
or
R
m
R
R
R
M
M
DR1P11
DR1DS
[
]
DR1P12
M
M
=
+
+
+
+
+
R
m
R
or
R
m
R
R
H
m
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
[
]
DR1P21
M
M
=
+
+
+
+
+
R
m
R
or
R
m
R
R
H
m
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
[
]
DR1P22
M
M
=
+
+
+
+
+
R
m
R
or
R
m
R
R
H
m
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
[
]
=
+
+
Q
DR1DT
1
1
'
R
Q
R
In the same way:
[
] [
] [
] [
] [
] [
]
DR8DS, DR8P11, DR8P12, DR8P21, DR8P22, DR8DT
It is then clear that:
[
] [
] [
]
DRDE
DRDS DSDE
=
.
And the contribution of the point of gauss to the tangent matrix
(
)
DF
G
el
I
P T
N
N
N
U
+
+
+
,
,
is obtained by:
(
)
[]
[
]
[]
DF
B
DRDE B
G
el
I U, P, T
N
N
N
+
+
+
=
G
el T
G
el
.
.
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
19/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
5 Diagrams
General
STAT_NON_LINE
finite element
Routine
TE
…
Knows unknown:
Calculate deformations:
Routine
EQUTHM
Arg In:
nature unknown factors
Cal behavior
Comp méca
Comp hydrau
Comp ther
Assemble contibution
not gauss with residue
and/or M tgte
Calculate
Loop points of gauss
Cal
EQUTHM
Q
M
M
M
M
,
;
,
,
;
,
,
;
,
,
;
,
,
;
,
'
2
2
2
2
2
2
1
2
12
12
2
1
2
1
2
1
1
1
1
1
1
1
'
Q
H
m
H
m
H
m
H
m
m
m
m
m
p
()
T
T
p
p
p
p
,
,
,
,
,
,
2
1
2
1
U
[]
el
G
B
U
2,
P
1,
P
T,
·
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
20/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
6
Specifications of under generic program
EQUTHM
6.1
Arguments of the routine
ARGUMENTS Of INPUT: IN
COMPOR
Description of the behavior
OPTION
Option to be calculated
NDIM
dimension spaces
2 or 3
NDDL
Numbers total degrees of
freedom of the appealing element
DIMDEF
dimension of the table of
deformations generalized with
not gauss
DIMCON
dimension of the table of
stresses generalized with
not gauss
NVIMEC
A number of internal variables
“mechanical”
ADVIME
Address variables
mechanical interns in
table of the internal variables
at the point of gauss
NVIHY
A number of internal variables
“hydraulic”
ADVIHY
Address variables
hydraulic interns in
table of the internal variables
at the point of gauss
NVITM
A number of internal variables
“thermal”
ADVITM
Address variables
thermal interns in
table of the internal variables
at the point of gauss
B (1:dimdef, 1:nddl)
Stamp
[]
B
G
el
DEFGEP (1:dimdef)
Values of deformations
generalized at the point of
gauss time more
DEFGEM (1:dimdef)
Values of deformations
generalized at the point of
gauss time less
CONGEM (1:dimcon)
Values of stresses
generalized at the point of
gauss time less
VINTM (1:nvimec+nvihy+
nvitm)
Values of the internal variables
at the point of gauss time
less
MECA (1:5)
YAMEC = MECA (1)
logic if 1 there is an equation of
mechanics
ADDEME = MECA (2)
Address in the tables of
deformations at the point of gauss
DEFGEP
and
DEFGEM
deformations
corresponding to mechanics
ADCOME = MECA (3)
