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Titrate:
Operator CALC_MATR_AJOU


Date:
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Author (S):
NR. GREFFET, F. STIFKENS, G. Key ROUSSEAU
:
U4.66.01-E Page
: 1/10

Organization (S): EDF-R & D/AMA, EDF-DPN/UTO

Handbook of Utilization
U4.6- booklet: Elementary matrices/Vecteurs and assembly
Document: U4.66.01

Operator CALC_MATR_AJOU

1 Goal

To calculate matrices of mass [R4.07.03], damping or rigidity added.

The matrices are induced by a fluid true, incompressible, at rest or in potential flow,
on a structure in 2D, axisymmetric 2D or in 3D.

The terms of these matrices are calculated on the basis of modal structure in the vacuum.

The calculation of the terms of the matrices is carried out by resolution of the equations of LAPLACE within the framework
of a thermal analogy. The calculated temperature plays the part of a pressure in the field
fluid. Guard thus should be taken to define fluid material by thermal characteristics, and
to assign a thermal model to the part of the grid which represents the fluid.

Thanks to this operator, one can determine for example, the added matrices of a beam of tubes,
regarded as only one structure immersed in the same fluid.

Within the framework of a calculation by dynamic under-structuring, it is also possible to evaluate
stamp of mass added on a generalized model.

For systematic uses of this command and to simplify the drafting of the file of
commands, macro-command MACRO_MATR_AJOU [U4.66.11] will be used effectively.

Product a structure of data of the matr_asse_gene_R. type.

Case-tests FDLV106 [V8.01.106] and FDLV107 [V8.01.107] present examples of use of
this operator.
Handbook of Utilization
U4.6- booklet: Elementary matrices/Vecteurs and assembly
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Titrate:
Operator CALC_MATR_AJOU


Date:
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:
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2 Syntax

massaj [matr_asse_gene_R] = CALC_MATR_AJOU


(
MODELE_FLUIDE
=
fluid
[model]




MODELE_INTERFACE
=
interf
[model]




CHAM_MATER
=
matflui [cham_mater]




CHARGE
=
charge
[char_ther]




/
MODE_MECA
=
modes
[mode_meca]



/
CHAM_NO =
chamno
[cham_no_DEPL_R]
/
MODELE_GENE
=
modgen
[modele_gene]






NUME_DDL_GENE
=
numgen
[nume_ddl_gene]



DIST_REFE
=
/
outdistance
[R]
/
1.E-2
[DEFAUT]



AVEC_MODE_STAT
=
/
“OUI”
[DEFAUT]










/“NON”



NUME_MODE_MECA
=
nume [l_I]



INFO
=
/
1
[DEFAUT]







/2



OPTION
= | “MASS_AJOU”







| “AMOR_AJOU”







| “RIGI_AJOU”



POTENTIEL
=
phi
[evol_ther]



SOLVEUR
=
to see
[U4.50.01]



NOEUD_DOUBLE
=/“OUI”
/
“NON”
[DEFAUT]


);
Handbook of Utilization
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HT-66/05/004/A

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Titrate:
Operator CALC_MATR_AJOU


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:
U4.66.01-E Page
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3 Operands

3.1 Operand
MODELE_FLUIDE

MODELE_FLUIDE = fluid

Thermal model which one assigns to the part of the grid which corresponds to the fluid. Elements of
edge with the fluid interface/structure must be present in the fluid model. It is on this model
that one solves the equation of Laplace with boundary condition of the type “flow fluid”, to have it
field of pressure in all the fluid and a fortiori the field of pressure to the interface
fluid/structure.

The nodes of the elements of the fluid grid must all be numbered so that it
jacobien of the element is of positive sign on all the fluid grid.

3.2 Operand
MODELE_INTERFACE

MODELE_INTERFACE = interf

Thermal model of interface gathering all the elements of edge defining the interface
fluid/structure. It is on this model that one calculates the terms of the added matrices.

Calculation depends on the orientation of the normal of these elements of interface. It is necessary to take care of it
that this normal is directed towards all these elements, from the structure towards the fluid (convention
adopted).

