Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 1/16
Organization (S): EDF-R & D/AMA, SINETICS
Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.52.03
Operator MODE_ITER_SIMULT
1 Goal
To calculate clean values and vectors by methods of the subspace type. For the problem
traditional of dynamics (without damping) or the problem of buckling of Euler, three
algorithms are available: Sorensen, Lanczos, Bathe and Wilson. For the problem of dynamics
with damping, only the methods of Sorensen and Lanczos are usable. Product one
concept mode_meca_ * (dynamic case) or mode_flamb (case buckling of Euler).
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 2/16
2 Syntax
mode_ [*] = MODE_ITER_SIMULT
# MODAL FACT OF THE CASE
(
MATR_A
=
With
/
[matr_asse_DEPL_R]
/
[matr_asse_DEPL_C]
/
[matr_asse_PRES_R]
/
[matr_asse_GENE_R]
MATR_B
=
B
/
[matr_asse_DEPL_R]
/
[matr_asse_PRES_R]
/
[matr_asse_GENE_R]
MATR_C
=
C
/
[matr_asse_DEPL_R]
# STANDARD OF PROBLEM
TYPE_RESU
=
/
“DYNAMIQUE”
[DEFAUT]
/
“MODE_FLAMB”
# CHOICE OF THE METHOD
METHODE
=
/
“SORENSEN” [DEFECT]
/
“TRI_DIAG”
/“JACOBI”
# If METHOD = “TRI_DIAG”
OPTION
=
/
“SANS”
[DEFAUT]
/
“MODE_RIGIDE”
# STANDARD OF MODAL CALCULATION
CALC_FREQ =_F (OPTION
=/“CENTER”
/
“BANDE”
/
“PLUS_PETITE”
[DEFAUT]
# CHARACTERISTIC OF CALCULATION
#
If TYPE_RESU = “DYNAMIC”
APPROCHE
=/
“REEL”
[DEFAUT]
/
“IMAG”
/
“COMPLEXE”
#
If
OPTION
=
“PLUS_PETITE”
NMAX_FREQ
=
/
10
[DEFAUT]
/
nf
[I]
#
If
OPTION
=
“CENTER”
FREQ
=
l_f
[l_R]
AMOR_REDUIT
=
l_a
[l_R]
NMAX_FREQ
=
/
10
[DEFAUT]
/
nf
[I]
#
If
OPTION
=
“BANDE”
FREQ
=
l_f
[l_R]
#
If TYPE_RESU = “MODE_FLAMB”
APPROCHE
=/
“REEL”
[DEFAUT]
/
“IMAG”
#
If
OPTION
=
“PLUS_PETITE”
NMAX_FREQ
=
/
10
[DEFAUT]
/
nf
[I]
#
If
OPTION
=
“CENTER”
CHAR_CRIT
=
l_c
[l_R]
NMAX_FREQ
=
/
10
[DEFAUT]
/
nf
[I]
#
If
OPTION
=
“BANDE”
CHAR_CRIT
=
l_c
[l_R]
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 3/16
# CHARACTERISTIC OF THE SPACE OF PROJECTION
DIM_SOUS_ESPACE
= of
[I]
COEF_DIM_ESPACE
= mse
[I]
EXCLUDE (“DIM_SOUS_ESPACE”,
“COEF_DIM_ESPACE”)
# FOR PRE AND POSTPROCESSINGS
PREC_SHIFT
=
/
0.05
[DEFAUT]
/
PS [R]
NMAX_ITER_SHIFT =/5 [DEFECT]
/
NS [I]
NPREC_SOLVEUR =/8 [DEFECT]
/
ndeci [R]
SEUIL_FREQ
=
/
1.E-2 [DEFAUT]
/
sf [R]
# PARAMETER SETTING INTERNS METHODS
#
If METHOD = “SORENSEN”
PREC_SOREN =
/0 [DEFAUT]
/
pso
[R]
NMAX_ITER_SOREN =/20
[DEFAUT]
/
nso
[I]
PARA_ORTHO_SOREN =/0.717
[DEFAUT]
/
porso
[I]
#
If METHOD = “TRI_DIAG”
PREC_ORTHO
=
/
1.E-12
[DEFAUT]
/Po
[R]
NMAX_ITER_ORTHO =/5 [DEFECT]
/
nio
[I]
PREC_LANCZOS =
/1.E-8
[DEFAUT]
/pl
[R]
NMAX_ITER_QR
=
/
30 [DEFAUT]
/
nim
[I]
#
If METHOD = “JACOBI”
PREC_BATHE
=
/
1.E-10
[DEFAUT]
/
pbat
[R]
NMAX_ITER_BATHE
=/
40
[DEFAUT]
/
nbat
[I]
PREC_JACOBI
=
/
1.E-2 [DEFAUT]
/
pjaco [R]
NMAX_ITER_JACOBI =/12
[DEFAUT]
/
njaco [I]
)
# FOR FINAL CHECKS
VERI_MODE
= _F (
STOP_ERREUR
=
/
“OUI”
[DEFAUT]
/
“NON”
SEUIL
=/
1.E-6
[DEFAUT]
/R
[R]
PREC_SHIFT
=
/
0.05 [DEFAUT]
/
prs
[R]
STURM
=/
“OUI”