Address in the tables of
stresses at the point of gauss
CONGEP
and
CONGEM
stresses
Code_Aster
®
Version
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Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
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C. CHAVANT
Key
:
D9.05.03-A
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:
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Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
corresponding to the equation ieq
NDEFME = MECA (4)
A number of mechanical deformations
NCONME = MECA (5)
A number of mechanical stresses
PRESS1 (1:5)
YAP1 = PRESS1 (1)
logic if 1 there is an equation
constituting 1
NBPHA1 = PRESS1 (2)
a number of phases for the component
1
ADDEP1 = PRESS1 (3)
Address in the tables of
deformations at the point of gauss
DEFGEP
and
DEFGEM
deformations
corresponding to the first pressure
ADCP11 = PRESS1 (4)
Address in the tables of
stresses at the point of gauss
CONGEP
and
CONGEM
stresses
corresponding to the first phase of
first component
ADCP12 = PRESS1 (5)
Address in the tables of
stresses at the point of gauss
CONGEP
and
CONGEM
stresses
corresponding to the second phase
first component
NDEFP1 = PRESS1 (6)
A number of deformations pressure 1
NCONP1 = PRESS1 (7)
A number of stresses for each
phase of component 1
PRESS2 (1:5)
YAP2 = PRESS2 (1)
logic if 1 there is an equation
constituting 2
NBPHA2 = PRESS2 (2)
a number of phases for the component
2
ADDEP2 = PRESS2 (3)
Address in the tables of
deformations at the point of gauss
DEFGEP
and
DEFGEM
deformations
agent with PRE2
ADCP21 = PRESS2 (4)
Address in the tables of
stresses at the point of gauss
CONGEP
and
CONGEM
stresses
corresponding to the first phase of
second component
ADCP22 = PRESS2 (5)
Address in the tables of
stresses at the point of gauss
CONGEP
and
CONGEM
stresses
corresponding to the second phase
second component
NDEFP2 = PRESS2 (6)
A number of deformations pressure 2
NCONP2 = PRESS2 (7)
A number of stresses for each
phase of component 2
TEMPLE (1:5)
YATE = TEMPLE (1)
logic if 1 there is an equation of
thermics
ADDETE = TEMPLE (2)
Address in the tables of
deformations at the point of gauss
DEFGEP
and
DEFGEM
deformations
corresponding to thermics
ADCOTE = TEMPLE (3)
Address in the tables of
stresses at the point of gauss
CONGEP
and first
CONGEM
stresses
corresponding to thermics
NDEFT = TEMPLE (4)
A thermal number of deformations
NCONT = TEMPLE (5)
A number of thermal stresses
Code_Aster
®
Version
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Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
22/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
ARGUMENTS OF EXIT: OUT
CONGEP (1:dimcon)
Values of stresses
generalized at the point of
gauss time more
VINTP (1:nvimec+nvihy+
nvitm)
Values of the internal variables
at the point of gauss time more
