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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_MATR_ELEM
Date:
09/02/05
Author (S):
J. PELLET
Key
:
U4.61.01-H
Page
:
1/8
Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA














Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
Document: U4.61.01



Operator
CALC_MATR_ELEM








1 Goal
To calculate compilable elementary matrices by control ASSE_MATRICE.
The possible options of calculations are:
“AMOR_ACOU”, “MASS_MECA”, “RIGI_FLUI_STRU”, “RIGI_ROTA”, “AMOR_MECA”,
“MASS_MECA_DIAG”, “RIGI_GEOM”, “RIGI_THER”, “IMPE_MECA”, “MASS_THER”, “RIGI_MECA”,
“MASS_ACOU”, “ONDE_FLUI”, “RIGI_MECA_HYST”, “MASS_FLUI_STRU”, “RIGI_ACOU”,
“RIGI_MECA_LAGR”, “MASS_ID_MDEP_R”, “MASS_ID_MDNS_R”, “MASS_ID_MTEM_R”,
“MASS_ID_MTNS_R”
Product a structure of data of the type
matr_elem_
*.
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Code_Aster
®
Version
7.4
Titrate:
Operator
CALC_MATR_ELEM
Date:
09/02/05
Author (S):
J. PELLET
Key
:
U4.61.01-H
Page
:
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Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
2 Syntax
mel
[matr_elem_ *] = CALC_MATR_ELEM
(
/
OPTION = “RIGI_MECA”,
|
MODEL
=
Mo,
[model]
CHAM_MATER
=
chmat,
[cham_mater]
CARA_ELEM
= caract
, [cara_elem]
MODE_FOURIER
=/nh
, [I]
/
0
,
[DEFECT]
|
CHARGE
=
l_char
,
[l_char_meca]
INST
=
/
tps
, [R]
/
0.0
, [DEFECT]
/
OPTION =
“RIGI_MECA_LAGR”,
MODEL
=
Mo
,
[model]
CHAM_MATER
=
chmat,
[cham_mater]
CHARGE
=
l_char
,
[l_char_meca]
INST =
/tps,
[R]
/
0.0
,
[DEFECT]
THETA
= ch_theta
,
[theta_geom]
PROPAGATION =
,
[R]
/
OPTION =/“MASS_MECA”,
/
“MASS_MECA_DIAG”
,
MODEL
=
Mo
,
[model]
CHAM_MATER
=
chmat,
[cham_mater]
CHARGE
=
tank,
[char_meca]
INST =
/tps,
[R]
/
0.0
,
[DEFECT]
CARA_ELEM
=
caract
,
[cara_elem]
/
OPTION =/“MASS_ID_MDEP_R”,
/
“MASS_ID_MDNS_R”
,
/
“MASS_ID_MTEM_R”
,
/
“MASS_ID_MTNS_R”
,
MODEL =
Mo, [model]
/
OPTION = “RIGI_GEOM”,
MODEL
=
Mo
,
[model]
CARA_ELEM
=
carac,
[cara_elem]
SIEF_ELGA = sig,
[cham_elem_SIEF_R]
MODE_FOURIER
=/nh
, [I]
/
0
,
[DEFECT]
/
OPTION = “RIGI_ROTA”,
MODEL = Mo, [model]
CHAM_MATER
=
chmat,
[cham_mater]
CHARGE
=
l_char, [l_char_meca]
INST =
/tps,
[R]
/
0.0
,
[DEFECT]
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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_MATR_ELEM
Date:
09/02/05
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J. PELLET
Key
:
U4.61.01-H
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:
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Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
/
OPTION = “AMOR_MECA”,
MODEL = Mo, [model]
|
CARA_ELEM = carac,
[cara_elem]
|
RIGI_MECA = rigiel,
[matr_elem_DEPL_R]
MASS_MECA = massel,
[matr_elem_DEPL_R]
CHAM_MATER
=
chmat,
[cham_mater]
CHARGE
=
tank,
[char_meca]
INST
=
/
tps
, [R]
/
0.0
, [DEFECT]
/
OPTION = “RIGI_MECA_HYST”,
MODEL = Mo,
CHAM_MATER
=
chmat,
[cham_mater]
CHARGE
=
l_char, [l_char_meca]
INST
=
/
tps
,
[R]
/
0.0
,
[DEFECT]
RIGI_MECA = rigiel,
[matr_elem_DEPL_R]
/
OPTION= “RIGI_THER”,
|
MODEL =
Mo, [model]
CHAM_MATER
=
chmat,
[cham_mater]
CARA_ELEM
=
carac,
[cara_elem]
MODE_FOURIER
=/nh
, [I]
/
0
,
[DEFECT]
|
CHARGE= lchar,
[l_char_ther]
/
OPTION= “MASS_THER”,
MODELE= Mo,
[model]
CHAM_MATER=
chmat
,
[cham_mater]
CARA_ELEM
=
carac
,
[cara_elem]
/
OPTION =
“RIGI_ACOU”,
MODEL =
Mo, [model]
CHAM_MATER
=
chmat,
[cham_mater]
CHARGE
=
lchar,
[l_char_acou]
/
OPTION =/“MASS_ACOU”,
/
“AMOR_ACOU”
,
MODEL =
Mo, [model]
CHAM_MATER=
chmat
,
[cham_mater]
/
OPTION =
“RIGI_FLUI_STRU”,
MODEL =
Mo, [model]
CARA_ELEM
=
carac
,
[cara_elem]
CHAM_MATER=
chmat
,
[cham_mater]
CHARGE
=
l_char, [l_char_meca]
INST =/tps,
[R]
/
0.0
,
[DEFECT]
OPTION =
“MASS_FLUI_STRU”,
MODEL =
Mo, [model]
CARA_ELEM
=
carac
,
[cara_elem]
CHAM_MATER=
chmat
,
[cham_mater]
CHARGE
=
tank,
[char_meca]
INST =/tps,
[R]
/
0.0
,
[DEFECT]
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Code_Aster
®
Version
7.4
Titrate:
Operator
CALC_MATR_ELEM
Date:
09/02/05
Author (S):
J. PELLET
Key
:
U4.61.01-H
Page
:
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Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
/
OPTION =
/“IMPE_MECA”,
/
“ONDE_FLUI”
,
MODEL
= Mo,
[model]
CHARGE
=
lchar
,
[l_char_meca]
CHAM_MATER=
chmat
,
[cham_mater]
)

