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Definition of initial fields for STAT_NON_LINE
Date
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Author (S):
J. Key PELLET
:
U2.01.09-A Page
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Organization (S): EDF/MTI/MN
Handbook of Utilization
U2.01 booklet:
Document: U2.01.09
Analytical definition of a stress field
and of a field of internal variables initial

Summary:

It is explained how to manufacture two of the fields constituting the initial state of a non-linear calculation
(STAT_NON_LINE): the stress field and the field of internal variables.

· the components of the stress field must have an “analytical” form (for example: state
of a ground subjected to the “weight of the grounds”),
· the components of the field of variables intern are nonnull constants.

In both cases, the solution consists in connecting a certain number of commands CREA_CHAMP.

For the stress field, the difficulty consists in evaluating the “analytical formulas” (OPERATION=' EVAL').
For the field of internal variables, the difficulty comes owing to the fact that the size associated with the internal variables
(VARI_R) has a number a priori unspecified of components: “V1”, “V2”,…

The solutions suggested are implemented in test ZZZZ130A.
Handbook of Utilization
U2.01 booklet:
HI-75/01/006/A

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Titrate:
Definition of initial fields for STAT_NON_LINE
Date
:
30/11/01
Author (S):
J. Key PELLET
:
U2.01.09-A Page
: 2/6

1
Definition of the analytical stress field

It is supposed that the model contains finite elements of continuous medium (MODELISATION=' 3d').
It is wanted that in each point of Gauss, the components of the constraints have the expressions
following:

SIZZ = RHO * G * Z
SIXX = SIYY = KP * SIZZ

where:
RHO: density
G: acceleration of gravity
Z: 3rd co-ordinate of space
KP: coefficient of “pushed” of the grounds

The solution suggested consists with:

1) to define three functions “formulas” corresponding to SIXX, SIYY and SIZZ,
2) to constitute a field whose components are the preceding functions,
3) to evaluate the formulas of the field by providing him the field of geometry necessary to their
evaluation.

1.1
Stage 1: to define the formulas

RHO=1000.
G=10.
KP=3.

SIZZ = FORMULA (REEL= """ (REAL:Z) = RHO * G * Z """)
SIXX = FORMULA (REEL= """ (REAL:Z) = KP * SIZZ (Z) """)
SIYY = FORMULA (REEL= """ (REAL:Z) = KP * SIZZ (Z) """)

1.2
Stage 2: to create the field of formulas SIG1

SIG1=CREA_CHAMP (OPERATION=' AFFE', TYPE_CHAM=' ELGA_NEUT_F',
MODELE=MO, PROL_ZERO=' OUI',
AFFE=_F (ALL = “YES”, NOM_CMP = (“X1”, “X2”, “X3”,),
VALE_F = (SIXX, SIYY, SIZZ,)))

Remarks

· the field SIG1 which one creates is a cham_elem at the points of Gauss (ELGA),
· the only fields being able to have components of the type “functions” are the fields of
size NEUT_F. It will thus have to be remembered that the CMP “X1” of SIG1 is actually
“SIXX”, etc…,
· key word PROL_ZERO=' OUI' is obligatory bus for all the types of element, them
cham_elem_NEUT_R currently has 6 components: “X1”, “X2”,…, “X6”. It is necessary
thus to agree “to prolong” by zero the field out of the 3 nonaffected components.
prolongation by “zero” for a field whose components are texts (names of
functions) consists in assigning the chain ““to each component absent from the field.
Attention thus, it is not a question of a null function. One can note it while using
INFO=2 to print field SIG1.
Handbook of Utilization
U2.01 booklet:
HI-75/01/006/A

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Titrate:
Definition of initial fields for STAT_NON_LINE
Date
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Author (S):
J. Key PELLET
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1.3
Stage 3: to evaluate the formulas of field SIG1

Field SIG1 is a field known at the points of Gauss of the elements of the model. In each point,
one will want to evaluate functions SIXX, SIYY and SIZZ. For that, it is necessary to have the values of
all variables appearing in functions (here Z). These variables must be known on
same points as the field of functions. It is thus necessary to have a field containing the geometry of
points of Gauss (cham_elem_GEOM_R/ELGA).

This field of geometry of the points of Gauss (CHXG) is obtained starting from grid (MA) by the 2
following commands:

CHXN=CREA_CHAMP (OPERATION=' EXTR', TYPE_CHAM=' NOEU_GEOM_R',
NOM_CHAM=' GEOMETRIE', MAILLAGE=MA)

CHXG=CREA_CHAMP (OPERATION=' DISC', TYPE_CHAM=' ELGA_GEOM_R',
MODELE=MO, CHAM_GD=CHXN

The first command extracts the field from geometry (with the nodes) of the grid. The second
transform the field of geometry to the nodes into a field of geometry at the points of Gauss in
using the functions of form of the finite elements of the model.

One can then evaluate the functions thanks to operator CREA_CHAMP/OPERATION=' EVAL':

SIG2=CREA_CHAMP (OPERATION=' EVAL', TYPE_CHAM=' ELGA_NEUT_R',
MODELE=MO, CHAM_F=SIG1, CHAM_PARA= (CHXG,))

Field (SIG2) obtained by evaluation of a field of size NEUT_F is a field of
size NEUT_R whose components have the same names as the components of NEUT_F:
“X1”, “X2”,…, “X6”.