V (1:nddl)
{}
[]
{}
V
B
G
el
=
G
el T
R
.
CHECHMATE (1:nddl, 1:nddl)
(
)
[]
[
]
[]
DF
B
DRDE B
G
el
I U, P, T
N
N
N
+
+
+
=
G
el T
G
el
.
.
TABLES OF WORK
R (1:dimdef)
DRDS
(1:dimdef, 1:dimcon)
DSDE
(1:dimcon, 1:dimdef)
6.2
Addressing in the tables of deformation and stress
6.2.1 Addressing in the deformations
6.2.1.1 Deformations time less
Part
(local name in routine
COMTHM
)
Significance
Address in
DEFGEM
DEMECM
()
U
U
,
ADDEME
DEP1M
p
p
1
1
,
ADDEP1
DEP2M
p
p
2
2
,
ADDEP2
DETM
T
T
,
ADDETE
6.2.1.2 Deformations time more
Part
(local name in routine
COMTHM
)
Significance
Address in
DEFGEP
DEMECP
()
U
U
,
ADDEME
DEP1P
p
p
1
1
,
ADDEP1
DEP2P
p
p
2
2
,
ADDEP2
DETP
T
T
,
ADDETE
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
23/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
6.2.2 Addressing in the stresses
6.2.2.1 Stresses time less
Part
(local name in routine
COMTHM
)
Significance
Address in
CONGEM
COMECM
,
p
ADCOME
CP11M
m
m
H
m
1
1
1
1
1
1
1
1
1
1
,
,
,
M
M
or
ADCP11
CP12M
m
m
H
m
1
2
1
2
1
2
1
2
1
2
,
,
,
M
M
or
ADCP12
CP21M
m
m
H
m
2
1
2
1
2
1
2
1
2
1
,
,
,
M
M
or
ADCP21
CP22M
m
m
H
m
2
2
2
2
2
2
2
2
2
2
,
,
,
M
M
or
ADCP22
COTM
Q', Q
ADCOTE
6.2.2.2 Stresses time more
Part
(local name in routine
COMTHM
)
Significance
Address in
CONGEP
COMECP
,
p
ADCOME
CP11P
m
m
H
m
1
1
1
1
1
1
1
1
1
1
,
,
,
M
M
or
ADCP11
CP12P
m
m
H
m
1
2
1
2
1
2
1
2
1
2
,
,
,
M
M
or
ADCP12
CP21P
m
m
H
m
2
1
2
1
2
1
2
1
2
1
,
,
,
M
M
or
ADCP21
CP22P
m
m
H
m
2
2
2
2
2
2
2
2
2
2
,
,
,
M
M
or
ADCP22
COTP
Q', Q
ADCOTE
6.2.3 Addressing in the variables intern (example)
6.2.3.1 Variables intern at time less
Part
(local name in routine
COMTHM
)
Significance
Address in
VINTM
VIMEM
ADVIME
VIHYM
lq
vp
lq
P
P
S
,
,
ADVIHY
6.2.3.2 Variables intern at time more
Part
(local name in routine
COMTHM
)
Significance
Address in
VINTP
VIMEP
ADVIME
VIHYP
lq
vp
lq
P
P
S
,
,
ADVIHY
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
24/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
6.3 Addressing
R
,
DRDS
,
DSDE
6.3.1 Addressing
in
R
Under part of
R
Associated
Address in
R
R1
v
ADDEME
R2
()
v
ADDEME+NDIM
R3
1
ADDEP1
R4
1
ADDEP1+1
R5
2
ADDEP2
R6
2
ADDEP2+1
R7
ADDETE
R8
ADDETE+1
6.3.2 Addressing
in
DRDS
Part of the table
DRDS
Significance
Address in
DRDS
DR1DS
+
+
p
R
R
1
1
ADDEME, ADCOME
DR2DS
ADDEME+NDIM-1, ADCOME
DR1P11
R
m
R
or
R
m
R
R
H
m
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+
+
+
+
+
M
M
ADDEME, ADCP11
DR2P11
ADDEME+NDIM-1, ADCP11
DR1P12
R
m
R
or
R
m
R
R
H
m
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
+
+
+
+
+
M
M
ADDEME, ADCP12
DR2P12
ADDEME+NDIM-1, ADCP12
DR1P21
R
m
R
or
R
m
R
R
H
m
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
+
+
+
+
+
M
M
ADDEME, ADCP21
DR2P21
ADDEME+NDIM-1, ADCP21
DR1P22
R
m
R
or
R
m
R
R
H
m
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
+
+
+
+
+
M
M
ADDEME, ADCP22
