Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
1/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA, SAMTECH
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
Document: V2.04.401
SDLV401 - Free-free full sphere
Summary:
This three-dimensional test of modal analysis consists in calculating the Eigen frequencies of a full sphere in
free-free.
The interest of this test is to evaluate the robustness and the performance of Code_Aster in the detection of the modes
rigid and of the multiple frequencies, during the use of voluminal elements.
The reference solution is numerical and is obtained using the computation software of structures by elements
stop the SAMCEF software.
In this test, one compares the results obtained with two types D `elements:
· element HEXA8 (modeling A)
· element HEXA20 (modeling B).
In order to determine the clean elements of this system, the method known as of SORENSEN is used.
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
2/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
Full sphere:
R
Interior radius R = 0.01 m
1.2
Material properties
The presumedly elastic material linear A following characteristics:
E = 1.E8 AP
= 0.3
= 10000 kg/m
3
1.3
Boundary conditions and loadings
The studied structure is free in space.
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
3/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is numerical: it is obtained with the computation software of structures by
finite elements the SAMCEF software.
The method of calculation of the Eigen frequencies is the method known as of SORENSEN (method by
defect in operator MODE_ITER_SIMULT).
2.2
Results of reference
The structure presenting six rigid modes, one is interested in the first 10 Eigen frequencies not
null.
The following table shows the values of the frequencies obtained (in Hz) according to the degree of the elements
voluminal.
Mode
Degree 1
Degree 2
1
2.54231 E3
2.47035 E3
2
2.54231 E3
2.47035 E3
3
2.60747 E3
2.47101 E3
4
2.60747 E3
2.47101 E3
5
2.60747 E3
2.47101 E3
6
2.74095 E3
2.61296 E3
7
2.74095 E3
2.61296 E3
8
2.74095 E3
2.61430 E3
9
2.76313 E3
2.61430 E3
10
2.76313 E3
2.61430 E3
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
4/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling A
Mesh made up of elements HEXA8
3.2
Characteristics of the mesh
A number of nodes: 417
A number of meshs and type: 160 HEXA8
3.3 Functionalities
tested
Controls
AFFE_MODELE AFFE MODELING
“3D”
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT METHOD
“SORENSEN”
CALC_FREQ
OPTION
FREQ
BANDAGE
(1, 3000 Hz)
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
5/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
4
Results of modeling A
4.1 Values
tested
(Frequencies in Hertz)
Identification
n° mode
Reference
Code_Aster
% difference
1
2.54231 E3
2.54231 E3
~ 1 E - 6
2
2.54231 E3
2.54231 E3
~ 1 E - 6
3
2.60747 E3
2.60747 E3
~ 1 E - 6
4
2.60747 E3
2.60747 E3
~ 1 E - 6
5
2.60747 E3
2.60747 E3
~ 1 E - 6
6
2.74095 E3
2.74095 E3
~ 1 E - 6
7
2.74095 E3
2.74095 E3
~ 1 E - 6
8
2.74095 E3
2.74095 E3
~ 1 E - 6
9
2.76313 E3
2.76313 E3
~ 1 E - 6
10
2.76313 E3
2.76313 E3
~ 1 E - 6
4.2 Remarks
Code_Aster detects well the 6 modes of rigid body.
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
6/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
5 Modeling
B
5.1
Characteristics of modeling B
Mesh made up of elements HEXA20
5.2
Characteristics of the mesh
A number of nodes: 815
A number of meshs and type: 160 HEXA20
5.3 Functionalities
tested
Controls
AFFE_MODELE AFFE
MODELING
“3D”
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT METHOD
“SORENSEN”
CALC_FREQ
OPTION
FREQ
BANDAGE
(1, 3000)
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
7/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
6
Results of modeling B
6.1 Values
tested
(Frequencies in Hertz)
Identification
n° mode
Reference
Code_Aster
% difference
1
2.47035 E3
2.46964
- 0.029
2 2.47035
E3
2.46964 - 0.029
3 2.47101
E3
2.47084 - 0.007
4 2.47101
E3
2.47084 - 0.007
5 2.47101
E3
2.47084 - 0.007
6 2.61296
E3
2.61344 0.019
7 2.61296
E3
2.61344 0.019
8 2.61430
E3
2.61345 - 0.033
9 2.61430
E3
2.61364 - 0.025
10 2.61430
E3
2.61364 - 0.025
6.2 Remarks
Code_Aster detects well the 6 modes of rigid body.
Code_Aster
®
Version
7.3
Titrate:
SDLV401 - Free-free full sphere
Date
:
25/10/04
Author (S):
E. BOYERE, G. ROBERT, F. SOULIE
Key
:
V2.04.401-A
Page:
8/8
Manual of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-66/04/005/A
7
Summary of the results
The results obtained are excellent since the instantaneous frequency deviations with the reference solution
are lower than 0.03%. Moreover, Code_Aster detects well the 6 modes of rigid body, which one does not have
not asked to calculate.
To calculate the rigid modes indeed, two possibilities exist. With the option “BANDAGES” on
frequency band (0, 3000 Hz), one can employ either the method of “SORENSEN”, or the method
LANCZOS (“TRI_DIAG”) by specifying option “MODE_RIGIDE”.