Code_Aster ®
Version
3
Titrate:
Harmonic SHLL100 Réponse of a bar by under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE Key
:
V2.06.100-A Page:
1/6

Organization (S): EDF/EP/AMV

Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
Document: V2.06.100

SHLL100 - Harmonic Réponse 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 modelled by
elements of the type “bars”. The modelled 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 grid skeleton, including the fields of
displacement, speed and of acceleration.
Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A

Code_Aster ®
Version
3
Titrate:
Harmonic SHLL100 Réponse of a bar by under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE Key
:
V2.06.100-A Page:
2/6

1
Problem of reference

1.1 Geometry

ep
With
F
X
D
L


L = 1 m

D = 0,2 m - circular Section

1.2
Material properties

E = 1.1010 Pa

= 0.3

= 1.104 kg/m3

Damping of Rayleigh per element: = 0.1
E
E = 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.
Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A

Code_Aster ®
Version
3
Titrate:
Harmonic SHLL100 Réponse of a bar by under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE Key
:
V2.06.100-A Page:
3/6

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

1 + 2
/2

R =
1 + 2 2


p
1 -
1 -
K = p+ iq =
R
+ I r+

2nd
1 + 2 2

1 + 2 2


Displacement in a point M (X) unspecified is given by:

(
NR
1
shpxcosqx+ ichpxsinqx
V X) =

EA (p+ iq) (1+ I) chLcosqL+ ishpLsinqL


Displacement (m)
Speed (m/s)
Acceleration (m/s2)
Real part
­ 7.00 10­11 ­ 3.18
10­6 2.76
10­5
Imaginary part
5.07 10­9 ­ 4.40
10­8 ­ 2.00
10­3

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”, Rapport EDF,
HP-61/93-104.
[2]
G. ROBERT, Solutions analytical in dynamics of the structures, Rapport Samtech n°121,
March 1996.
[3]
P. RICHARD, Méthodes of under-structuring in Code_Aster, internal Rapport
EDF-DER, HP-61/92-149.
Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A

Code_Aster ®
Version
3
Titrate:
Harmonic SHLL100 Réponse of a bar by under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE Key
:
V2.06.100-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

F
L/2
L/2

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
type CRAIG-BAMPTON HARMONIQUE.

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

Commands


Keys
DEFI_INTERF_DYNA INTERFACES
TYPE
“CB_HARMO” [U4.55.03]
DEFI_INTERF_DYNA FREQ
300

[U4.55.03]
MACR_ELEM_DYNA OPTION
“CLASSIQUE”

[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 grid

A number of nodes: 5

A number of meshs and types: 5 SEG 2
Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A

Code_Aster ®
Version
3
Titrate:
Harmonic SHLL100 Réponse of a bar by under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE Key
:
V2.06.100-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Displacement
(m)



Reference
Aster
% difference
Tolerance
Real part
­ 7.00 10­11 ­ 7.00
10­11
­ 0.007
2.10­3
Imaginary part
5.07 10­9 5.07
10­9
­ 0.097
2.10­3

Speed (m/s)


Real part
­ 3.18 10­6 ­ 3.18
10­6
­ 0.078
2.10­3
Imaginary part
­ 4.40 10­8 ­ 4.40
10­8
0.033
2.10­3

Acceleration
(m/s2)


Real part
2.76 10­5 2.76
10­5
0.133
2.10­3
Imaginary part
­ 2.00 10­3 ­ 2.00
10­3
­ 0.019
2.10­3

4.2 Parameters
of execution

Version: STA3.0.9
Machine: CRAY C90

System:
UNICOS 6.0
Obstruction memory:
8 megawords
Time CPU To use:
8.6 seconds

Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A

Code_Aster ®
Version
3
Titrate:
Harmonic SHLL100 Réponse of a bar by under-structuring
Date:
29/05/96
Author (S):
G. ROUSSEAU, C. VARE Key
:
V2.06.100-A Page:
6/6

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.

Handbook of Validation
V2.06 booklet: Harmonic response of the linear structures
HP-51/96/024/A

Outline document