[DEFAUT]
/
“NON”
)
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 4/16
# SENSIBILITE
SENSIBILITE = (
… to see [U4.50.02]….
)
# DIVERS
STOP_FREQ_VIDE
=
/
“OUI”
[DEFAUT]
/
“NON”
INFO
=
/
1
[DEFAUT]
/
2
[I]
TITER = Ti
);
# GIVEN RESULT
If MATR_C = [matr_asse_DEPL_R]
then [*]
- > meca_c
If
TYPE_RESU
=
“MODE_FLAMB”
then [*]
- > mode_flamb
If MATR_A = [matr_asse_DEPL_C]
then [*]
- > meca_c
If MATR_A = [matr_asse_DEPL_R]
then [*]
- > meca
If MATR_A = [matr_asse_PRES_R]
then [*]
- > acou
If MATR_A = [matr_asse_GENE_R]
then [*]
- > embarrassment
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 5/16
3 Operands
3.1 Principles
This operator solves the problem generalized with the eigenvalues according to [R5.01.01]:
To find (, X) such as Ax = Bx, X 0, where A and B are symmetrical matrices with coefficients
realities. To model a damping hysteretic in the study of the free vibrations of a structure,
matrix A can be complex [U2.06.03] [R5.05.04]. This type of problem corresponds, in
mechanics, in particular with:
·
The study of the free vibrations of a not deadened and nonrevolving structure. For this
structure, one seeks the smallest eigenvalues or those which are in one
interval given to know if an exiting force can create a resonance. In this case,
matrix A is the matrix of material rigidity, noted K (real or complex),
_éventuellement increased geometrical matrix of rigidity noted kg, if the structure
is précontrainte_, and B is the matrix of mass or noted inertia Mr. Les eigenvalues
obtained are the squares of the pulsations associated with the sought frequencies.
The system to be solved can be written: (K + K
where = () 2
2 F is the square of
G) X = {
MX
4
1 4
2 3
B
With
pulsation, F the Eigen frequency and X the vector of associated clean displacement.
If K is complex, and F it are too.
·
The search for linear mode of buckling. Within the framework of the linearized theory, in
supposing a priori that the phenomena of stability are suitably described by
system of equations obtained by supposing the linear dependence of displacement by
report/ratio at the level of critical load, the search of the mode of buckling X associated it
level of critical load µ = -, brings back itself to a problem generalized to the eigenvalues
form: (K + µ K
=
=
with K stamps material rigidity and
G) X
0
{
Kx
K X
{G
With
B
Kg stamps geometrical rigidity.
Caution:
In the code, one treats only the eigenvalues of the generalized problem, them. For
to obtain the true critical loads, the µ, it is necessary to multiply them by 1.
This operator allows also the study of the dynamic stability of an involved structure
depreciation viscous (and/or quadratic) and gyroscopic effects. That led to
resolution of a modal problem of a nature higher, known as quadratic [R5.01.02]. One seeks then
complex values and clean vectors by the method of Lanczos after having carried out a reduction
linear of the problem.
