Code_Aster
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
1/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
V2.07.100 document
SHLV 100 - Harmonic response of a cylinder
hollow in plane deformations
Summary:
This axisymmetric three-dimensional test makes it possible to validate calculations of the matrices of rigidity, mass and of
vectors of pressure on all the elements 3D and 2D plane and axisymmetric deformations (10 modelings).
Displacements are imposed:
·
maybe by ddl,
·
maybe by face of element.
For four modelings 3D, the pressures applied are provided with the minus sign, because the faces
elements 3D are badly directed in the files of mesh used.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
2/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
1 Problem of reference
1.1 Geometry
Z
X
R
y
face locked according to Z
face locked according to Z
P
With
B
45°
C
D
E
F
internal radius has = 0.1 m
external radius B = 0.2 m
Co-ordinates of the points:
With
B
C
D
E
F
X
0.100
0.200
0.1 COS (22.5)
0.2 COS (22.5)
2 2
/
2
y
0.
0.
0.1 SIN (22.5)
0.2 SIN (22.5)
2 2
/
2
Z
0.
0.
0.
0.
0.
0.
1.2 Material properties
E = 26 NR/m
2
= 0.3
= 35 kg/m
3
The very low value of the Young modulus does not have anything physics.
1.3 Boundary conditions and loadings
Pressure interns P = p E
J
T
with p = 1 Mpa
and
= 0.2 rad/S
1.4 Initial conditions
·
without initial conditions,
·
direct calculation of the harmonic solution.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
3/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
2 Reference solution
2.1 Method of calculation used for the reference solution
()
()
(
)
()
()
()
()
(
)
()
()
()
()
U
WITH J
K R
B Y
K R
U
U
K
With
J
K R
K R J
K R
B
Y
K R
K R Y
K R
K
With
J
K R
K R J
K R
B
Y
K R
K R Y
K R
R
L
L
Z
rr
L
L
L
L
L
L
L
L
L
L
L
L
L
L
=
+
=
=
=
-
-
+
-
=
-
+
+
+
1
1
2
0
1
2
0
1
2
0
1
2
0
1
0
2
2
1
1
2
1
2
2
1
1
2
1
µ
µ
(
)
()
()
[
]
(
)
=
-
+
=
=
=
=
+
=
-
-
=
=
=
+
µ
µ
µ
µ
zz
L
L
L
R
rz
Z
K
WITH J
K R
B Y
K R
K L
C L
J
J
Y
Y
2
2
1
0
2
0
0
2
2
4
1
2 1
1
4 2
2
1
0
1
0
with:
: Functions of Bessel.
,
,
,
Constants
With
and
B
are calculated by solving the linear system obtained while writing:
()
()
rr
rr
has
p
B
= -
=
0
One obtains:
for
0.1
for
0.2
R
U
R
U
R
R
rr
rr
zz
zz
=
=
=
=
=
=
=
=
=
=
-
-
7 3398 10
4 6816 10
0
1 6685
0 66738
0 20055
0 20031
3
3
.
.
1
.
.
.
.
.
Passage in the system of Cartesian axes:
(
)
xx
rr
R
yy
rr
R
xy
rr
R
=
+
-
=
+
+
=
-
-
-
= °
=
°
= °
cos
sin
sin
cos
sin
cos
sin
cos
sin cos
sin cos
cos
sin
2
2
2
2
2
2
2
2
2
with
0 at points A and B
22.5 at the points C and D
45 at the points E and F
2.2 Results of reference
Displacements (U, v) and forced
(
)
xx
yy
zz
xy
,
,
,
at the points A, B, C, D, E, F.
2.3 Uncertainty on the solution
Precision of the calculation of the Functions of Bessel.
2.4 Bibliographical references
[1] Mr. BONNET: Methods of the integral equations regularized into elastodynamic - Bulletin
DER - Series C - N°1/2 - (1987).
[2] ERINGEN - SUHUBI - Elastodynamics, Vol.2: linear theory Academic Close (1975).
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
4/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
3 Modeling A
3.1 Characteristics of modeling
Elements 3D (PENTA6 and HEXA8) (resulting from the mesh 2D below).
