Code_Aster ®
Version
7.4
Titrate:
Procedure IMPR_STURM
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.01-H Page
: 1/6
Organization (S): EDF-R & D/AMA, SINETICS
Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.52.01
Procedure IMPR_STURM
1 Goal
To calculate the number of eigenvalues included/understood in an interval and to print out it. This procedure is
advised like checking a priori of the model and to define intervals of search containing
a reasonable number of eigenvalues in order to optimize the calculating time of the operators
MODE_ITER_SIMULT or MODE_ITER_INV.
The execution of this procedure requires two factorizations LDLT.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Procedure IMPR_STURM
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.01-H Page
: 2/6
2 Syntax
IMPR_STURM
(
MATR_A
=
With
/
[matr_asse_DEPL_R]
/
[matr_asse_TEMP_R]
/
[matr_asse_PRES_R]
MATR_B
=
B
/
[matr_asse_DEPL_R]
/
[matr_asse_TEMP_R]
/
[matr_asse_PRES_R]
TYPE_RESU=/
“DYNAMIQUE”
[DEFAUT]
/“MODE_FLAMB”
# If TYPE_RESU = “DYNAMIC”
FREQ_MIN=
/
f_min
[R]
/
0.
[DEFAUT]
FREQ_MAX=
f_max
[R]
# If TYPE_RESU = “MODE_FLAMB”
CHAR_CRIT_MIN= _min
[R]
CHAR_CRIT_MAX= _max
[R]
SEUIL_FREQ=
/
f_seuil [R]
/
0.01 [DEFAUT]
PREC_SHIFT=
/
p_shift [R]
/
0.01 [DEFAUT]
NMAX_ITER_SHIFT=/
n_shift [I]
/
5
[DEFAUT]
NPREC_SOLVEUR =/
ndeci
[I]
/
8
[DEFAUT]
UNITE
=/
nunite
[I]
/
8
[DEFAUT]
);
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Procedure IMPR_STURM
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.01-H Page
: 3/6
3 Operands
3.1 Operands
MATR_A and MATR_B
MATR_A: A
MATR_B: B
With and B being names of the assembled matrices, the problem generalized with the eigenvalues
studied is:
(A B) v = 0
In the traditional case of dynamics, A is the matrix of rigidity and B the matrix of mass.
2
eigenvalue is then connected to the Eigen frequency F by the formula: = (
2 F).
In the case of the theory of linear buckling, A is the matrix of rigidity and B the matrix of
geometrical rigidity. The eigenvalue is called critical load.
This procedure allows, before carrying out the search for eigenvalues, to know it
numbers in a tape stipulated by the user.
Method of calculation:
One applies the property of the continuations of STURM and the theorem of SYLVESTER (Cf. [R5.01.01
§2.5 and §2.6]). If µ is a given spectral shift, the appearing number of negative pivots
during symmetrical factorization (by LDLT) of (A - µ B) is equal to the number of values
clean real lower than µ.
3.2 Operand
TYPE_RESU
TYPE_RESU=/
“DYNAMIQUE”
[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) or search for critical loads (case of the theory of
linear buckling).
3.3 Operands
FREQ_MIN and FREQ_MAX
FREQ_MIN = F min
FREQ_MAX = F max
These key words must be used if TYPE_RESU = “DYNAMIQUE”. They define the terminals
lower and higher as Hertz of the frequency band in which one seeks it
a number of Eigen frequencies. These two terminals are positive realities. One seeks then
2
the number of eigenvalues in the tape [
,
min
max] with: = (
*
2 F *)
Action by defect:
If FREQ_MIN misses then one the number of Eigen frequencies included/understood calculates enters
0. and F max.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Procedure IMPR_STURM
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.01-H Page
: 4/6
3.4 Operands
CHAR_CRIT_MIN and CHAR_CRIT_MAX
CHAR_CRIT_MIN = min
CHAR_CRIT_MAX = max
These key words must be used if TYPE_RESU = “MODE_FLAMB”. They define the terminals
lower and higher of the tape of critical loads in which one seeks the number
clean critical loads. These two terminals are realities positive or negative. One seeks
then the number of eigenvalues in the tape [
,
min
max].
3.5 Operands
PREC_SHIFT and NMAX_ITER_SHIFT
PREC_SHIFT
=
pshift
NMAX_ITER_SHIFT
=
nshift
If F min (min) or F max (max) is detected as being eigenvalues or being
located near eigenvalues (loss of more than eight decimals (ndeci) at the time of
factorization of the shiftée matrix (A - B)), they are then modified:
·
F - = F
-
min
min × (1 - pshift) (
=
min
min × (1 - pshift))
·
F + = F
+
max
max × (1 + pshift) (
=
max
max × (1+ pshift))
One then seeks the number of eigenvalues in the new interval [F -, F +
min
max]
([-, +
min
max])
One is not authorized more nshift modifications of the terminals of the interval.
3.6 Operand
SEUIL_FREQ
SEUIL_FREQ = F threshold
If F
F
min threshold and if F min is detected like eigenvalue, then one seeks it
a number of Eigen frequencies in the interval [- F
F
threshold, max].
It is considered whereas F min is associated a mode of rigid body. Modification of
limit lower interval allows a priori to enter all the modes of body
rigid.
In the case of the theory of linear buckling, one replaces F by and one defines:
= (
2
threshold
2 F threshold)
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Procedure IMPR_STURM
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.01-H Page
: 5/6
3.7 Operand
NPREC_SOLVEUR
NPREC_SOLVEUR = ndeci
ndeci represents the number of decimals which one is authorized to lose during factorization
shiftée matrix (A - B).
3.8 Operand
UNITE
UNITE
Number of the logical unit corresponding to the file of writing. By defect, it is worth 8,
i.e. file RESU.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Procedure IMPR_STURM
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.01-H Page
: 6/6
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Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
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