If the fluids bathing the structure are different densities, the model should be defined interfaces
by as many groups of meshs not confused geometrically than there are fluids with the contact
structure. For example, a piping can have its interior surface in contact with a fluid
of density 1, and its surface external in contact with a fluid of density 2. The model interface is
thus built on two groups of meshs not confused geometrically, one in contact with
fluid of density 1 (interfa1) and the other in contact with the fluid of density 2 (interfa2).

interfa2
I
NR
interfa1
T
fluid 1
E
R
F
With
C
E
fluid 2
structure

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Code_Aster ®
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Titrate:
Operator CALC_MATR_AJOU


Date:
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Author (S):
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:
U4.66.01-E Page
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3.3 Operands
CHAM_MATER/LOAD

CHAM_MATER = matflui

Material field defining the fluid immersing the structure. This material is defined by
equivalent thermal characteristics in operator DEFI_MATERIAU [U4.43.01].
thermal conductivity (key word LAMBDA) is always taken equalizes to 1. Specific heat
(key word RHO_CP) the role of density of the fluid plays.

CHARGE = load

Thermal load of type [char_ther] necessary to the resolution of the linear system rising
equation of Laplace in the fluid. One must impose an unspecified temperature (which plays in
fact the role of a pressure) on an unspecified node of the fluid grid, in order to return the system
not singular. This operation is carried out with operator AFFE_CHAR_THER [U4.44.02].

3.4 Operands
MODE_MECA/CHAM_NO/MODELE_GENE

/MODE_MECA = modes

Dynamic modes calculated on the model structure. If there are several structures not
related immersed in the same fluid, for which one wants to determine the matrices
added including/understanding the terms of coupling by the fluid, the model structure which one defines
gather the totality of the immersed structures. The modes used by the operator are them
modes calculated for the total structure.


/CHAM_NO = chamno

Defining field with the nodes of displacements affected on groups of nodes
the fluid interface/structure. By affecting such a field of displacement on (S) the group (S) of
nodes of interface thanks to operator AFFE_CHAM_NO [U4.44.11], one can for example
to easily simulate modes of rigid body of the structures. This operand is to be used if
one wants to estimate the terms of the added matrices and coupling for a plane geometry
without making as a preliminary modal calculation of the structure in the vacuum, and which one wants
to affect these terms in discrete elements (modeling DIS_T). Operand INFO must
imperatively to be active to print the calculated terms.

Caution:

The use of this operand excludes that from operand NUME_DDL_GENE. One cannot
thus not to make modal, transitory calculation or harmonic by using the operand
CHAM_NO.

Indeed, to make calculation of modes out of water, it is necessary to have a matrix of mass
generalized and a matrix of rigidity generalized of the structure. This supposes to have
fact a modal calculation on the structure in the vacuum (what one wants precisely to avoid).

This operand is used ultimately only to evaluate the matrix of mass, of
rigidity and of damping added, and to use them to couple structures of the type
beam by discrete elements of mass, for example.
Handbook of Utilization
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Titrate:
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:
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/MODELE_GENE = modgen

Generalized model built by operator DEFI_MODELE_GENE [U4.65.02]. This key word is with
to use when one makes a calculation by dynamic under-structuring, and that one wants to calculate
stamp of added mass coupling the whole of the substructures. In this case, under
structures can be in different files of grid, these files being able to be them
same distinct from the fluid file of grid. The substructures which present one
repetitivity within the fluid are to be netted only only once, but one will take care with
level of the fluid grid to net all the interfaces fluid/structure. Moreover, it is necessary to take care
so that the nodes of fluid interface coincide as well as possible with the nodes of interface of
structure, in order to be able to recopy, on the basis of geometrical criterion of proximity, them
values of the fields of displacement of structure on the nodes of fluid interface (see
operand DIST_REFE).

Caution:

The use of this operand makes compulsory that of operand NUME_DDL_GENE.

3.5 Operand
OPTION

This key word specifies the calculation of mass, rigidity or damping added that one wants to make, while using
respectively “MASS_AJOU”, “RIGI_AJOU”, or “AMOR_AJOU”. Two last options of
calculation require the presence of a potential (thermal) stationary (see operand POTENTIEL).

3.6 Operand
DIST_REFE

Outdistance reference to be informed when one makes a calculation of mass added on a model
generalized. This distance is a geometrical absolute criterion intended to recopy values of
structural displacements in a thermal fluid model, in order to solve the equation of Laplace there of
non stationary field of pressure. By defect, it is equal to 10­2 Mr.

3.7 Operand
NOEUD_DOUBLE


NOEUD_DOUBLE = “YES”

This operand is to be used when one makes a calculation of mass added starting from a model
generalized which includes/understands a substructure with a grid by a telegraphic or surface grid (i.e without
thickness like beam or hull) and surrounded by two fluids. It is necessary in this case for the level of
grid to duplicate the nodes of the fluid interfaces of those of the structure, in order to be able
to calculate the hydrodynamic jump of pressure on both sides of the structure (cf appears
below).