·
The problem consists in finding (, X) (C, C NR) such as (2B + C + A) X = 0 where
typically, in linear mechanics, A = K will be the matrix of rigidity, B = M the matrix of
mass and C the matrix of damping. The matrices K, M and C are matrices with
real coefficients. The eigenvalue complexes is connected to the Eigen frequency F and to
the damping reduced by: = (2) ± (2) 1 - 2
F
I
F
.
K can be also complex to moreover simulate, one damping hysteretic
[U2.06.03] [R5.05.04].
Handbook of Utilization
U4.5- booklet: Methods of resolution
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Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 6/16
To solve these generalized or quadratic modal problems, Code_Aster proposes
various approaches. Beyond their numerical specificities and functional calculuses which are taken again
in the document [R5.01.01], one can synthesize them in the shape of table below (the values
by defect are materialized in fat).
Operator/
Algorithm Key word Advantages
Disadvantages
Perimeter
of application
MODE_ITER_INV
1ère phase
(heuristics)
Calculation of some
Bisection
“SEPARE”
modes
Calculation of some
Bisection +
“AJUSTE”
Better precision
Cost calculation
modes
Secant (gene.)
Muller (quad.)
Improvement of
Initialization by
“PROCHE”
Resumption of values
No the capture
some estimates
the user
clean estimated
of multiplicity
by another
process.
Cost calculation of this
phase quasi-no one
2nd phase
(method of
powers properly
said)
Basic method
Powers
“DIRECT”
Very good
Not very robust
opposite
construction of
clean vectors
Option of acceleration
Quotient of
“RAYLEIGH”
Improve
Cost calculation
Rayleigh
convergence
Not carried in
quadratic
MODE_ITER_SIMULT
Calculation of part of
Bathe & Wilson
“JACOBI”
Little
robust
spectrum
Not carried in
quadratic
Lanczos
“TRI_DIAG”
Little
robust
(Newman- Pipano)
IRAM
(Sorensen)
Increased “SORENSEN” Robustesse.
Better
calculation complexities
and memory.
Control
quality of the modes.
Table 3.1-1: Summary of the modal methods of Code_Aster
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 7/16
When it is a question of determining some simple eigenvalues discriminated well or to refine
some estimates, operator MODE_ITER_INV, is often clearly shown. On the other hand, for
to capture a part significant of the spectrum, one A resorts to MODE_ITER_SIMULT, via the methods
known as “of subspace”.
It is this class of method which will interest us here.
It consists in projecting advisedly the operator of work in order to obtain a modal problem
standard of more reduced size and comprising a canonical matrix of form (tridiagonale or of
Higher Hessenberg). It is on the latter that total modal solveurs will be able
then to operate (algorithm QR, QL or Jacobi). They are in general very robust, but they provide
all the spectrum of the treated operator and they are very expensive. From where the idea to fix quotas for their efforts
on only one “projected” spectrum.
It is completely recommended besides to benefit from the strong points of the two classes from
method by refining the clean vectors obtained by MODE_ITER_SIMULT, via
MODE_ITER_INV (OPTION=' PROCHE'). That will make it possible to reduce the standard of the final residue
(cf [§3.7.2]).
Note:
One strongly advises a preliminary reading of the reference materials [R5.01.01],
[R5.01.02]. It gives to the user the properties and the limitations, theoretical and practical,
modal methods approached while connecting these considerations, which can sometimes
to appear a little éthérées, with a precise parameter setting of the options.
3.2 Operands
MATR_A, _B, _C
MATR_A
= A
Stamp assembly of concept [matr_asse_ * _R/C] of the system to be solved.
MATR_B
= B
Stamp assembly of concept [matr_asse_ * _R] of the system to be solved.
MATR_C
= C
Stamp assembly of concept [matr_asse_ * _R] of the quadratic system to solve.