If
OPTION “AMOR_ACOU”
then
[*]
PRES_C
“AMOR_MECA”
DEPL_R
“IMPE_MECA”
DEPL_R
“MASS_ACOU”
PRES_C
“MASS_FLUI_STRU”
DEPL_R
“MASS_MECA”
DEPL_R
“MASS_MECA_DIAG”
DEPL_R
“MASS_THER”
TEMP_R
“ONDE_FLUI”
DEPL_R
“RIGI_ACOU”
PRES_C
“RIGI_FLUI_STRU”
DEPL_R
“RIGI_GEOM”
DEPL_R
“RIGI_MECA”
DEPL_R
“RIGI_MECA_HYST”
DEPL_C
“RIGI_MECA_LAGR”
DEPL_R
“RIGI_ROTA”
DEPL_R
“RIGI_THER”
TEMP_R
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Code_Aster
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Version
7.4
Titrate:
Operator
CALC_MATR_ELEM
Date:
09/02/05
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J. PELLET
Key
:
U4.61.01-H
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:
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Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
3 Operands
3.1 Operand
OPTION
OPTION =
The table which follows gives the list of the matrices calculated by an option as well as the type of element
which the option applies.
This type of element is given either by the name of the phenomenon having made it possible to define the model,
maybe by the name of the operator having produced the concept
charge
.
Option Phenomenon
or
operator
Stamp
MECHANICAL “AMOR_MECA”
Damping of the elements calculated by combination
linear of rigidity and the mass [U2.06.03] or by
direct assignment for the discrete elements.
MECHANICAL “IMPE_MECA”
Acoustic impedance of the surface elements
belonging to modelings
“3d_FLUIDE”
or
“2d_FLUIDE”
model
Mo
[U4.53.11].
MECHANICAL “MASS_FLUI_STRU” *
Mass elements of the model
Mo
with taking into account
fluids external and intern with the structure and coefficient
of containment.
MECHANICAL “MASS_MECA”
Mass elements of the model
Mo
.
MECHANICAL “MASS_MECA_DIAG”
Mass (diagonal) elements of the model
Mo
.
“MASS_ID_MDEP_R”
“MASS_ID_MDNS_R”
“MASS_ID_MTEM_R”
“MASS_ID_MTNS_R”
MECHANICS
Stamp “identity”. This matrix can be used to calculate them
eigenvalues and clean modes of another matrix
(for example rigidity to test the movements of
solid body).
There are 4 different options adapted to the 4 possibilities:
symmetrical mechanics + matrix - >
MDEP_R
not-symmetrical mechanics + matrix - >
MDNS_R
symmetrical thermics + matrix - >
MTEM_R
not-symmetrical thermics + matrix - >
MTNS_R
MECHANICAL “ONDE_FLUI”
Acoustic impedance of the surface elements of
model
Mo
belonging to modelings
“3d_FLUIDE”
and
“2d_FLUIDE”
.
This impedance corresponds to the influence of a wave
incidental harmonic of pressure [U4.53.11].
MECHANICAL “RIGI_FLUI_STRU” *
Rigidity of the elements of the model
Mo
with taking into account
fluids external and intern with the structure and coefficient
of containment.
MECHANICAL “RIGI_GEOM”
Geometrical rigidity of the elements of the model
Mo
.
MECHANICAL “RIGI_MECA”
Rigidity of the elements of the model
Mo
.
AFFE_CHAR_MECA
Stamp associated with the multipliers with LAGRANGE with
lchar
.
MECHANICAL “RIGI_MECA_HYST”
Hysteretic rigidity (complex) calculated by
multiplication by a complex number simple rigidity
[U2.06.03].
AFFE_CHAR_MECA
Stamp associated with the multipliers with LAGRANGE with
lchar
.
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Code_Aster
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Version
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Titrate:
Operator
CALC_MATR_ELEM
Date:
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J. PELLET
Key
:
U4.61.01-H
Page
:
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Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
MECHANICAL “RIGI_MECA_LAGR”
Rigidity of the elements of the model
Mo
“deformed” by one
field
[U4.82.03].
AFFE_CHAR_MECA
Stamp associated with the multipliers with LAGRANGE with
lchar
.
MECHANICAL “RIGI_ROTA”
Rigidity of rotation of the elements of the model
Mo