With
B
C
D
E
F
y
X
45°
Normally locked face
Face locked out of Dy
Face with imposed pressure
along axis Z: 2 layers of elements total thickness: 0.01
Limiting conditions:
DDL_IMPO:
(All:“yes”
Dz: 0. )
face AB
(Group_no:BordAB
Dy: 0. )
face EFF
FACE_IMPO:
(Group_ma:FaceEF
Dnor: 0. )
pressure on face AE
PRES_REP:
(Group_ma:FaceAE
Near: - 1. )
Names of the nodes:
A=No1
B=No119
C=No36
D=No166
E=No41
F=No171
3.2 Characteristics of the mesh
A number of nodes: 513
A number of meshs and types: 400 PENTA6 100 HEXA8 40 QUAD4
3.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
3.4 Remarks
The pressure has a negative sign (instead of positive) because the faces of the elements 3D are badly directed.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
5/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
4 Results of modeling A
4.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
1.6685
0.20055
0.
7.3243 10
3
eps
0.8789
1.6241
0.2235
0.0922
0.21
12.1
2.66
11.75
10
2
0.2
0.2
C
U
v
xx
yy
zz
xy
6.78109 10
3
2.80882 10
3
0.60921
1.27771
0.20055
0.94346
6.7670 10
3
2.8012 10
3
0.5121
1.3300
0.2454
0.8567
0.21
0.27
15.94
4.09
22.39
9.20
10
2
0.3
0.3
0.3
0.3
0.3
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1784 10
3
5.1784 10
3
0.4319
0.5315
0.289
1.269
0.22
0.22
29.23
59.04
44.50
4.87
10
2
0.6
0.6
0.6
0.6
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.66738
0.20021
0.
4.6641 10
3
eps
0.0132
0.6724
0.1977
0.0219
0.16
0.75
1.25
10
2
2.10
2
D
U
v
xx
yy
zz
xy
4.32523 10
3
1.79157 10
3
0.09774
0.56964
0.20021
0.23595
4.3084 10
3
1.7854 10
3
0.0739
0.5728
0.1941
0.2348
0.39
0.34
24.39
0.56
3.05
0.49
10
2
0.3
0.3
0.3
0.3
0.3
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.2974 10
3
3.2974 10
3
0.2977
0.3245
0.1866
0.3415
0.39
0.39
10.78
2.75
6.80
2.34
10
2
0.2
0.2
0.2
0.2
0.2
4.2 Remarks
The mesh is insufficient for linear elements.
4.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 10.23 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
6/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
5 Modeling B
5.1 Characteristics of modeling
Elements 3D (PENTA15 and HEXA20) (resulting from the mesh 2D below).
X
y
With
B
D
F
E
C
45°
Face with imposed pressure
Face locked in dx
Normally locked face
along axis Z: 2 layers of elements total thickness: 0.01
Limiting conditions:
DDL_IMPO:
(All:“yes”
Dz: 0. )
face AB
(Group_no:BordAB
Dx: 0. )
face EFF
FACE_IMPO:
(Group_ma:FaceEF
Dnor: 0. )
pressure on face AE
PRES_REP:
(Group_ma:FaceAE
Near: - 1. )
Names of the nodes:
A=No2
B=No361
C=No121
D=No584
E=No155
F=No503
5.2 Characteristics of the mesh
A number of nodes: 2115
A number of meshs and types: 400 PENTA15 100 HEXA20 40 QUAD8
5.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
NUME_DDL
RENUM
“RCMK”
“EXTRACTION”
[U4.42.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
5.4 Remarks
The pressure has a negative sign (instead of positive) because the faces of the elements 3D are badly directed.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
7/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
6 Results of modeling B
6.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
0.
7.3398 10
3
1.6685
1.
0.20055
0.
eps
7.3326 10
3
1.6669
0.9959
0.2013
3.3234 10
3
0.10
0.09
0.41
0.37
10
2
10
2
10
2
10
2
10
2
C
U
v
xx
yy
zz
xy
2.80882 10
3
6.78109 10
3
1.27771
0.60921
0.20055
0.94346
2.8063 10
3
6.7745 10
3
1.278
0.6078
0.20107
0.94027
0.09
0.10
0.02
0.23
0.26
0.34
10
2
10
2
10
2
10
2
10
2
10
2
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1851 10
3
5.1851 10
3
0.3346
0.3340
0.2006
1.331
0.09
0.10
0.10
0.07
0.02
0.24
10
2
10
2
10
2
10
2
10
2
10
2
B
U
v
xx
yy
zz
xy
0.
4.6716 10
3
0.66738
0.
