Code_Aster
®
Version
3
Titrate:
Harmonic SHLL100 Response of a bar per under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE
Key
:
V2.06.100-A
Page:
1/6
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A
Organization (S):
EDF/EP/AMV
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
Document: V2.06.100
SHLL100 - Harmonic response of a bar
by dynamic under-structuring
Summary:
The applicability of this test relates to the dynamics of the structures, and more particularly the calculation of
harmonic response by dynamic under-structuring.
It is a question of calculating the harmonic response in traction and compression of a embed-free beam modelized by
elements of the type “bars”. The modelized structure is deadened (damping of Rayleigh by elements).
The results of reference result from a direct harmonic calculation. This test thus makes it possible to validate the tools of
calculations of harmonic response per under-structuring established in Code_Aster and more particularly:
·
the catch in depreciation account by element,
·
the calculation of the second member including the harmonic loading,
·
restitution of the harmonic response on a mesh skeleton, including the fields of
displacement, speed and of acceleration.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLL100 Response of a bar per under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE
Key
:
V2.06.100-A
Page:
2/6
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A
1
Problem of reference
1.1 Geometry
With
F
D
X
L
E
p
L = 1 m
D = 0,2 m - circular Section
1.2
Material properties
E = 1.10
10
AP
= 0.3
= 1.10
4
kg/m
3
Damping of Rayleigh per element:
E
E
=
=
0.1
0.1
1.3
Boundary conditions and loadings
Embedding in end a: U (0) = N (0) = W (0) = 0.
For any point M (X): N (0) = W (0) = 0.
Harmonic loading in time, at the loose lead:
·
orientation: according to X,
·
amplitude: 100 NR,
·
frequency: 100 Hz.
1.4 Conditions
initial
Without object for a harmonic calculation of answer.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLL100 Response of a bar per under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE
Key
:
V2.06.100-A
Page:
3/6
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A
2
Reference solution
2.1
Method of calculation used for the reference solution
There is an analytical solution detailed in the reference [bib2].
Let us use the following notations:
E
: Young modulus
L
: length of the bar
With
: section of the bar
NR
: normal effort directed according to axis X
,
: damping coefficients of Rayleigh
: frequency
of excitation
and let us pose
R
/
K
p iq
p
E
R
I R
=
+
+
= +
=
-
-
+
+
+
-
+
1
1
2
1
1
1
1
2
2
2
2
2
2
2
2
Displacement in a point M (X) unspecified is given by:
()
(
)
(
)
V X
NR
EA p iq
I
shpxcosqx ichpxsinqx
chLcosqL ishpLsinqL
=
+
+
+
+
1
1
Displacement (m)
Speed (m/s)
Acceleration (m/s
2
)
Real part
7.00 10
11
3.18
10
6
2.76
10
5
Imaginary part
5.07 10
9
4.40
10
8
2.00
10
3
2.2
Results of reference
Fields of displacement, speed and acceleration of the loose lead of the bar.
2.3
Uncertainty on the solution
Numerical solution.
2.4 References
bibliographical
[1] T.
KERBER
“harmonic Under-structuring in Code_Aster”, Report/ratio EDF,
HP-61/93-104.
[2]
G. ROBERT, analytical Solutions in dynamics of the structures, Report/ratio Samtech n°121,
March 1996.
[3]
P. RICHARD, Methods of under-structuring in Code_Aster, Internal report
EDF-DER, HP-61/92-149.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLL100 Response of a bar per under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE
Key
:
V2.06.100-A
Page:
4/6
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A
3 Modeling
With
3.1
Characteristics of modeling
L/2
L/2
F
The bar is cut out in 2 parts of equal size. Each substructure considered is
with a grid in segments to which are affected elements “bars”.
The structure is studied using the method of the harmonic under-structuring with interfaces of
HARMONIC type CRAIG-BAMPTON.
The modal base used is made up of 4 clean modes for the substructure of straight line, of
5 clean modes for the substructure of left to which are added the constrained modes
harmonics associated with the interfaces (calculated to 300 Hz. This value of the pulsation does not have any
influence on the result, it is arbitrary [bib3]).
3.2 Functionalities
tested
Controls
Keys
DEFI_INTERF_DYNA INTERFACES
TYPE
“CB_HARMO”
[U4.55.03]
DEFI_INTERF_DYNA FREQ
300
[U4.55.03]
MACR_ELEM_DYNA OPTION
“CONVENTIONAL”
[U4.55.05]
MACR_ELEM_DYNA MATR_AMOR
[U4.55.05]
ASSE_MATR_GENE OPTION
AMOR_GENE
[U4.55.08]
ASSE_VECT_GENE NUME_DDL_GENE
[U4.55.09]
ASSE_VECT_GENE CHAR_SOUS_STRUC
SOUS_STRUC
[U4.55.09]
ASSE_VECT_GENE CHAR_SOUS_STRUC
VECT_ASSE
[U4.55.09]
3.3
Characteristics of the mesh
A number of nodes: 5
A number of meshs and types: 5 SEG 2
Code_Aster
®
Version
3
Titrate:
Harmonic SHLL100 Response of a bar per under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE
Key
:
V2.06.100-A
Page:
5/6
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A
4
Results of modeling A
4.1 Values
tested
Displacement
(m)
Reference
Aster
% difference
Tolerance
Real part
7.00 10
11
7.00
10
11
0.007
2.10
3
Imaginary part
5.07 10
9
5.07
10
9
0.097
2.10
3
Speed (m/s)
Real part
3.18 10
6
3.18
10
6
0.078
2.10
3
Imaginary part
4.40 10
8
4.40
10
8
0.033
2.10
3
Acceleration
(m/s
2
)
Real part
2.76 10
5
2.76
10
5
0.133
2.10
3
Imaginary part
2.00 10
3
2.00
10
3
0.019
2.10
3
4.2 Parameters
of execution
Version: STA3.0.9
Machine: CRAY C90
System:
UNICOS 6.0
Overall dimension memory:
8 megawords
Time CPU To use:
8.6 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLL100 Response of a bar per under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE
Key
:
V2.06.100-A
Page:
6/6
Manual of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A
5
Summary of the results
Precision on the complex co-ordinates of the fields of displacement speed and acceleration
is lower than 0,1%.
This test thus validates the operators of harmonic under-structuring.