Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
1/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
Document: V2.03.109
SDLS109 - Eigen frequencies of a ring
cylindrical thick
Summary:
This test is inspired by a vibratory study carried out on collector VVP of the N4 sections. This collector is
thick and a maximum report/ratio thickness presents on average radius of 0,13. This value, being able to be typical
of an industrial structure, is slightly higher than the limiting value of usually recognized validity
for the plates and hulls. In this study, the modeling of the collector in hulls is then evaluated by
comparison with a voluminal model on a ring.
This test makes it possible to evaluate the algorithm of search for eigenvalues
MODE_ITER_SIMULT
[U4.52.03] with
operators of rigidity and mass corresponding to following modelings:
1) plates of the type
DKQ
(finite element
MEDKQU4
) and
DSQ
(finite element
MEDSQU4
),
2) plates of the type
DKT
(finite element
MEDKTR3
) and
DST
(finite element
MEDSTR3
) with an ear mesh
and in star mesh,
3) three-dimensional hulls of type
COQUE_3D
(finite elements
MEC3QU9H
and
MEC3TR7H
),
4) sections of hull in plane stresses of type
COQUE_C_PLAN
(finite element
METCSE3
),
5) telegraphic elements with kinematics of beam and modes of Fourier
PIPE
(finite element
METUSEG3
) and
TUYAU_6M
(finite element
MET6SEG3
).
The results obtained are compared with the solution resulting from a voluminal modeling of the ring (element
finished
MECA_HEXA8
) revealing the modes of Fourier of command 2 (ovalization) and 3 (trifoliate) like 2
modes except plan. The variations on the frequencies of the modes of ovalization and trifoliate are close to:
·
0.4% in DSQ and COQUE_3D in QUAD9,
·
0.7% in COQUE_3D in TRIA7, COQUE_C_PLAN, PIPE and TUYAU_6M,
·
1% for the DKQ, DKT and DST.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
2/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
L
T
R
m
It is about a cylindrical ring, of average radius R
m
= 0.369 m, thickness T = 0.048 m and of
length L = 0.05 Mr.
1.2
Properties of material
The material is homogeneous, isotropic, elastic linear. The elastic coefficients are:
E = 185.000 MPa and
= 0.3.
The density is constant and is worth:
= 7800 kg.m
3
.
1.3
Boundary conditions and loadings
The structure is free in space.
1.4
Order of magnitude of the Eigen frequencies
The required clean modes correspond to the modes of Fourier of command 2 and 3 of the ring.
frequencies of a ring can be estimated starting from an analytical model of curved beam
of Euler [bib1]. For a mode of Fourier of command N, the frequency is worth:
(
) ()
F
N N
R
E I
m N
N
m
y
=
-
+
2
2
2
1
2
1
where:
I
Lt
y
=
3
12
and
m
Lt
=
For the modes of ovalization (N = 2) and trifoliate (N = 3), the corresponding frequencies are worth
respectively 211.65 Hz and 598.64 Hz. The search for clean modes is carried out on the tape
200 - 800 Hz in order to collect these 2 modes of Fourier.
1.5 Reference
bibliographical
[1]
Blevins R.D., Formulated for natural frequency and shape mode, N.Y.: Van Nostrand Reynhold
Company, 1979, 492 p.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
3/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
2
Modeling of reference
2.1
Characteristics of the modeling of reference
Voluminal elements
3D
The discretized geometry is represented above. Elements
3D
are voluminal with 8 nodes of
type
HEXA8
. The number of nodes on the circumference is 600, on thickness 9 and length 9.
2.2
Characteristics of the mesh
A number of nodes: 48600
A number of meshs and type: 38400
HEXA8
2.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “3D”
CALC_MATR_ELEM OPTION “RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
4/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
3
Results of the modeling of reference
3.1
Values of reference tested
Frequencies of the clean modes of ovalization, trifoliate and except plan.
Mode
Eigen frequencies (Hz)
ovalization 210.55
210.55
trifoliate 587.92
587.92
except plan
205.89
205.89
588.88
588.88
3.2 Remarks
The axisymmetric problem has double modes in the plan and except plan.