0.20021
0.
eps
4.6682 10
3
0.6675
3.2779 10
4
0.2003
5.0918 10
4
0.07
0.02
0.04
10
2
10
2
10
2
10
2
10
2
D
U
v
xx
yy
zz
xy
1.79157 10
3
4.32523 10
3
0.56964
0.09774
0.20021
0.23595
1.7864 10
3
4.3129 10
3
0.56957
0.09803
0.20027
0.23623
0.29
0.29
0.01
0.30
0.03
0.12
10
2
10
2
10
2
10
2
10
2
10
2
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.3009 10
3
3.3009 10
3
0.3337
0.3337
0.2002
0.3339
0.29
0.29
0.003
0.003
0.
0.06
10
2
10
2
10
3
10
3
10
3
10
3
6.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 94.09 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
8/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
7 Modeling C
7.1 Characteristics of modeling
Elements 3D (TETRA4)
along axis Z: 2 layers of elements total thickness: 0.01
Limiting conditions:
DDL_IMPO:
(All:“yes”
Dz: 0. )
face AB
(Group_no:BordAB
Dy: 0. )
face EFF
FACE_IMPO:
(Group_ma:FaceEF
Dnor: 0. )
pressure on face AE
PRES_REP:
(Group_ma:FaceAE
Near: - 1. )
Names of the nodes:
A=No3
B=No7
C=No4
D=No8
E=No154
F=No156
plan Z = 0.005
A2=No1
B2=No5
C2=No2
D2=No6
E2=No153
F2=No155
plan Z = 0.01
A3=No283
B3=No285
C3=No284
D3=No286
E3=No359
F3=No360
7.2 Characteristics of the mesh
A number of nodes: 423
A number of meshs and types: 1416 TETRA4 72 TRIA3
7.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
7.4 Remarks
The pressure has a negative sign (instead of positive) because the faces of the elements 3D are badly directed.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
9/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
8 Results of modeling C
8.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
1.6685
0.20055
0.
7.3331 10
3
eps
0.9000
1.6809
0.2343
0.1016
0.10
-
+10.00
0.74
16.83
-
10
2
0.02
0.02
0.02
0.02
C
U
v
xx
yy
zz
xy
6.78109 10
3
2.80882 10
3
0.60921
1.27771
0.20055
0.94346
6.7783 10
3
2.8077 10
3
0.5061
1.3184
0.2437
0.9123
0.04
0.04
16.92
3.18
21.51
3.30
10
2
0.04
0.04
0.04
0.04
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1853 10
3
5.1853 10
3
0.2888
0.4920
0.2343
1.2905
0.09
0.09
13.60
47.19
16.83
3.28
10
2
0.5
0.5
0.5
0.5
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.66738
0.20021
0.
4.6634 10
3
eps
0.0146
0.6570
0.1976
0.0159
0.18
-
-
1.55
1.30
-
10
2
5.10
2
5.10
2
5.10
2
D
U
v
xx
yy
zz
xy
4.32523 10
3
1.79157 10
3
0.09774
0.56964
0.20021
0.23595
4.2960 10
3
1.7795 10
3
0.0824
0.5809
0.1921
0.2378
0.68
0.67
15.69
1.97
4.05
7.84
10
2
0.2
0.2
0.2
0.2
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.2976 10
3
3.2975 10
3
0.3052
0.3371
0.1921
0.3358
0.39
0.39
8.54
1.02
4.05
0.63
10
2
0.1
0.1
0.1
0.1
8.2 Remarks
One notes a variation (< 0.24%) displacements for the points of the z=0.005 plan.
The mesh is insufficient for linear elements.
8.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 18.55 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
10/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
9 Modeling D
9.1 Characteristics of modeling
Elements 3D (TETRA10)
along axis Z: 2 layers of elements total thickness: 0.01
Limiting conditions:
DDL_IMPO:
(All:“yes”
Dz: 0. )
face AB
(Group_no:BordAB
Dy: 0. )
face EFF
FACE_IMPO:
(Group_ma:FaceEF
Dnor: 0. )
pressure on face AE
PRES_REP:
(Group_ma:FaceAE
Near: - 1. )
Names of the nodes:
A=No3
B=No7
C=No4
D=No8
E=No1228
F=No230
plan Z = 0.005
A2=No1
B2=No5
C2=No2
D2=No6
E2=No227
F2=No229
plan Z = 0.01
A3=No420
B3=No422
C3=No421
D3=No423
E3=No573
F3=No574
9.2 Characteristics of the mesh
A number of nodes: 703
A number of meshs and types: 356 TETRA10 36 TRIA6
9.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
9.4 Remarks
The pressure has a negative sign (instead of positive) because the faces of the elements 3D are badly directed.