DR2P22
ADDEME+NDIM-1, ADCP22
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
25/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
DR1DT
R
Q
R
1
1
'
+
+
Q
ADDEME, ADCOTE
DR2DT
ADDEME+NDIM-1, ADCOTE
DR3DS
ADDEP1, ADCOME
DR4DS
ADDEP1+1, ADCOME
DR3P11
ADDEP1, ADCP11
DR4P11
ADDEP1+1, ADCP11
DR3P21
ADDEP1, ADCP21
DR4P21
ADDEP1+ 1, ADCP21
DR3DT
ADDEP1, ADCOTE
DR4DT
ADDEP1+ 1, ADCOTE
DR5DS
ADDEP2, ADCOME
DR6DS
ADDEP2+ 1, ADCOME
DR5P11
ADDEP2, ADCP11
DR6P11
ADDEP2+ 1, ADCP11
DR5P21
ADDEP2, ADCP21
DR6P21
ADDEP2+1, ADCP21
DR5DT
ADDEP2, ADCOTE
DR6DT
ADDEP2+ 1, ADCOTE
DR7DS
ADDETE, ADCOME
DR8DS
ADDETE+ 1, ADCOME
DR7P11
ADDETE, ADCP11
DR8P11
ADDETE+ 1, ADCP11
DR7P21
ADDETE, ADCP21
DR8P21
ADDETE+ 1, ADCP21
DR7DT
ADDETE, ADCOTE
DR8DT
ADDETE+1, ADCOTE
6.3.3 Addressing
in
DSDE
Part
(local name with
COMTHM
)
Significance
Address in
DSDE
DMECDE
p
ADCOME, ADDEME
DMECP1
p
p
p
p
p
p
1
1
1
1
ADCOME, ADDEP1
DMECP2
p
p
p
p
p
p
2
2
2
2
ADCOME, ADDEP2
DMECDT
T
T
T
T
p
p
ADCOME, ADDETE
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
26/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
DP11DE
m
H
m
1
1
1
1
1
1
M
ADCP11, ADDEME
DP11P1
m
p
m
p
p
p
H
p
H
p
m
m
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
M
M
ADCP11, ADDEP1
DP11P2
m
p
m
p
p
p
H
p
H
p
m
m
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
M
M
ADCP11, ADDEP2
DP11DT
m
T
m
T
T
T
H
T
H
T
m
m
1
1
1
1
1
1
1
1
1
1
1
1
M
M
ADCP11, ADDETE
DP12DE
m
H
m
1
2
1
2
1
2
M
ADCP12, ADDEME
DP12P1
m
p
m
p
p
p
H
p
H
p
m
m
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
M
M
ADCP12, ADDEP1
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
27/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
DP12P2
m
p
m
p
p
p
H
p
H
p
m
m
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
M
M
ADCP12, ADDEP2
DP12DT
m
T
m
T
T
T
H
T
H
T
m
m
1
2
1
2
1
2
1
2
1
2
1
2
M
M
ADCP12, ADDETE
DP21DE
m
H
m
2
1
2
1
2
1
M
ADCP21, ADDEME
DP21P1
m
p
m
p
p
p
H
p
H
p
m
m
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
M
M
ADCP21, ADDEP1
DP21P2
m
p
m
p
p
p
H
p
H
p
m
m
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
M
M
ADCP21, ADDEP2
DP21DT
m
T
m
T
T
T
H
T
H
T
m
m
2
1
2
1
2
1
2
1
2
1
2
1
M
M
ADCP21, ADDETE
DP22DE
m
H
m
2
2
2
2
2
2
M
ADCP22, ADDEME
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
28/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
DP22P1
m
p
m
p
p
p
H
p
H
p
m
m
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
M
M
ADCP22, ADDEP1
DP22P2
m
p
m
p
p
p
H
p
H
p
m
m
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
M
M
ADCP22, ADDEP2
DP22DT
m
T
m
T
T
T
H
T
H
T
m
m
2
2
2
2
2
2
2
2
2
2
2
2
M
M
ADCP22, ADDETE
DTDE
Q
'
Q
ADCOTE, ADDEME
DTDP1
Q
p
Q
p
p
p
'
'
1
1
1
1
Q
Q
ADCOTE, ADDEP1
DTDP2
Q
p
Q
p
p
p
'
'
2
2
2
2
Q
Q
ADCOTE, ADDEP2
DTDT
Q
T
Q
T
T
T
'
'
Q
Q
ADCOTE, ADDETE
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