THERMAL “MASS_THER”
Mass elements of the model
Mo
.
THERMAL “RIGI_THER”
Rigidity of the elements of the model
Mo
.
AFFE_CHAR_THER
Rigidity coming from the conditions of exchange from
lchar
.
AFFE_CHAR_THER
Stamp associated with the multipliers with LAGRANGE with
lchar
.
ACOUSTIC “AMOR_ACOU”
Damping of the elements of the model
Mo
.
ACOUSTIC “MASS_ACOU”
Mass elements of the model
Mo
.
ACOUSTIC “RIGI_ACOU”
Rigidity of the elements of the model
Mo
.
AFFE_CHAR_ACOU
Stamp associated with the multipliers with LAGRANGE with
lchar
.
The marked options * relate to the resorption of software FLUSTRU:
These two options:
“RIGI_FLUI_STRU”
and
“MASS_FLUI_STRU”
allow to calculate them
matrices of mass and rigidity (and thus a modal base) for a structure of beam (
SEG2
)
bathed by an external fluid. The relation of behavior of material must be
ELAS_FLU
.

3.2 Operands
MODEL
/
CHAM_MATER
/
CARA_ELEM
MODEL =
This operand is used to indicate the elements for which calculations must be carried out
elementary: it is reminded the meeting that the finite elements for the majority are defined in the model.
There are two exceptions:
1) Elements of dualisation of the conditions of DIRICHLET, i.e. elements
allowing to impose conditions on the degrees of freedom of displacement in
mechanics, degrees of freedom of temperature in thermics and degrees of freedom of
pressure in accoustics.
2) Nodal useful loads.
These elements are defined in the concepts of the type
char_meca
,
char_ther
or
char_acou
.
One must thus provide the argument
l_char
for the calculation of the elementary matrices of rigidity:
RIGI_MECA
,
RIGI_THER
,
RIGI_ACOU
,
RIGI_MECA_HYST
and
RIGI_MECA_LAGR
.
CHAM_MATER =
Name of the material field where the characteristics of materials of the elements are defined.
This argument is almost always necessary.
In practice, one can do some:
·
for the discrete elements whose elementary matrices are defined in the concept
cara_elem
. See
AFFE_CARA_ELEM
[U4.42.01],
·
for the calculation of rigidities due to the dualisation of the boundary conditions.
CARA_ELEM = carac
Elementary characteristics
carac
are necessary if there exists in the model of
elements of beam, hull or of the discrete elements or if a reference mark of anisotropy were defined on
solid elements (key word
SOLID MASS
control
AFFE_CARA_ELEM
).
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Code_Aster
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Version
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Titrate:
Operator
CALC_MATR_ELEM
Date:
09/02/05
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J. PELLET
Key
:
U4.61.01-H
Page
:
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Instruction manual
U4.6- booklet: Elementary matrices/Vectors and assembly
HT-66/05/004/A
3.3 Operand
CHARGE
and
INST
CHARGE = tank
This operand has several distinct functions:
1) to specify the elements for which elementary calculations of rigidity are made
(conditions of DIRICHLET),
2) for the options of mechanics, to specify a possible field of temperature when it
material is a function of the temperature (cf key word
INST
). In this case, to make
attention so that there are not several different temperatures in the argument
lchar
,
the temperature used is then the first found in the list of the loads
(Cf.
AFFE_CHAR_MECA_
…, key word
TEMP_CALCULEE
[U4.44.01 § 3.3]),
3) for
the option