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
11/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
10 Results of modeling D
10.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
1.6685
0.20055
0.
7.3522 10
3
eps
0.9925
1.6725
0.2040
0.0365
0.10
-
0.75
0.24
1.72
-
10
2
10
2
5.10
2
5.10
2
5.10
2
5.10
2
C
U
v
xx
yy
zz
xy
6.78109 10
3
2.80882 10
3
0.60921
1.27771
0.20055
0.94346
6.7836 10
3
2.8099 10
3
0.5977
1.294
0.2088
0.9457
0.04
0.04
1.89
1.28
4.11
0.24
10
2
10
2
5.10
2
5.10
2
5.10
2
5.10
2
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1988 10
3
5.1988 10
3
0.3035
0.3766
0.2040
1.332
0.17
0.17
9.20
12.67
1.72
0.17
10
2
10
2
0.15
0.15
0.15
0.15
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.66738
0.20021
0.
4.6711 10
3
eps
8.597 10
4
0.6679
0.2006
1.0181 10
3
0.01
-
-
0.08
0.19
-
10
2
10
2
10
2
10
2
10
2
10
2
D
U
v
xx
yy
zz
xy
4.32523 10
3
1.79157 10
3
0.09774
0.56964
0.20021
0.23595
4.3134 10
3
1.7867 10
3
0.09418
0.5652
0.1978
0.2355
0.28
0.28
3.64
0.78
1.20
0.19
10
2
10
2
5.10
2
5.10
2
5.10
2
5.10
2
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.3029 10
3
3.3029 10
3
0.3357
0.3334
0.2007
0.3336
0.23
0.23
0.60
0.09
0.24
-
10
2
10
2
10
2
10
2
10
2
10
2
10.2 Remarks
One notes a variation (< 0.23%) displacements for the points of the z=0.005 plan.
10.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 21.05 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
12/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
11 Modeling E
11.1 Characteristics of modeling
Elements
D_PLAN
(TRIA3 + QUAD4)
With
B
C
D
E
F
y
X
45°
Normally locked face
Face locked out of Dy
Face with imposed pressure
Limiting conditions:
side AB
DDL_IMPO:
(Group_no:GRNM11
Dy: 0. )
side EFF
FACE_IMPO:
(Group_ma:GRMA12
Dnor: 0. )
pressure on AE
PRES_REP:
(Group_ma:GRMA13
Near: 1. )
Names of the nodes:
A=N1
B=N119
C=N36
D=N166
E=N41
F=N171
11.2 Characteristics of the mesh
A number of nodes: 171
A number of meshs and types: 200 TRIA3 50 QUAD4
11.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“D_PLAN”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
13/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
12 Results of modeling E
12.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
1.6685
0.20055
0.
7.3243 10
3
eps
0.8790
1.6241
0.2235
0.0922
0.21
-
12.10
2.66
11.44
-
10
2
0.15
0.15
0.15
0.15
C
U
v
xx
yy
zz
xy
6.78109 10
3
2.80882 10
3
0.60921
1.27771
0.20055
0.94346
6.7670 10
3
2.8012 10
3
0.5122
1.3302
0.2454
0.8567
0.21
0.27
15.92
4.11
22.36
9.19
10
2
0.3
0.3
0.3
0.3
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1784 10
3
5.1784 10
3
0.4318
0.5315
0.2890
1.2686
0.22
0.22
29.18
59.01
44.10
4.92
10
2
0.6
0.6
0.6
0.6
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.66738
0.20021
0.
4.6641 10
3
eps
1.3198 10
2
0.6723
0.1977
0.0219
0.16
-
-
0.74
1.25
-
10
2
0.05
0.05
0.05
0.05
D
U
v
xx
yy
zz
xy
4.32523 10
3
1.79157 10
3
0.09774
0.56964
0.20021
0.23595
4.3084 10
3
1.7854 10
3
0.07393
0.5728
0.1940
0.2347
0.39
0.39
24.36
0.55
3.10
0.53
10
2
0.3
0.3
0.3
0.3
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.2974 10
3
3.2974 10
3
0.2976
0.3245
0.1866
0.3415
0.39
0.39
10.81
2.75
6.80
2.34
10
2
0.15
0.15
0.15
0.15
12.2 Remarks
The mesh is insufficient for linear elements.