The modes except plan have the following deformations:
205.89 Hz:
588.88 Hz:
3.3 Uncertainties
Uncertainty results from the analysis of convergence of the mesh where Eigen frequencies with
mesh of reference 600x8x8 are compared with those of the mesh 500x7x9.
A number of elements
Eigen frequencies (Hz)
Circumference Thickness
Length
Ovalization Trifoliate
100
200
400
500
600
3
3
5
7
8
3
3
8
9
8
232.03
225.20
221.02
210.64
210.55
648.62
628.74
616.34
588.18
587.92
Uncertainty is 0.05% on the frequency.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
5/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
4 Modeling
With
4.1
Characteristics of modeling
Plates
DKQ
and
DSQ
.
The discretized geometry is represented above. Elements
DKQ
and
DSQ
are breakages
plane with four nodes of the type
QUAD4
. The number of nodes on the circumference is 100 and on
length 5.
4.2
Characteristics of the mesh
A number of nodes: 500
A number of meshs and type: 400
QUAD4
4.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “DKT” or “DST”
AFFE_CARA_ELEM
HULL
THICK = 0.048
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
6/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
5
Results of modeling A
5.1 Values
tested
(Frequencies in Hertz)
Reference mode
Aster
DKQ
%
difference Aster
DSQ
%
difference
ovalization 210.55
210.55
211.48
211.48
0.44
0.44
209.57
209.57
0.46
0.46
trifoliate 587.92
587.92
598.23
598.23
1.75
1.75
586.30
586.30
0.27
0.27
except plan
205.89
205.89
588.88
588.88
234.70
234.70
646.34
646.34
13.99
13.99
9.75
9.75
533.02
533.02
9.49
9.49
5.2 Remarks
Modelings in plates
DKQ
and
DSQ
do not allow to represent the modes correctly
except plan. One can think that that is due to the number of meshs over the too low length (4 with the place
from 8 in the modeling of reference). The first frequency except plan in plates
DSQ
must be
lower than 200 Hz.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
7/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
6 Modeling
B
Plates
DKT
and
DST
- ear mesh
Geometry discretized on the average radius R
m
= 0.369 m is represented above. Elements
DKT
and
DST
are plane breakages with three nodes of the type
TRIA3
laid out out of ears. The number of
nodes on the circumference is 100 and over length 5.
6.1
Characteristics of the mesh
A number of nodes: 500
A number of meshs and type: 800
TRIA3
6.2 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “DKT” or “DST”
AFFE_CARA_ELEM
HULL
THICK = 0.048
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
8/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
7
Results of modeling B
7.1 Values
tested
(Frequencies in Hertz)
Reference mode
Aster
DKT
%
difference Aster
DST
%
difference
ovalization 210.55
210.55
211.54
211.54
0.47
0.47
203.69
203.69
3.25
3.25
trifoliate 587.92
587.92
598.64
598.64
1.82
1.82
568.70
568.70
3.27
3.27
except plan
205.89
205.89
588.88
588.88
254.89
254.89
707.53
707.53
23.80
23.80
20.14
20.14
202.38
202.38
617.18
617.18
1.70
1.70
4.81
4.81
7.2 Remarks
Modeling in plates
DKT
does not allow to represent the modes except plan correctly.
Errors on the frequencies in plates
DST
are relatively important.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
9/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
8 Modeling
C
Plates
DKT
and
DST
- star mesh
Geometry discretized on the average radius R
m
= 0.369 m is represented above. Elements
DKT
and
DST
are plane breakages with three nodes of the type
TRIA3
laid out out of stars. The number
nodes on the circumference is 100 and over length 5.
8.1
Characteristics of the mesh
A number of nodes: 500
A number of meshs and type: 800
TRIA3
8.2 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “DKT” or “DST”
AFFE_CARA_ELEM
HULL
THICK = 0.048
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
10/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
9
Results of modeling C
9.1 Values
tested
(Frequencies in Hertz)
Reference mode
Aster
DKT
%
difference Aster
DST
%
difference
ovalization 210.55
210.55
211.54
211.54
0.47
0.47
208.20
208.20
1.11
1.11
trifoliate 587.92
587.92
598.58
598.58
1.81
1.81
581.00
581.00
1.18
1.18
except plan
205.89
205.89
588.88
588.88
284.38
284.38
797.24
797.24
38.12
38.12
35.38
35.38
225.23
225.23
690.73
690.73
9.39
9.39
17.29
17.29
9.2 Remarks
Modelings in plates
DKT
and
DST
do not allow to represent the modes correctly
except plan.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
11/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
10 Modeling
D
10.1 Characteristics of modeling
COQUE_3D
mesh in
QUAD9
.