29/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
6.4 Algorithm
routine
EQUTHM
YAMEC = MECA (1)
ADDEME = MECA (2)
ADCOME = MECA (3)
NDEFME = MECA (4)
NCONME = MECA (5)
YAP1 = PRESS1 (1)
NBPHA1 = PRESS1 (2)
ADDEP1 = PRESS1 (3)
ADCP11 = PRESS1 (4)
ADCP12 = PRESS1 (5)
NDEFP1 = PRESS1 (6)
NCONP1 = PRESS1 (7)
YAP2 = PRESS2 (1)
NBPHA2 = PRESS2 (2)
ADDEP2 = PRESS2 (3)
ADCP21 = PRESS2 (4)
ADCP22 = PRESS2 (5)
NDEFP2 = PRESS2 (6)
NCONP2 = PRESS2 (7)
YATE = TEMPLE (1)
ADDETE = TEMPLE (2)
ADCOTE = TEMPLE (3)
NDEFT = TEMPLE (4)
NCONT = TEMPLE (5)
CAL COMTHM (
COMPOR OPTION NDIM
NDDL
DIMDEF
DIMCON
NVIMEC
NVIHY, NVITM
NDEFME
NDEFP1
NDEFP2
NDEFT
NCONME
NCONP1
NCONP2
NCONT
YAP1 NBPHA1
YAP2 NBPHA2
DEFGEM (ADDEME) DEFGEM (ADDEP1) DEFGEM (ADDEP2) DEFGEM (ADDETE)
DEFGEP (ADDEME) DEFGEP (ADDEP1) DEFGEP (ADDEP2) DEFGEP (ADDETE)
CONGEM (ADCOME) CONGEM (ADCOTE)
CONGEM (ADCP11) CONGEM (ADCP12) CONGEM (ADCP21) CONGEM (ADCP21)
VINTM (ADVIME) VINTM (ADVIHY) VINTM
(ADVITM)
CONGEP (ADCOME) CONGEP (ADCP11) CONGEP (ADCP21) CONGEP (ADCOTE)
VINTP (ADVIME) VINTP (ADVIHY) VINTP
(ADVITM)
DSDE
(ADCOME, ADDEME)
DSDE
(ADCOME, ADDEP1)
DSDE
(ADCOME, ADDEP2)
DSDE
(ADCOME, ADDETE)
DSDE
(ADCP11, ADDEP1)
DSDE
(ADCP11, ADDEME)
DSDE
(ADCP11, ADDEP2)
DSDE
(ADCP11, ADDETE)
DSDE
(ADCP12, ADDEP1)
DSDE
(ADCP12, ADDEME)
DSDE
(ADCP12, ADDEP2)
DSDE
(ADCP12, ADDETE)
DSDE
(ADCP21, ADDEP2)
DSDE
(ADCP21, ADDEME)
DSDE
(ADCP21, ADDEP1)
DSDE
(ADCP21, ADDETE)
DSDE
(ADCP22, ADDEP2)
DSDE
(ADCP22, ADDEME)
DSDE
(ADCP22, ADDEP1)
DSDE
(ADCP22, ADDETE)
DSDE
(ADCOTE, ADDETE)
DSDE
(ADCOTE, ADDEME)
DSDE
(ADCOTE, ADDEP1)
DSDE
(ADCOTE, ADDEP2)
)
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
30/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
If FULL_MECA or RAPH_MECA
If YAMEC
Injection of the terms
+
+
+
p
I
in R (ADDEME+NDIM-1)
Injection of the terms:
-
+
R
m
0
F
in R (ADDEME)
If YAP1
Injection of the terms
-
+
-
-
+
+
+
-
+
+
-
-
m
m
m
m
m
m
1
1
1
1
1
1
1
2
1
1
1
2
or
in R (ADDEP1)
Injection of the terms
(
)
(
)
(
)
(
)
T
T
T
T
M
M
M
M
M
M
1
1
1
1
1
1
1
2
1
1
1
2
1
1
+
-
+
+
-
-
+ -
+
+ -
+
or
in R (ADDEP1+1)
IF YAMEC
Injection of the terms:
(
)
-
+
+
+
+
+
+
m
m
m
m
m
1
1
1
1
1
2
F
F
or -
in R (ADDEME)
If YATE
Injection of the terms:
(
)
(
) (
)
(
)
(
)
(
) (
)
(
)
(
) (
)
(
)
(
)
T H
H
m
m
T
T
T H
H
m
m
T H
H
m
m
T
T
T
T
m
m
m
m
m
m
m
m
m
m
m
m
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+ -
-
-
- -
+ -
-
+
+ -
-
-
- -
-
- -
MR. F
MR. F
MR. F
MR. F
MR. F
MR. F
or
in R (ADDETE)
Injection of the terms
(
)
(
)
(
)
(
)
-
- -
-
+
- -
+
+
+
-
-
+
+
+
+
-
-
-
-
HT
HT
T H
H
T H
H
m
m
m
m
m
m
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
M
M
M
M
M
M
or
in R (ADDETE+1)
If YAP2
Injection of the terms
+
-
+
+
-
-
+
-
+
+
-
-
m
m
m
m
m
m
2
1
2
1
2
1
2
2
2
1
2
2
or
in R (ADDEP2)
Injection of the terms
(
)
(
)
(
)
(
)
T
T
T
T
M
M
M
M
M
M
2
1
2
1
2
1
2
2
2
1