12.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 5.87 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
14/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
13 Modeling F
13.1 Characteristics of modeling
Elements
D_PLAN
(QUAD8 + TRIA6)
X
y
With
B
D
F
E
C
45°
Face with imposed pressure
Face locked in dx
Normally locked face
Limiting conditions:
side AB
DDL_IMPO:
(Group_no:GRNM11
Dy: 0. )
side EFF
FACE_IMPO:
(Group_ma:GRMA12
Dnor: 0. )
pressure on AE
PRES_REP:
(Group_ma:GRMA13
Near: 1. )
Names of the nodes:
A=N2
B=N361
C=N121
D=N584
E=N155
F=N503
13.2 Characteristics of the mesh
A number of nodes: 591
A number of meshs and types: 200 TRIA6 50 QUAD8
13.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“D_PLAN”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
15/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
14 Results of modeling F
14.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
0.
7.3398 10
3
1.6685
1.
0.20055
0.
0.
7.3326 10
3
1.6669
0.9959
0.20129
0.00332
-
0.10
0.09
0.41
0.37
-
10
2
10
2
10
2
10
2
10
2
10
2
C
U
v
xx
yy
zz
xy
2.80882 10
3
6.78109 10
3
1.27771
0.60921
0.20055
0.94346
2.8063 10
3
6.7745 10
3
1.27799
0.60779
0.20106
0.94027
0.09
0.10
0.02
0.23
0.25
0.34
10
2
10
2
10
2
10
2
10
2
10
2
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1851 10
3
5.1851 10
3
0.33462
0.33403
0.20059
1.33117
0.09
0.09
0.11
0.066
0.02
0.23
10
2
10
2
10
2
10
2
10
2
10
2
B
U
v
xx
yy
zz
xy
0.
4.6716 10
3
0.66738
0.
0.20021
0.
eps
4.6682 10
3
0.66758
0.00033
0.20037
5.1132 10
4
-
0.07
0.03
-
0.08
-
10
2
10
2
10
2
10
2
10
2
10
2
D
U
v
xx
yy
zz
xy
1.79157 10
3
4.32523 10
3
0.56964
0.09774
0.20021
0.23595
1.7865 10
3
4.3129 10
3
0.56962
0.09805
0.200298
0.23623
0.28
0.28
0.003
0.32
0.044
0.12
10
2
10
2
10
2
10
2
10
2
10
2
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.3009 10
3
3.3009 10
3
0.33371
0.33366
0.20021
0.33392
0.29
0.29
0.006
0.009
0.
0.069
10
2
10
2
10
2
10
2
10
2
10
2
14.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 6.05 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
16/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
15 Modeling G
15.1 Characteristics of modeling
D_PLAN
(QUAD9)
45°
y
X
With
B
C
D
F
E
Face locked out of Dy
Normally locked face
Face with imposed pressure
Limiting conditions:
side AB
DDL_IMPO:
(Group_no:GRNM11
Dy: 0. )
side EFF
FACE_IMPO:
(Group_ma:GRMA12
Dnor: 0. )
pressure on AE
PRES_REP:
(Group_ma:GRMA13
Near: 1. )
Names of the nodes:
A=N1
B=N347
C=N21
D=N432
E=N39
F=N229
15.2 Characteristics of the mesh
A number of nodes: 441
A number of meshs and types: 100 QUAD9
15.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“D_PLAN”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
17/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
16 Results of modeling G
16.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
1.6685
0.20055
0.
7.3329 10
3
eps
0.9968
1.6655
0.20059
2.97 10
4
0.09
-
0.32
0.18
0.02
-
10
2
10
2
10
2
10
2
10
2
10
2
C
U
v
xx
yy
zz
xy
6.78109 10
3
2.80882 10
3
0.60921
1.27771
0.20055
0.94346
6.7747 10
3
2.8062 10
3
0.60695
1.27563
0.20060
0.94128
0.09
0.09
0.37
0.16
0.02
0.23
10
2
10
2
10
2
10
2
10
2
10
2
E
U
v
xx
yy
zz
xy
5.19002 10
3
5.19002 10
3
0.33425
0.33425
0.20055
1.33425
5.1851 10
3
5.1851 10
3
0.33403
0.33463
0.20059
1.33117
0.09
0.09
0.06
0.11
0.02
0.23
10
2
10
2
10
2
10
2
10
2
10
2
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.66738
0.20021
0.