Geometry discretized on the average radius R
m
= 0.369 m is represented above. Elements
COQUE_3D
are meshs with 9 nodes of the type
QUAD9
allowing to take into account the radius of
curvature of the ring. The nodes mediums are of course the average circumference. The number of
nodes on the circumference is 40 and over length 5.
10.2 Characteristics of the mesh
A number of nodes: 200
A number of meshs and type: 40
QUAD9
10.3 Functionalities
tested
Controls
CREA_MAILLAGE
MODI_MAILLAGE
OPTION = “QUAD8_9”
AFFE_MODELE
AFFE
MODELING = “COQUE_3D”
AFFE_CARA_ELEM
HULL
A_CIS = 0.833333
COEF_RIGI_DRZ = 1.E-5
THICK = 0.048
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
12/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
11
Results of modeling D
11.1 Values
tested
(Frequencies in Hertz)
Reference mode
Code_Aster %
difference
ovalization 210.55
210.55
209.91
209.91
0.30
0.30
trifoliate 587.92
587.92
586.51
586.51
0.24
0.24
except plan
205.89
205.89
588.88
588.88
205.14
205.14
587.55
587.55
0.36
0.36
0.23
0.23
11.2 Remarks
All the frequencies are correctly estimated.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
13/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
12 Modeling
E
12.1 Characteristics of modeling
COQUE_3D
mesh in
TRIA7
.
Geometry discretized on the average radius R
m
= 0.369 m is represented above. Elements
COQUE_3D
are meshs with 7 nodes of the type
TRIA7
allowing to take into account the radius of
curvature of the ring. The nodes mediums are of course the average circumference. The number of
nodes on the circumference is 40 and over length 5.
12.2 Characteristics of the mesh
A number of nodes: 280
A number of meshs and type: 160
TRIA7
12.3 Functionalities
tested
Controls
CREA_MAILLAGE
MODI_MAILLAGE
OPTION = “TRIA6_7”
AFFE_MODELE
AFFE
MODELING = “COQUE_3D”
AFFE_CARA_ELEM
HULL
A_CIS = 0.833333
COEF_RIGI_DRZ = 1.E-5
THICK = 0.048
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
14/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
13
Results of modeling E
13.1 Values
tested
(Frequencies in Hertz)
Reference mode
Code_Aster %
difference
ovalization 210.55
210.55
211.19
211.19
0.30
0.30
trifoliate 587.92
587.92
590.98
590.98
0.52
0.52
except plan
205.89
205.89
588.88
588.88
205.81
205.81
595.38
595.38
0.04
0.04
1.10
1.10
13.2 Remarks
The frequencies are less better estimated that with the elements
QUAD9
.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
15/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
14 Modeling
F
14.1 Characteristics of modeling
COQUE_C_PLAN
.
Geometry discretized on the average radius R
m
= 0.369 m is represented above. Elements
COQUE_C_PLAN
are meshs with 3 nodes of the type
SEG3
allowing to take into account the radius
of curvature of the ring. The nodes mediums are of course the average circumference. The number of
nodes on the circumference is 100.
14.2 Characteristics of the mesh
A number of nodes: 100
A number of meshs and type: 50
SEG3
14.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “COQUE_C_PLAN”
AFFE_CARA_ELEM
HULL
A_CIS = 0.833333
MODI_METRIQUE = “NOT”
THICK = 0.048
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
16/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
15
Results of modeling F
15.1 Values
tested
(Frequencies in Hertz)
Reference mode
Code_Aster %
difference
ovalization 210.55
210.55
209.14
209.14
0.67
0.67
trifoliate 587.92
587.92
583.28
583.28
0.79
0.79
except plan
205.89
205.89
588.88
588.88
15.2 Remarks
Modeling in plane stresses does not make it possible to reveal the modes except plan of
the ring.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
17/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
16 Modeling
G
16.1 Characteristics of modeling
PIPE
and
TUYAU_6M
.