3.3 Word
key
TYPE_RESU
TYPE_RESU =/“DYNAMIC”
[DEFAUT]
/“MODE_FLAMB”
This key word makes it possible to define the nature of the modal problem to treat: search for frequencies of
vibration (traditional case of dynamics with or without damping) or search for loads
critical (case of the theory of linear buckling). According to this class of membership, them
results are displayed and stored differently in the structure of data:
·
In dynamics, the frequencies are ordered by order ascending of the module of their
variation with the shift (cf [§2.9], [§4.4] [R5.01.01]). It is the value of the variable of access
NUM_ORDRE of the structure of data. The other variable of access, NUME_MODE, is equal to
the true modal position in the spectrum of the eigenvalue (determined by the test of
Sturm cf [§2.5], [§2.6] [R5.01.01]).
·
In buckling, the eigenvalues are stored by order ascending algebraic.
variables NUM_ORDRE and NUM_MODE take the same value equal to this command.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_SIMULT
Date:
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Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 8/16
3.4 Word
key
METHODE
Three methods of resolution are available for the problem to the eigenvalues
·
Method IRA (known as of Sorensen), makes it possible to treat the two types of problems
generalized and quadratic. It is the method by defect and is based on:
-
obtaining a matrix of Hessenberg by using a factorization of the Arnoldi type
-
the calculation of the eigenvalues of this problem projected by a method QR
-
a certain number of restartings allowing to refine the sought eigenvalues
by the user, the other eigenvalues necessary to the method being used as values
auxiliaries.
·
The method of Lanczos, makes it possible to treat the two types of problems generalized and
quadratic. It is based on:
-
obtaining a matrix tridiagonale projected via the method of Lanczos,
-
the resolution of the system tridiagonal reduced by a method QR,
·
The iterative method of Bathe and valid Wilson only for the generalized problem, is
based on:
-
construction with each iteration of a projected generalized problem of smaller size,
-
the calculation of the eigenvalues of this problem projected by a method of Jacobi.
METHODE
=
/“SORENSEN” [DEFECT]
One uses the method of Sorensen (cf [§5] [R5.01.01]) to calculate the values and vectors
clean of the generalized or quadratic problem. This option cannot be used for one
quadratic problem.
/“TRI_DIAG”
One uses the method of Lanczos (then method QR on the projected system) to calculate them
values and clean vectors of the generalized or quadratic problem (cf [§4] [R5.01.01]).
/“JACOBI”
One uses the method of Bathe & Wilson (cf [§6] [R5.01.01]) (then method of Jacobi on
system projected) to calculate the values and clean vectors of the generalized problem. This
option cannot be used for a quadratic problem.
3.5 Word
key
OPTION
OPTION =
/“MODE_RIGIDE”
/“SANS”
[DEFAUT]
Key word usable only with the method of Lanczos for a generalized modal problem. It
allows to detect and calculate as a preliminary, by an algebraic method the modes of body
of rigid (modes associated with a null eigenvalue) (cf [§5.5.4] [R5.01.01]). They are used by
the continuation to calculate the other modes with the algorithm of Lanczos. They are provided to the user
only if they belong to the modes requested. If the modes of rigid body are calculated without
to use this option, the eigenvalues calculated by the algorithm of Lanczos are not null
but very close to zero.
3.6 Word
key
CALC_FREQ
CALC_FREQ
=_F (…
Key word factor for the definition of the parameters of calculation of the eigenvalues and their number.
Handbook of Utilization
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Code_Aster ®
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Titrate:
Operator MODE_ITER_SIMULT
Date:
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Author (S):
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:
U4.52.03-G Page
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3.6.1 Operand
OPTIONS
OPTION
=
“BANDE”
One seeks all the eigenvalues in a given tape. This
tape is defined by the argument of FREQ: (F F) or by that of
1
2
CHAR_CRIT: ().
1
2
This option is not usable with a quadratic modal problem.
“CENTER”
One seeks the NMAX_FREQ the eigenvalues closest to
frequency F (argument of key word FREQ: F) or closest to
the critical load (argument of key word CHAR_CRIT: ).
“PLUS_PETITE” One seeks the NMAX_FREQ smaller eigenvalues.
[DEFAUT]
See [§2.9] and [§4.4] [R5.01.01].
3.6.2 Operand
APPROCHE
APPROCHE
=/
“REEL”
[DEFAUT]
/
“IMAG”
/
“COMPLEXE”
This key word defines the type of approach (real, imaginary or complex) for the choice of pseudo
scalar product of the quadratic problem (cf [§5.5.2] [R5.01.02]). In general the default value
(reality) is valid.