Caution:

The components “X4”, “X5”, “X6” are indefinite (actually they contain reality it
larger possible), because they correspond to a non-existent function.

It still remains to change the size of field SIG2 (NEUT_R - > SIEF_R) to finish
manufacture of our analytical stress field:

SIGINI=CREA_CHAMP (OPERATION=' ASSE', TYPE_CHAM=' ELGA_SIEF_R',
MODELE=MO, PROL_ZERO=' OUI',
ASSE=_F (ALL = “YES”, CHAM_GD = SIG2,
NOM_CMP = (“X1”, “X2”, “X3”,),
NOM_CMP_RESU = (“SIXX”, “SIYY”, “SIZZ”,)))

Note:

· only the components “X1”, “X2” and “X3” of field SIG2 are recopied in this
operation to give components “SIXX”, “SIYY”, “SIZZ” of field SIGINI.
This stress field must also contain the components related to
shearings (“SIXY”, “SIYZ”, “SIXZ”). To obtain them (with a zero value), it is necessary
to use the prolongation by zero (PROL_ZERO=' OUI'),
· handling made to obtain the null components of shearing, would have been
simpler if there were explicitly affected on these 3 components a null function.
One would not have had “to play” with the prolongations. But one would have profited from
coincidence which sizes SIEF_R and NEUT_R have all the two 6 components
for cham_elem (ELGA) on the elements of the model.
Handbook of Utilization
U2.01 booklet:
HI-75/01/006/A

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Titrate:
Definition of initial fields for STAT_NON_LINE
Date
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J. Key PELLET
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2
Definition of the field of variables intern not no one

2.1 Problem

One wants to create a field of initial internal variables for command STAT_NON_LINE. This field
does not have to be null everywhere. More precisely, one wants:

STAT_NON_LINE:
COMP_INCR= (_F (GROUP_MA=' MASSIF', RELATION = “CJS”),
_F (GROUP_MA=' BETON', RELATION = “ENDO_LOCAL”),),

for the relation of behavior “CJS” (16 variables intern), one wants to affect:
V1 = 1.0 and V9 = 9.0

for the relation of behavior “ENDO_LOCAL” (2 variables intern), one wants to affect:
V2 = 2.0

2.2 1ère
method

The operator to be used is CREA_CHAMP/OPERATION=' AFFE'. He makes it possible to affect (by mesh or
GROUP_MA) the values which one wishes. The difficulty comes owing to the fact that the size associated with
internal variables (VARI_R) is different from the different one: one does not know a priori which are its
components. Moreover the name of its components translates this ignorance: “V1”, “V2”,…
According to the behavior which the user in STAT_NON_LINE will choose, the number of variables
interns changes. In our example, behavior “CJS” requires 16 variables whereas
“ENDO_LOCAL” uses only 2 of them.

The operation of assignment is thus done in two stages: one creates initially a CARTE of NEUT_R (VAIN1)
with TOUTES components wanted including the null components:

VAIN1=CREA_CHAMP (OPERATION=' AFFE', TYPE_CHAM=' CART_NEUT_R',
MODELE=MO,
AFFE= (
_F (GROUP_MA= “CONCRETE”, NOM_CMP= (“X1”, “X2”,), VALE = (0., 2.,)),
_F (GROUP_MA= “MASSIVE”,
NOM_CMP= (“X1”, “X2”, “X3”, “X4”, “X5”, “X6”, “X7”, “X8”, “X9”, “X10”,
“X11”, “X12”, “X13”, “X14”, “X15”, “X16”,),

VALE = (1., 0., 0., 0., 0., 0., 0., 0., 9., 0., 0., 0., 0., 0., 0., 0.,)),
)
)

One transforms then carte_ NEUT_R into cham_elem_VARI_R (VAIN11):

VAIN11=CREA_CHAMP (OPERATION=' ASSE', TYPE_CHAM=' ELGA_VARI_R', MODELE=MO,
ASSE= (
_F (CHAM_GD = VAIN1, GROUP_MA= “CONCRETE”,
NOM_CMP= (“X1”, “X2”,),
NOM_CMP_RESU= (“V1”, “V2”,),),
_F (CHAM_GD = VAIN1, “MASSIVE” GROUP_MA=,
NOM_CMP= (“X1”, “X2”, “X3”, “X4”, “X5”, “X6”, “X7”,
“X8”, “X9”, “X10”, “X11”, “X12”, “X13”,
“X14”, “X15”, “X16”,),
NOM_CMP_RESU= (“V1”, “V2”, “V3”, “V4”, “V5”, “V6”,
“V7”, “V8”, “V9”, “V10”, “V11”, “V12”,
“V13”, “V14”, “V15”, “V16”,),),
)
)
)
Handbook of Utilization
U2.01 booklet:
HI-75/01/006/A

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Titrate:
Definition of initial fields for STAT_NON_LINE
Date
:
30/11/01
Author (S):
J. Key PELLET
:
U2.01.09-A Page
: 5/6

Note:

It is very important for non-linear calculation to come that the field of variables intern is
coherent with the behaviors which one will choose. Here, it is necessary that the meshs of the group
“BETON” have 2 internal variables (and only 2) and those of group “MASSIF” have some
16.