X X X
X X
X
X
X
X
X
X
Structure with a grid
fluid 1
X
X
(without thickness)
X
X
X
X
X
X
Duplicated nodes
X
X
X
X
X X
(nodes having the same ones
co-ordinates but not it
fluid 2
even name)

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3.8 Operand
POTENTIEL


POTENTIEL = phi

Potential (thermal) stationary necessary to the calculation of damping and rigidity added
structure subjected to a potential flow. This potential is produced by the operator
THER_LINEAIRE [U4.54.01].

3.9 Operand
NUME_DDL_GENE

NUME_DDL_GENE = numgen

Generalized classification based on the mechanical modes of the total structure. The presence
of this operand allows to calculate a matrix of added mass of matr_asse_gene_R. type.
It must be necessarily present if one wants to make modal, harmonic calculation thereafter or
transient.

3.10 Operand
INFO

INFO
=

Indicate the level of impression of the results of the operator on file MESSAGE.

1:
no impression,
2:
impression of the higher triangular part of the matrices of added mass,
added damping or rigidity.

Presentation in column.
3.11 Key word factor SOLVEUR

See [U4.50.01].

3.12 Operand
AVEC_MODE_STAT

Allows to disconnect the calculation of the terms of mass added on the static modes contained in
the modal base of the substructures in the case of a calculation with a generalized model (cf [§3.4]).

3.13 Operand
NUME_MODE_MECA
Allows to specify a list of numbers of modes retained for calculation.

4 Phase
of execution

It is checked that the models fluid and interface are quite thermal.

It is checked that the storage of the added matrices is done on a full profile.

It is checked that the coefficients of added car-mass (diagonal terms of the matrix) are well all
positive. In the contrary case, a message of alarm is transmitted so that the user checks the orientation
normals.

It is checked that, for a calculation of added damping or rigidity, key word POTENTIEL is well
informed.

In the case of a calculation of mass added on a generalized model, one informs the user on
recopies of fields of structural displacements in the fluid (a number of recopied values) and one
indicate how to change the distance from reference (DIST_REFE).
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5 Example

5.1 Example 1: Calculation of the matrix of mass added of a structure
composed of two concentric cylinders separated by a fluid
incompressible

The cylinders are supported each one by springs. The matrix of added mass is calculated for
the first two modes of the structure, namely the modes of rigid body of each cylinder
in direction OX (cf diagram).

N
R2
M
R
k2
R
k1

X
R 1
()
1
m1
()
2
m2


1) Definition of fluid material by equivalent thermal characteristics:

water = DEFI_MATERIAU (THER = _F (LAMBDA = 1. , RHO_CP = 1000. ))

2) Assignment of this fluid material on the fluid grid including the defining group of mesh
the fluid interface/structure.

chammat1 = AFFE_MATERIAU (MAILLAGE = Maya,
AFFE = _F (GROUP_MA = “fluid”, MATER = water),
_F (GROUP_MA = “interface”, MATER = water))

3) Assignment of the fluid thermal model (also including/understanding the interface)

fluid = AFFE_MODELE (MAILLAGE = MAYA,
AFFE = (_F (GROUP_MA = “fluid”,
MODELING = “PLANE”,
PHENOMENON = “THERMAL”),
_F (GROUP_MA = “interface”,
MODELING = “PLANE”,
PHENOMENON = “THERMAL”)))

4) Assignment of the thermal model of interface

interf = AFFE_MODELE (MAILLAGE = MAYA
AFFE = _F (GROUP_MA = “interface”,
MODELING = “PLANE”,
PHENOMENON = “THERMAL”))
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5) Assignment of the total model structure (including/understanding the two cylinders and their springs of
self-supporting quality)

struct = AFFE_MODELE (MAILLAGE = MAYA,
AFFE = (_F (GROUP_MA = “cylinder”,
MODELING = “D_PLAN”,
PHENOMENON = “MECHANICAL”),
_F (GROUP_MA = “cylext”,
MODELING = “D_PLAN”,
PHENOMENON = “MECHANICAL”),
_F (GROUP_MA = “arises”,
MODELING = “DIS_T',
PHENOMENON = “MECHANICAL”),
_F (GROUP_MA = “ressorex”,
MODELING = “DIS_T',
PHENOMENON = “MECHANICAL”)))

6) Assignment of a temperature imposed in the fluid grid

charge = AFFE_CHAR_THER (MODELE = fluid,
TEMP_IMPO = _F (GROUP_NO = “tempimpo”, TEMP = 0.))