This operand does not have a direction that for the analysis of the free vibrations of a deadened structure (modes
proper complexes; key word MATR_C must be indicated). In buckling, that does not have any
interest.
3.6.3 Operand
FREQ
FREQ = l_f
List frequencies (can be used only if TYPE_RESU = “DYNAMIQUE”): its use
depends on the selected OPTION.
OPTION = “TAPE”
One awaits two values (F F) which define the tape
1
2
of search,
OPTION = “CENTER”
Only one value of frequency is awaited,
The values stipulated under this key word must be positive.
3.6.4 Operand
AMOR_REDUIT
AMOR_REDUIT = l_a
Value of the reduced damping which makes it possible to define the eigenvalue complexes around
which one seeks the eigenvalues closest. (can be used only if
TYPE_RESU = “DYNAMIQUE” and well informed MATR_C).
OPTION = “CENTER”
One awaits only one value of reduced damping,
The value stipulated under this key word must be positive and lie between 0 and 1. In buckling, that
no interest has.
Handbook of Utilization
U4.5- booklet: Methods of resolution
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Code_Aster ®
Version
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Titrate:
Operator MODE_ITER_SIMULT
Date:
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Author (S):
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:
U4.52.03-G Page
: 10/16
3.6.5 Operand
CHAR_CRIT
CHAR_CRIT = l_c
List critical loads (can be used only if TYPE_RESU = “MODE_FLAMB”): its
use depends on the selected OPTION.
OPTION = “TAPE”
One awaits two values () which define the tape
1
2
of search,
OPTION = “CENTER”
One awaits only one value of critical load,
The values stipulated under this key word are positive or negative.
3.6.6 Operand
NMAX_FREQ
NMAX_FREQ
= nf
(10)
[DEFAUT]
Numbers maximum eigenvalues to calculate.
This key word is ignored with option “BANDE” because one calculates all the eigenvalues then
contained in the stipulated tape.
In the two cases, if nf is strictly higher than the number of “ddl active”, nactif (cf [§2.2]
[R5.01.01]), then one forces it to take this value ceiling.
3.6.7 Operand
DIM_SOUS_ESPACE
DIM_SOUS_ESPACE
= of
COEF_DIM_ESPACE
= mse
EXCLUDE (“DIM_SOUS_ESPACE”, “COEF_DIM_ESPACE”)
If key word DIM_SOUS_ESPACE is not indicated or is initialized with a value strictly
lower than the number of required frequencies nf, the operator calculates one automatically
acceptable dimension for the subspace of projection (cf [§5.2] of this document and [§4.3],
[§5.5.2], [§6.5.3], [§7.3.1] [R5.01.01]) with assistance COEF_DIM_ESPACE.
Thanks to given of this multiplicative factor, mse, one can project on a space whose size is
proportional to the number of frequencies contained in the interval of study. In
the encapsulation of MODE_ITER_SIMULT, MACRO_MODE_MECA [U4.52.02], one can thus optimize
the size of the subspaces which remains proportional to the number of required frequencies:
subspaces rich in eigenvalues thus do not penalize poorest (in term of
CPU).
One can however arbitrarily fix the size of this subspace, via the value of the catch by
key word DIM_SOUS_ESPACE (which must be higher than nf to be taken into account).
In both cases, if the size of the subspace of projection ndim is strictly higher than
number “active ddl”, nactif (cf [§2.2] [R5.01.01]), then one forces it to take this value
ceiling.
Note:
·
If one uses the method of Sorensen (IRAM) and that ndim - nf < 2, of the requirements
numérico-data processing force to impose ndim = nf + 2.