2
2
1
1
+
-
+
+
-
-
+ -
+
+ -
+
or
in R (ADDEP2+1)
IF YAMEC
Injection of the terms:
(
)
-
+
+
+
+
+
+
m
m
m
m
m
2
1
2
1
2
2
F
F
or -
in R (ADDEME)
If YATE
Injection of the terms:
(
)
(
) (
)
(
)
(
)
(
) (
)
(
)
(
) (
)
(
)
(
)
T H
H
m
m
T
T
T H
H
m
m
T H
H
m
m
T
T
T
T
m
m
m
m
m
m
m
m
m
m
m
m
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
2
2
2
2
2
2
2
2
1
2
1
2
2
2
2
1
1
1
1
1
1
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+ -
-
-
- -
+ -
-
+
+ -
-
-
- -
-
- -
MR. F
MR. F
MR. F
MR. F
MR. F
MR. F
or
in R (ADDETE)
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
31/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
Injection of the terms
(
)
(
)
+
-
-
+
-
-
-
-
-
-
-
-
+
+
+
+
-
-
+
+
2
2
2
2
12
1
2
2
2
2
2
12
1
2
12
1
2
12
1
2
1
1
M
M
M
M
M
M
m
m
m
m
m
m
H
H
T
H
H
T
HT
H
T
or
in R (ADDETE+1)
If YATE
Injection of the terms:
Q
Q
'
'
+
-
-
in R (ADDETE)
Injection of the terms
(
)
-
- -
+
-
T
T
Q
Q
1
in R (ADDETE+1)
Accumulation in vector V:
{} {}
[]
{}
V
V
B
=
+
G
el T
R
.
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
32/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
IF RAPH_MECA or RIGI_MECA_TANG
IF YAMEC
calculation of DR1DS and injection in DRDS (ADDEME, ADCOME)
calculation of DR2DS and injection in DRDS (ADDEME+NDIM-1, ADCOME)
IF YAP1
calculation of DR1P11 and injection in DRDS (ADDEME, ADCP11)
calculation of DR2P11 and injection in DRDS (ADDEME+NDIM-1, ADCP11)
IF NBPHA1 > 1
calculation of DR1P12 and injection in DRDS (ADDEME, ADCP12)
calculation of DR2P12 and injection in DRDS (ADDEME+NDIM-1, ADCP12)
IF YAP2
calculation of DR1P21 and injection in DRDS (ADDEME, ADCP21)
calculation of DR2P21 and injection in DRDS (ADDEME+NDIM-1, ADCP21)
IF NBPHA2 > 1
calculation of DR1P22 and injection in DRDS (ADDEME, ADCP22)
calculation of DR2P22 and injection in DRDS (ADDEME+NDIM-1, ADCP22)
IF YATE
calculation of DR1DT and injection in DRDS (ADDEME, ADCOTE)
calculation of DR2DT and injection in DRDS (ADDEME+NDIM-1, ADCOTE)
IF YAP1
calculation of DR3P11 and injection in DRDS (ADDEP1, ADCP11)
calculation of DR4P11 and injection in DRDS (ADDEP1+1, ADCP11)
IF NBPHA1 > 1
calculation of DR3P12 and injection in DRDS (ADDEP1, ADCP12)
calculation of DR4P12 and injection in DRDS (ADDEP1+1, ADCP12)
IF YAMEC
calculation of DR3DS and injection in DRDS (ADDEP1, ADCOME)
calculation of DR4DS and injection in DRDS (ADDEP1+1, ADCOME)
IF YAP2
calculation of DR3P21 and injection in DRDS (ADDEP1, ADCP21)
calculation of DR4P21 and injection in DRDS (ADDEP1+ 1, ADCP21)
IF NBPHA2 > 1
calculation of DR3P22 and injection in DRDS (ADDEP1, ADCP22)
calculation of DR4P21 and injection in DRDS (ADDEP1+ 1, ADCP22)
IF YATE
calculation of DR3DT and injection in DRDS (ADDEP1, ADCOTE)
calculation of DR4DT and injection in DRDS (ADDEP1+ 1, ADCOTE)
IF YAP2
calculation of DR5P21 and injection in DRDS (ADDEP2, ADCP21)