Caution:

If the model comprises other types of behavior (for which one does not wish
to initialize the field with nonnull values), it is also necessary to explicitly affect to them
zero values. This disadvantage (of having to know TOUS behaviors used and
their number of variables intern) can be raised with the 2nd method below (but
it is more complicated).

2.3 2nd
method

This method (more complicated) makes it possible to affect explicitly only the meshs which have
nonnull components.

The problem is to obtain a field containing the good number of internal variables for each mesh
according to the behavior which will be affected for him in STAT_NON_LINE. To solve this problem,
one will carry out a non-linear calculation “can” (with the real behaviors). The field of variables
interns produced will be then a “model” good of field.

One will thus make:

1) non-linear calculation can => UBID
2) extraction of the field of variables intern (VBID) result UBID
3) assignment of the nonnull values in field VAIN2
4) resetting of VBID + overload of the values of VAIN2 to produce result VAIN22

2.3.1 non-linear calculation can

BETON=DEFI_MATERIAU (ELAS=_F (E = 20000., NAKED = 0.),
ECRO_LINE=_F (SY = 6., D_SIGM_EPSI = - 10000.) )

MASSIF=DEFI_MATERIAU (ELAS=_F (E = 35.E3, NAKED = 0.15),
CJS=_F (BETA_CJS = - 0.55, GAMMA_CJS = 0.82, PA = - 100.0,
RM = 0.289, N_CJS = 0.6, KP = 25.5E3, RC = 0.265, A_CJS =
0.25,))

CHMAT=AFFE_MATERIAU (MAILLAGE=MA, AFFE= (
_F (GROUP_MA = “MASSIVE”, MATER = MASSIVE),
_F (GROUP_MA = “CONCRETE”, MATER = CONCRETE),))

TEMPS1=DEFI_LIST_REEL (VALE= (0., 1.) )
CHAR_U1=AFFE_CHAR_MECA (MODELE=MO,
DDL_IMPO=_F (NODE = (“N1”, “N2”, “N3”,), DX=0., DY=0., DZ=0.))

UBID=STAT_NON_LINE (MODELE=MO, CHAM_MATER=CHMAT,
EXCIT= _F (LOAD = CHAR_U1,),
COMP_INCR= (_F (GROUP_MA=' MASSIF', RELATION = “CJS”),
_F (GROUP_MA=' BETON', RELATION = “ENDO_LOCAL”),),
NEWTON=_F (MATRIX = “ELASTIC”),
CONVERGENCE=_F (ARRET = “NON”, # to continue without convergence
ITER_GLOB_MAXI = 1, ITER_INTE_MAXI = 1),
INCREMENT=_F (LIST_INST = TEMPS1),
)
Handbook of Utilization
U2.01 booklet:
HI-75/01/006/A

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Titrate:
Definition of initial fields for STAT_NON_LINE
Date
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Author (S):
J. Key PELLET
:
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2.3.2 Recovery of the field of variables intern “model”

VABID=CREA_CHAMP (OPERATION=' EXTR', TYPE_CHAM=' ELGA_VARI_R', INFO=1,
NOM_CHAM=' VARI_ELGA', RESULTAT=UBID, NUME_ORDRE=1,)

Note:

VABID is not null.

2.3.3 Assignment of the nonnull values in a cham_elem_NEUT_R

VAIN2=CREA_CHAMP (OPERATION=' AFFE', TYPE_CHAM=' CART_NEUT_R', MODELE=MO,
AFFE= (
_F (GROUP_MA= “CONCRETE”, NOM_CMP= (“X2”,), VALE = (2.,)),
_F (GROUP_MA= “MASSIVE”, NOM_CMP= (“X1”, “X9”,), VALE = (1., 9.,)),
)
)

2.3.4 Resetting of the field of variables intern “model” and overload of the values
nonnull

VAIN22=CREA_CHAMP (OPERATION=' ASSE', TYPE_CHAM=' ELGA_VARI_R', MODELE=MO,
# put at zero:
ASSE= (_F (TOUT= = “YES”, CHAM_GD = VABID, CUMUL=' OUI', COEF_R=0.),
# overloads nonnull values:
_F (GROUP_MA= “CONCRETE”, CHAM_GD = VAIN2, CUMUL=' OUI', COEF_R=1.,
NOM_CMP= (“X2”,), NOM_CMP_RESU= (“V2”,),),
_F (GROUP_MA= “MASSIVE”, CHAM_GD = VAIN2, CUMUL=' OUI', COEF_R=1.,
NOM_CMP= (“X1”, “X3”), NOM_CMP_RESU= (“V1”, “V9”,),),
)
)

Notice;

For the resetting and overloads it nonnull values, one uses the key words
CUMUL=' OUI' and COEF_R.

Handbook of Utilization
U2.01 booklet:
HI-75/01/006/A

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