·
Into quadratic one works on a real problem of double size: 2 * nf, 2 * ndim.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
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Titrate:
Operator MODE_ITER_SIMULT
Date:
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Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.03-G Page
: 11/16
3.6.8 Operands of IRAM (if METHODE = “SORENSEN”)
PREC_SOREN = pso
(0. )
[DEFAUT]
Note:
The method considers whereas it must work with the smallest possible precision, it
“zero machine”. To have an order of magnitude of it, in double precision on the machines
standards, this value is close to 2.22 .10-16)
NMAX_ITER_SOREN = nso
(20)
[DEFAUT]
PARA_ORTHO_SOREN
= porso
(0.717)
[DEFAUT]
They are parameters of adjustment of the necessary precision on the modes (by defect, the precision
machine is selected), of the number of restartings authorized of the method of Sorensen
(cf [§5.4.2] and [§6.4] [R5.01.01]) and of the coefficient of orthogonalization of the IGSM of Kahan-Parlett
(cf [§11.4] [R5.01.01]).
Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with
values standards.
3.6.9 Operands of the method of Lanczos (if METHODE = “TRI_DIAG”)
PREC_ORTHO = Po
(1.10-12) [DEFAUT]
NMAX_ITER_ORTHO = nio
(5)
[DEFAUT]
PREC_LANCZOS
=
pl
(1.10-8)
[DEFAUT]
NMAX_ITER_QR
= nim
(30)
[DEFAUT]
The first two parameters make it possible, respectively, to adjust the precision
of orthogonalization and the number of réorthogonalisations in the method of Lanczos for
to obtain independent vectors generating the subspace (cf [§5.5.1] [R5.01.01]).
The third is a parameter of adjustment to determine the nullity of a term on
surdiagonale of the matrix tridiagonale characterizing the reduced problem obtained by the method of
Lanczos. It is right a criterion of deflation and not, as opposed to what could let believe
its name, a quality standard of the modes (cf [§5.4.1] [R5.01.01]).
The last fixes the maximum iteration count for the resolution of the system reduced by
method QR ([§5.5.2] and [§10] [R5.01.01]).
Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with
values standards.
3.6.10 Operands of the method of Bathe & Wilson (if METHODE = “JACOBI”)
PREC_BATHE = pbat (1.10-10) [DEFAUT]
NMAX_ITER_BATHE = nbat (40)
[DEFAUT]
PREC_JACOBI = pjaco (1.10-2)
[DEFAUT]
NMAX_ITER_JACOBI
= njaco
(12)
[DEFAUT]
The first two parameters make it possible, respectively, to adjust the precision of convergence
and the maximum number of allowed iterations of the method of Bathe & Wilson (cf [§7]
[R5.01.01]).
The two others make it possible to adjust the precision of convergence and the maximum number
iterations permitted by the method of JACOBI (cf [§12] [R5.01.01]) who allows to exhume them
clean modes of the matrix projected by the preceding method.
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:
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Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with
values standards.
3.6.11 Operands SEUIL_FREQ, PREC_SHIFT and NMAX_ITER_SHIFT
PREC_SHIFT = PS
(0.05)
[DEFAUT]
SEUIL_FREQ = sf
(0.01)
[DEFAUT]
NMAX_ITER_SHIFT = NS
(5)
[DEFAUT]
For three possible options “PLUS_PETITE”, “BANDE” or “CENTER”, one carries out one
2
factorization LDLT of matrix (A - (2 F *) B). F * depends on the method used. If F * is
detected as being an Eigen frequency or being located near Eigen frequencies
(loss of more than decimal ndeci=8 during the factorization of the matrices), the frequency F * is
then modified (cf [§2.6] and [§2.9] [R5.01.01]):
F -
F
(1 PS) or F +
=
× -
= F × (1+ PS
*
*
*
*
)
2
If (A - (2 F *) B) is not factorisable LDLT and (F
sf
*
), one carries out
following modification: F - = - sf
*
. It is considered whereas F * is associated a mode of body
rigid. The modification of this frequency makes it possible a priori to enter all the modes of
rigid body. One does not carry out more NS modifications of the value F *.
In the case of linear buckling, the transposition is immediate by replacing F * (frequency
2
2
of vibration) by * (critical load), (2 F *) by * and sf by (2 sf).
Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with
values standards.
3.6.12 Operand NPREC_SOLVEUR
NPREC_SOLVEUR
= ndeci (8)
[DEFAUT]
ndeci represents the number of decimals which one is authorized to lose during the factorization of
2
stamp shiftée (A - (2 F *) B) or (A - B). If one loses more decimal ndeci, the matrix
is regarded as noninvertible (cf [§2.6] and [§2.9] [R5.01.01]).