7) Calculation of the clean modes of the structure in the vacuum

modes = MODE_ITER_SIMULT (MATR_A = matasks,
MATR_B = matasms,
CALC_FREQ = _F (OPTION = “PLUS_PETITE”,
NMAX_FREQ = 2))

8) Generalized classification based on the calculated mechanical modes

numgen = NUME_DDL_GENE (MODE_MECA = modes, STOCKAGE = “PLEIN”)

9) Calculation of the matrix of added mass of matr_asse_gene_r type (operand NUME_DDL_GENE
present). So one can then calculate the clean modes of the “wet” structure

matraj = CALC_MATR_AJOU (MODELE_FLUIDE = fluid,
MODELE_INTERFACE = interf,
CHAM_MATER = chammat1,
CHARGE = load,
OPTION = “MASS_AJOU”,
MODE_MECA = modes,
NUME_DDL_GENE = numgen,
INFO =1)

10) Calculation of the matrices of mass and stiffness generalized on generalized classification based
on the calculated mechanical modes numgen. These matrices are of type [matr_asse_gene_r]

MACRO_PROJ_BASE (BASE = modes,
MATR_ASSE_GENE = (_F (MATRICE = matasms,
MATR_ASSE = mgene),
_F (MATRICE = matasks,
MATR_ASSE = riggen)))

11) Calculation of the matrix of total mass of the structure (matrix of more generalized mass matrix
of added mass)

mastot = COMB_MATR_ASSE (COMB_R = (_F (MATR_ASSE = mgene,
COEF_R = 1. ),
_F (MATR_ASSE = matraj,
COEF_R = 1. )))

12) Calculation of the modes of the immersed structure.

modhumi = MODE_ITER_SIMULT (MATR_A = riggen,
MATR_B = mastot,
CALC_FREQ = _F (OPTION = “PLUS_PETITE”,
NMAX_FREQ = 2))

13) Restitution of the modes “wet” on physical basis.

mode_mou = REST_BASE_PHYS (RESU_GENE = modhumi, MODE_MECA = modes)
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5.2
Example 2: Use of operand CHAM_NO: Calculation of the matrix
of mass added for a line of 3 tubes in a fluid channel

Are three tubes plunged in a fluid channel (see diagram). One wants to determine the matrix of mass
added including/understanding the terms of following coupling inter-tubes for the modes of rigid body
direction OX of the three tubes. Without making modal calculation on the structure in the vacuum, to simulate these
three modes of rigid body, one assigns a field to the nodes of unit displacement on each
group nodes defining the fluid interface structure of the three tubes.

GROUP_NO tube1
GROUP_NO tube2
GROUP_NO tube3
fluid


1) Assignment on the groups of nodes of interface of a field to the nodes of unit displacement
according to OX. It is obligatory to support this field with the nodes on the classification of the ddl of the model
structure.

chamno1 = CREA_CHAM (MAILLAGE = Maya,
TYPE_CHAM = “NOEU_DEPL_R”,
OPERATION = “AFFE”,
AFFE = _F (GROUP_NO = “TUBE1”,
NOM_CMP = (“DX”, “DY”),
VALE = (1. , 0.) )
NUME_DDL = nustruct)

chamno2 = CREA_CHAM (MAILLAGE = Maya,
TYPE_CHAM = “NOEU_DEPL_R”,
OPERATION = “AFFE”,
AFFE = _F (GROUP_NO = “TUBE2”,
NOM_CMP = (“DX”, “DY”),
VALE = (1. , 0.) )
NUME_DDL = nustruct)

chamno3 = CREA_CHAM (MAILLAGE = Maya,
TYPE_CHAM = “NOEU_DEPL_R”,
OPERATION = “AFFE”,
AFFE = _F (GROUP_NO = “TUBE3”,
NOM_CMP = (“DX”, “DY”),
VALE = (1. , 0.) )
NUME_DDL = nustruct)

2) Call
with
CALC_MATR_AJOU: the operator calculates the matrix 3 * 3 of mass added of the three tubes. It
is impossible to make modal, harmonic, or transitory calculation thereafter.

matraj = CALC_MATR_AJOU (MODELE_FLUIDE = fluid,
MODELE_INTERFACE = interf,
CHAM_MATER = chammat1,
CHARGE = load,
OPTION = “MASS_AJOU”,
CHAM_NO = (chamno1, chamno2, chamno3),
INFO =2)
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3) The terms of the matrix of added mass can be read on file “MESSAGE” and used
in another model describing the structure. The terms of added mass calculated here translate it
coupling by the fluid in a transverse plan with the three tubes. If from now on one wants to study it
coupling of the tubes modelled by beams, one can affect the terms of mass of the matrix
calculated in discrete elements of mass (modeling DIS_T) which connect the elements of
beam in opposite.

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