calculation of DR6P21 and injection in DRDS (ADDEP2+1, ADCP21)
IF NBPHA2 > 1
calculation of DR5P22 and injection in DRDS (ADDEP2, ADCP22)
calculation of DR6P22 and injection in DRDS (ADDEP2+1, ADCP22)
IF YAMEC
calculation of DR5DS and injection in DRDS (ADDEP2, ADCOME)
calculation of DR6DS and injection in DRDS (ADDEP2+ 1, ADCOME)
YAP1 thus:
calculation of DR5P11 and injection in DRDS (ADDEP2, ADCP11)
calculation of DR6P11 and injection in DRDS (ADDEP2+ 1, ADCP11)
IF NBPHA1 > 1
calculation of DR5P12 and injection in DRDS (ADDEP2, ADCP12)
calculation of DR6P12 and injection in DRDS (ADDEP2+ 1, ADCP12)
IF YATE
calculation of DR5DT and injection in DRDS (ADDEP2, ADCOTE)
calculation of DR6DT and injection in DRDS (ADDEP2+ 1, ADCOTE)
IF YATE
calculation of DR7DT and injection in DRDS (ADDETE, ADCOTE)
calculation of DR8DT and injection in DRDS (ADDETE+1, ADCOTE)
IF YAMEC
calculation of DR7DS and injection in DRDS (ADDETE, ADCOME)
calculation of DR8DS and injection in DRDS (ADDETE+ 1, ADCOME)
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
33/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
IF YAP1
calculation of DR7P11 and injection in DRDS (ADDETE, ADCP11)
calculation of DR8P11 and injection in DRDS (ADDETE+ 1, ADCP11)
IF NBPHA1 > 1
calculation of DR7P12 and injection in DRDS (ADDETE, ADCP12)
calculation of DR8P12 and injection in DRDS (ADDETE+ 1, ADCP12)
IF YAP2
calculation of DR7P21 and injection in DRDS (ADDETE, ADCP21)
calculation of DR8P21 and injection in DRDS (ADDETE+ 1, ADCP21)
IF NBPHA1 > 1
calculation of DR7P22 and injection in DRDS (ADDETE, ADCP22)
calculation of DR8P22 and injection in DRDS (ADDETE+ 1, ADCP22)
[
] [
] [
]
DRDE
DRDS DSDE
=
.
(
)
[]
[
]
[]
DF
B
DRDE B
G
el
I U, P, T
N
N
N
+
+
+
=
G
el T
G
el
.
.
accumulated in CHECHMATE
6.5
Arguments of the routine of call of the laws of behavior
SUBROUTINE COMTHM (
ARGUMENTS Of INPUT: IN
COMPOR OPTION NDIM
NDDL
DIMDEF
DIMCON
NVIMEC
NVIHY, NVITM
NDEFME
NDEFP1
NDEFP2
NDEFT
NCONME
NCONP1
NCONP2
NCONT
YAP1 NBPHA1
YAP2 NBPHA2
DEMECM
()
U
U
,
time less
DEP1M
p
p
1
1
,
time less
DEP2M
p
p
2
2
,
time less
DETM
T
T
,
time less
DEMECP
()
U
U
,
time more
DEP1P
p
p
1
1
,
time more
DEP2P
p
p
2
2
,
time more
DETP
T
T
,
time more
COMECM
,
p
time less
COTM
Q
', Q
time less
CP11M
m
1
1
1
1
, M
or
m
H
m
1
1
1
1
1
1
,
,
M
time less
CP12M
m
1
2
1
2
, M
or
m
H
m
1
2
1
2
1
2
,
,
M
time less
CP21M
m
2
1
2
1
, M
or
m
H
m
2
1
2
1
2
1
,
,
M
time less
CP21M
m
2
2
2
2
, M
or
m
H
m
2
2
2
2
2
2
,
,
M
time less
VIMEM
internal variables
méca
time less
VIHYM
internal variables
hydro
time less
VITMM
internal variables
therm
time less
ARGUMENTS OF EXIT: OUT
COMECP
,
p
time more
COTP
Q
', Q
time more
CP11P
m
1
1
1
1
, M
or
m
H
m
1
1
1
1
1
1
,
,
M
time more
CP12P
m
1
2
1
2
, M
or
m
H
m
1
2
1
2
1
2
,
,
M
time more
CP21P
m
2
1
2
1
, M
or
m
H
m
2
1
2
1
2
1
,
,