Note:
At the time of the first passages, it is strongly advised not to modify this parameter which
rather relate to a mystery of the algorithm and which is initialized empirically with a value
standard.
3.7 Word
key
VERI_MODE
VERI_MODE = _F (…
Key word factor for the definition of the parameters of the checking of the clean modes ([§2.9]
[R5.01.01]).
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3.7.1 Operand
STOP_ERREUR
STOP_ERREUR =/
“OUI”
[DEFAUT]
/
“NON”
Allows to indicate to the operator if it must stop (“OUI”) or continue (“NON”) if
one of criteria SEUIL or STURM is not checked.
By defect the concept of output is not produced.
3.7.2 Operand
SEUIL
SEUIL = R (1.10-6
)
[DEFAUT]
Tolerance level for the standard of error relating of the mode to the top of which the mode is
regarded as forgery.
The standard of relative error of the mode is:
(A -)
B X 2, for 0 for the generalized problem and
Ax 2
(2B + C - A) X 2,
Ax
for the quadratic problem
2
3.7.3 Operand
STURM
STURM =/
“OUI”
[DEFAUT]
/
“NON”
Checking known as of STURM (“OUI”) allowing to make sure that the algorithm used in
the operator determined the exact number of eigenvalues in the interval of search
([§2.5] [§2.6] [R5.01.01]).
3.7.4 Operand
PREC_SHIFT
PREC_SHIFT = prs
(0.05)
[DEFAUT]
This parameter (which is a percentage) makes it possible to define an interval containing the values
clean calculated, for which the checking of Sturm will be carried out ([§2.6] [R5.01.01]).
3.8 Operands
SENSIBLITE
SENSIBILITE =
Activate the calculation of derived from the modes compared to a significant parameter of the problem.
It is it should be noted that at present, the derivative of the multiple modes is not available, because it
pose theoretical and practical problems particular.
The document [U4.50.02] specifies the operation of the key word.
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3.9 Operand
STOP_FREQ_VIDE
STOP_FREQ_VIDE =/
“OUI”
[DEFAUT]
/
“NON”
“OUI” stops calculation if no eigenvalue is detected in the tape stipulated by
the user: an exception (named BandeFrequenceVide) is emitted. It can be treated
to continue the course of the study. One can find an example under the case SDLL11a: test
try:
MODE1=MODE_ITER_SIMULT (MATR_A=K_ASSE, MATR_B=M_ASSE,
CALC_FREQ=_F (
OPTION = “TAPE”,
FREQ = (100., 200. )))
except aster.BandeFrequenceVideError:
MODE1=MODE_ITER_SIMULT (MATR_A=K_ASSE, MATR_B=M_ASSE,
CALC_FREQ=_F (
OPTION = “TAPE”,
FREQ = (200., 3500.,)))
“NON” does not stop calculation (emission only of one ALARME) if no eigenvalue is
detected in the tape stipulated by the user.
This key word is used in macro-command MACRO_MODE_MECA [U4.52.02] in order to allow
the absence of eigenvalues in a tape of search.
3.10 Operand
INFO
INFO
=/
1
[DEFAUT]
/2
Indicate the level of impression in file MESSAGE.
1: Impression on file “MESSAGE” of the eigenvalues, their modal position, of
reduced damping, of the standard of error a posteriori and certain useful parameters
to follow the course of calculation (Cf. [§5.2])
2: Impression rather reserved for the developers.
3.11 Operand
TITER
TITER = Ti
Titrate attached to the concept produced by this operator [U4.03.01].
4
Phase of checking
One checks according to options':
OPTION = “TAPE”
the argument of key word FREQ or key word CHAR_CRIT must provide two values exactly,
OPTION = “CENTER”
the argument of key word FREQ or key word CHAR_CRIT must provide only one value exactly,
OPTION = “PLUS_PETITE”
the argument of key word FREQ or key word CHAR_CRIT, is ignored.
If the maximum precise details and numbers of iterations are unrealistic (for example precise details
lower than the precision machine or of the negative iteration counts), calculation is not carried out.