“IMPE_MECA”
: to give the value of the acoustic impedance of the meshs of
edge,
4) for
the option
“ONDE_FLUI”
: to give the value of the pressure of the incidental wave,
5) for
the option
“RIGI_ROTA”
: to give the value of the rotation imposed on the model.
Example:
If one wants to distinguish two concepts
matr_elem
different for the same option
RIGI_MECA
:
·
for the elements of the model,
·
for the elements of DIRICHLET.
and that the material is a function of the temperature, one can write:
chtemp
=
AFFE_CHAR_MECA
(TEMP_CALCULEE = temper1)
chabloc =
AFFE_CHAR_MECA
(DDL_IMPO = ......)
melmo
=
CALC_MATR_ELEM
(MODEL = Mo,
OPTION
=
“RIGI_MECA”
,
CHAM_MATER
=
......,
CHARGE
=
chtemp
,
INST
=1.,
)
melbloc =
CALC_MATR_ELEM
(OPTION = “RIGI_MECA”,
CHARGE
=
chabloc,
)
INST = tps
The argument
tps
is used only into thermomechanical.
Lorsqu '' there exists a temperature in one of the concepts
charge
, one uses the field then of
temperature possibly interpolated at the moment
tps
. This field of temperature can vary
characteristics of the material field if the material is a function of the temperature;
if not this argument is useless.

3.4 Operand
MODE_FOURIER
MODE_FOURIER = nh
Positive or null entirety indicating the harmonic of FOURIER on which one calculates the matrices
elementary.
By defect:
nh
=
0
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Code_Aster
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Version
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Titrate:
Operator
CALC_MATR_ELEM
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U4.61.01-H
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3.5 Operand
SIEF_ELGA
(option
“RIGI_GEOM”
)
SIEF_ELGA = sig
The stress field
sig
given for the calculation of the option
“RIGI_GEOM”
must have in theory
summer calculated with the option
“SIEF_ELGA_DEPL”
(stress field at the points of GAUSS of
elements) (cf controls
CALC_CHAM_ELEM
[U4.81.03] or
CALC_ELEM
[U4.81.01]).
The theory of fambement linear indeed supposes a theory of small displacements
rubber bands.

3.6 Operands
RIGI_MECA
and
MASSE_MECA
(options
“AMOR_MECA”
and
“RIGI_MECA_HYST”
)
RIGI_MECA
=
Elementary matrices of rigidity (option:
“RIGI_MECA”
) necessary to the calculation of the matrices
of damping (
“AMOR_MECA”
) or of hysteretic rigidity (
“RIGI_MECA_HYST”
) to see “Note
of use of damping and hysteretic rigidity " [U2.06.03].
MASS_MECA =
Elementary matrices of mass (option:
“MASS_MECA”
or
“MASS_MECA_DIAG”
) necessary
with the calculation of the matrices of damping (
“AMOR_MECA”
).
Note:
For the option
“RIGI_MECA_HYST”
, the result of calculation will contain in addition to rigidity
hysteretic of the elements of the model, the “rigidity” of the elements of Lagrange of the loads
provided.

3.7 Operands
THETA
and
PROPAGATION
(option
“RIGI_MECA_LAGR”
)
THETA = ch_theta
These key words relate to only the Lagrangian propagation [U4.82.03].


4
Examples of calculations with
CALC_MATR_ELEM
4.1
Stamp geometrical rigidity for the buckling of EULER
rigigeom = CALC_MATR_ELEM (
OPTION = “RIGI_GEOM”, MODELS = Mo,
CARA_ELEM
=
carac
,
SIEF_ELGA
=
chsig
)

4.2
Stamp of “mass” in accoustics
massacou = CALC_MATR_ELEM (
OPTION = “MASS_ACOU”, MODELS = Mo,
CHAM_MATER
=
chmat
,
CHARGE
=
tank
)

4.3
Stamp rigidity of the elements of LAGRANGE in mechanics
rigibloc = CALC_MATR_ELEM (
OPTION = “RIGI_MECA”, LOAD = ch_bloc)