CENTER in SEG3
The geometry discretized on the axis of the ring is represented above. Elements
PIPE
and
TUYAU_6M
are meshs with 3 nodes of the type
SEG3
representing the axis of the ring. The number of
nodes on the axis is 5.
16.2 Characteristics of the mesh
A number of nodes: 5
A number of meshs and type: 2
SEG3
16.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “PIPE” or “TUYAU_6M'
AFFE_CARA_ELEM
BEAM
SECTION = “CIRCLE”
MODI_METRIQUE = “NOT”
CARA = (“R” “EP”)
VALE = (0.395, 0.048)
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
18/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
17
Results of modeling G
17.1 Values
tested
(Frequencies in Hertz)
Reference mode
Aster
PIPE
%
difference Aster
TUYAU_6M
%
difference
ovalization 210.55
210.55
209.02
209.02
0.72
0.72
209.02
209.02
0.72
0.72
trifoliate 587.92
587.92
591.00
591.00
0.52
0.52
591.00
591.00
0.52
0.52
except plan
205.89
205.89
588.88
588.88
259.74
259.74
649.57
649.57
26.15
26.15
10.31
10.31
259.74
259.74
649.57
649.57
26.15
26.15
10.31
10.31
17.2 Remarks
Modelings in
PIPE
(limited by construction to 3 modes of Fourier) and
TUYAU_6M
do not allow to represent the modes except plan correctly. On the other hand, they provide them
same results on the outline views, close to the reference.
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
19/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
18 Modeling
H
18.1 Characteristics of modeling
Modeling SHB8
The discretized geometry is represented above. Elements
SHB8
are pressed on meshs
HEXA8. The number of elements on the circumference is 100 and over length 5.
18.2 Characteristics of the mesh
A number of nodes: 1000
A number of meshs and type: 400 HEXA8, 400
QUAD4
18.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “SHB8”
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
BANDAGE FREQ = (200., 800.)
CREA_MAILLAGE COQU_VOLU
Code_Aster
®
Version
7.2
Titrate:
SDLS109 - Eigen frequencies of a thick cylindrical ring
Date:
06/02/04
Author (S):
J.M. PROIX, S. CAILLAUD
Key
:
V2.03.109-B
Page:
20/20
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/04/005/A
19
Results of modeling H
19.1 Values
tested
(Frequencies in Hertz)
Reference mode
Aster
DKQ
%
difference
ovalization 210.55
210.55
210.71
210.71
0.08
0.08
trifoliate 587.92
587.92
590.84
590.84
0.5
0.5
except plan
205.89
205.89
588.88
588.88
208.05
208.05
595.3
595.3
1.05
1.05
1.09
1.09
20
Summary of the results
·
Even if the results obtained are honourable, the models
DKQ
,
DSQ
,
DKT
,
DST
,
COQUE_C_PLAN
,
PIPE
and
TUYAU_6M
do not allow to estimate the modes except plan of
the ring. Only the model
COQUE_3D
with a mesh in
QUAD9
provides a good estimate
frequential of these modes with an error lower than 0.4%.
·
Models
DSQ
and
COQUE_3D
in
QUAD9
give an error close to 0.3% for the modes
of ovalization and trifoliate. For the models
COQUE_3D
in
TRIA7
,
COQUE_C_PLAN
,
PIPE
and
TUYAU_6M
, this error borders 0.7% and is higher than 1% for
DKQ
,
DKT
and
DST
.
·
Best results of
DSQ
compared to
DKQ
confirm that the effect of shearing
transverse is not negligible in the hulls notable thickness.
·
On a developable geometry like that of the cylinder studied here, finite elements
quadrangular provide better results which triangular finite elements.
DST
,
tested on an ear mesh and a symmetrical star mesh, are much less
goods that them
DSQ
. The same remark is also valid for
COQUE_3D
in
TRIA7
by
report/ratio with
COQUE_3D
in
QUAD9
.
·
Performances of
COQUE_3D
are good quantitatively and in calculating times.
richness of the interpolation, the taking into account of the curvature of the cylinder in the elements and
metric correction carried out in the thickness of the hull seem to explain these good results.
·
Elements SHB8 make it possible to about obtain all the modes with a maximum change
1%.