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5 Phase
of execution
5.1 Checking
The matrices A, B (and C) arguments of key words MATR_A and MATR_B (and MATR_C), must be
coherent between them (i.e. to be based on the same classification and the same mode of
storage).
5.2
Actions by defect
If key word DIM_SOUS_ESPACE is not indicated or is initialized with a value strictly
lower than the number of required frequencies nf (operand NMAX_FREQ), the operator calculates
automatically an acceptable dimension for the subspace of projection via the formulas
empirical (cf [§3.6.7]):
METHOD = “SORENSEN”
ndim = MIN (MAX (2+nf, mse * nf), nactif) with mse = 2 per defect.
METHOD = “TRI_DIAG”
ndim = MIN (MAX (7+nf, mse * nf), nactif) with mse = 4 per defect.
METHOD = “JACOBI”
ndim = MIN (MAX (7+nf, mse * nf), nactif) with mse = 2 per defect.
where nactif of ddl active (i.e. the total number of ddl less the number of ddls is the number of
LAGRANGE and less the number of linear relations which bind ddls between them, cf [§2.2] [R5.01.01])
and mse is the factor of proportionality fixed by COEF_DIM_ESPACE.
If one solves a quadratic problem with the eigenvalues, the dimension of the subspace is
doubled.
The values of these various parameters are printed in file MESSAGE.
6
Modal parameters/Norme of the modes/Position modal
At output of this operator, the real or complex clean modes are standardized with largest
components which is not a multiplier of LAGRANGE. To choose another standard, it is necessary
to use command NORM_MODE [U4.52.11].
In the case of a dynamic calculation, the structure of data mode_meca_ *, contains, in addition to
frequencies of vibration and the associated modal deformations, the modal parameters (mass
generalized, generalized stiffness, factor of participation, mass effective). One will find the definition of
these parameters in [R5.01.03].
In the case of a linear calculation of buckling, the structure of data mode_flamb, only contains
critical loads and associated deformations.
In the case of a dynamic calculation, the modal position of the modes corresponds to the position of the mode
in the whole of the spectrum defined by the initial matrices.
In the case of a linear calculation of buckling, the modal positions of the critical loads are
allotted of 1 to nf (nf being the number of calculated critical loads) by classifying the loads
critical by order ascending algebraic. All the modal positions are thus positive.
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7
Impression of the results
To display the modal parameters associated with each mode and the co-ordinates with the modes, it is necessary
to use operator IMPR_RESU [U4.91.01] in the following way:
· Display of the modal parameters only in the form of table:
IMPR_RESU
(
RESU
=
_F (
RESULTAT = mode,
TOUT_PARA
=
“OUI”,
TOUT_CHAM
=
“NON”))
;
· Display of the modal parameters and the clean vectors:
IMPR_RESU
(RESU =_F (RESULTAT = mode,
TOUT_PARA
=
“OUI”,
TOUT_CHAM
=
“OUI”))
;
8
Sorting of modes/Caractérisation of mode_meca_ *
For example, at the time of seismic stresses in modal analysis, the modal base used must contain
the modes which have an important unit effective mass in the direction of the seism.
Command EXTR_MODE [U4.52.12] makes it possible to extract in a structure of data of the type
mode_meca_ * of the modes which check a certain criterion and of concaténer several structures of
data of the mode_meca_ type *.
A macro-command, allowing to connect commands MODE_ITER_SIMULT, NORM_MODE and
EXTR_MODE was created: MACRO_MODE_MECA [U4.52.02].
9 Examples
9.1 Calculation of the 5 clean modes closest to a frequency
data (100 Hz)
mode = MODE_ITER_SIMULT
(MATR_A = rigid,
MATR_B
=
mass,
CALC_FREQ
=_F (
OPTION
=
“CENTER”,
FREQ
=
100.,
NMAX_FREQ
=
5
)
);
9.2
Calculation of the critical loads contained in a tape
mode = MODE_ITER_SIMULT
(MATR_A = rigid,
MATR_B
=
riggeo,
TYPE_RESU
=
“MODE_FLAMB”,
CALC_FREQ
=_F (
OPTION
=
“BANDE”,
CHAR_CRIT
=
(- 1.E8
,
1.5E8))
);
Handbook of Utilization
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