M
time more
CP21P
m
2
2
2
2
, M
or
m
H
m
2
2
2
2
2
2
,
,
M
time more
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
34/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
VIMEP
internal variables
méca
time more
VIHYP
internal variables
hydro
time more
VITMP
internal variables
therm
time more
DMECDE
p
DMECP1
p
p
p
p
p
p
1
1
1
1
DMECP2
p
p
p
p
p
p
2
2
2
2
DMECDT
T
T
T
T
p
p
DP11DE
m
H
m
1
1
1
1
1
1
M
DP11P1
m
p
m
p
p
p
H
p
H
p
m
m
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
M
M
DP11P2
m
p
m
p
p
p
H
p
H
p
m
m
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
M
M
DP11DT
m
T
m
T
T
T
H
T
H
T
m
m
1
1
1
1
1
1
1
1
1
1
1
1
M
M
DP12DE
m
H
m
1
2
1
2
1
2
M
DP12P1
m
p
m
p
p
p
H
p
H
p
m
m
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
M
M
DP12P2
m
p
m
p
p
p
H
p
H
p
m
m
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
M
M
DP12DT
m
T
m
T
T
T
H
T
H
T
m
m
1
2
1
2
1
2
1
2
1
2
1
2
M
M
DP21DE
m
H
m
2
1
2
1
2
1
M
DP21P1
m
p
m
p
p
p
H
p
H
p
m
m
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
M
M
DP21P2
m
p
m
p
p
p
H
p
H
p
m
m
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
M
M
DP21DT
m
T
m
T
T
T
H
T
H
T
m
m
2
1
2
1
2
1
2
1
2
1
2
1
M
M
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
35/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
DP22DE
m
H
m
2
2
2
2
2
2
M
DP22P1
m
p
m
p
p
p
H
p
H
p
m
m
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
M
M
DP22P2
m
p
m
p
p
p
H
p
H
p
m
m
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
M
M
DP22DT
m
T
m
T
T
T
H
T
H
T
m
m
2
2
2
2
2
2
2
2
2
2
2
2
M
M
DTDE
Q
'
Q
DTDP1
Q
p
Q
p
p
p
'
'
1
1
1
1
Q
Q
DTDP2
Q
p
Q
p
p
p
'
'
2
2
2
2
Q
Q
DTDT
Q
T
Q
T
T
T
'
'
Q
Q
)
REAL * 8
DEMECM (NDEFME), DEP1M (NDEFP1), DEP2M (NDEFP2), DETM (NDEFT)
DEMECP (NDEFME), DEP1P (NDEFP1), DEP2P (NDEFP2), DETP (NDEFT)
COMECM (NCONME), CP11M (NCONP1), CP21M (NCONP2), COTM (NCONT)
VIMEM (NVIMEC), VIHYM (NVIHY), VITMM (NVITM)
COMECP (NCONME), CP11P (NCONP1), CP21P (NCONP2), COTP (NCONT)
VIMEP (NVIMEC), VIHYP (NVIHY), VITMP (NVITM)
DMECDE (NCONME, NDEFME), DMECP1 (NCONME, NDEFP1),
DMECP2 (NCONME, NDEFP2), DMECDT (NCONME, NDEFT)
DP11DE (NCONP1, NDEFME), DP11P1 (NCONP1, NDEFP1),
DP11P2 (NCONP1, NDEFP2), DP11DT (NCONP1, NDEFT)
DP21DE (NCONP2, NDEFME), DP21P1 (NCONP2, NDEFP1,
DP21P2 (NCONP2, NDEFP2, DP21DT (NCONP2, NDEFT)
DP12DE (NCONP1, NDEFME), DP12P1 (NCONP1, NDEFP1),
DP12P2 (NCONP1, NDEFP2), DP12DT (NCONP1, NDEFT)
DP22DE (NCONP2, NDEFME), DP22P1 (NCONP2, NDEFP1,
DP22P2 (NCONP2, NDEFP2, DP22DT (NCONP2, NDEFT)
DTDE (NCONT2, NDEFME), DTDP1 (NCONT2, NDEFP1),
DTDP2 (NCONT2, NDEFP2), DTDT (NCONT2, NDEFT)
Code_Aster
®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations
Date
:
22/06/05
Author (S):
C. CHAVANT
Key
:
D9.05.03-A
Page
:
36/36
Data-processing manual of Description
D9.05 booklet: -
HT-66/05/003/A
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