4.6682 10
3
eps
2.394 10
3
0.66759
0.200207
2.65 10
5
0.07
-
-
0.03
0.001
-
10
2
10
2
10
2
10
2
10
2
10
2
D
U
v
xx
yy
zz
xy
4.32523 10
3
1.79157 10
3
0.09774
0.56964
0.20021
0.23595
4.3128 10
3
1.7864 10
3
0.09756
0.56979
0.200206
0.23611
0.29
0.29
0.18
0.02
0.002
0.07
10
2
10
2
10
2
10
2
10
2
10
2
F
U
v
xx
yy
zz
xy
3.31039 10
3
3.31039 10
3
0.33369
0.33369
0.20021
0.33369
3.3009 10
3
3.3009 10
3
0.33366
0.33371
0.20021
0.33392
0.29
0.29
0.009
0.006
0.
0.07
10
2
10
2
10
2
10
2
10
2
10
2
16.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 5.38 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
18/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
17 Modeling H
17.1 Characteristics of modeling
Elements axis (TRIA3 + QUAD4)
y
X
Face locked out of Dy
Face locked out of Dy
Face with imposed pressure
With
B
C
E
F
D
Center cylinder
0.01m
Limiting conditions:
side AB
DDL_IMPO:
(Group_no:GRNM11
Dy: 0. )
side EFF
FACE_IMPO:
(Group_ma:GRMA12
Dnor: 0. )
pressure on AE
PRES_REP:
(Group_ma:GRMA13
Near: 1. )
Names of the nodes:
A=N111
B=N1
C=N112
D=N3
E=N113
F=N4
17.2 Characteristics of the mesh
A number of nodes: 113
A number of meshs and types: 40 QUAD4 80 TRIA3
17.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“AXIS”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
19/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
18 Results of modeling H
18.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3390 10
3
eps
0.9430
0.2248
1.6923
eps
0.01
-
5.72
12.19
1.46
-
10
2
0.2
0.2
0.2
0.2
C
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3390 10
3
eps
0.9430
0.2248
1.6923
eps
0.01
-
5.72
12.19
1.46
-
10
2
0.2
0.2
0.2
0.2
E
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3390 10
3
0.
0.9430
0.2248
1.6923
eps
0.01
-
5.72
12.19
1.46
-
10
2
0.2
0.2
0.2
0.2
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6713 10
3
eps
0.0110
0.1954
0.6625
0.0011
0.01
-
-
2.35
0.72
-
10
2
0.05
0.05
0.05
0.05
D
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6713 10
3
eps
0.0110
0.1954
0.6625
eps
0.01
-
-
2.35
0.72
-
10
2
0.05
0.05
0.05
0.05
F
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6713 10
3
eps
0.0110
0.1954
0.6625
+0.0011
0.01
-
-
2.35
0.72
-
10
2
0.05
0.05
0.05
0.05
18.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 5.60 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
20/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
19 Modeling I
19.1 Characteristics of modeling
Elements axis (TRIA6 + QUAD8)
y
Center cylinder
0.01m
X
With
B
C
E
D
F
Face locked out of Dy
Face locked out of Dy
Face with imposed pressure
Limiting conditions:
side AB
DDL_IMPO:
(Group_no:GRNM11
Dy: 0. )
side EFF
FACE_IMPO:
(Group_ma:GRMA12
Dnor: 0. )
pressure on AE
PRES_REP:
(Group_ma:GRMA13
Near: 1. )
Names of the nodes:
A=N8
B=N174
C=N5
D=N170
E=N3
F=N159
19.2 Characteristics of the mesh
A number of nodes: 175
A number of meshs and types: 20 QUAD8 40 TRIA6
19.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“AXIS”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
21/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
20 Results of modeling I
20.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3397 10
3
eps
0.9984
0.20055
1.669
eps
0.00
-
0.16
-
0.57
-
10
2
10
2
10
2
10
2
10
2
10
2
C
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3397 10
3
eps
0.9984
0.20055
1.669
eps
0.00
-
0.16
-
0.57
-
10
2
10
2
10
2
10
2
10
2
10
2
E
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3397 10
3
eps
0.9984
0.20055
1.669
eps
0.00
-
0.16
-
0.57
-
10
2
10
2
10
2
10
2
10
2
10
2
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6716 10
3
eps
3.8 10
4
0.2002
0.66716 10
5
0.00
-
-
-
0.03
-
10
2
10
2
10
2
10
2
10
2
10
2
D
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6716 10
3
eps
3.8 10
4
0.2002
0.66716
eps
0.00
-
-
-
0.03
-
10
2
10
2
10
2
10
2
10
2
10
2
F
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6716 10
3
eps
3.8 10
4
0.2002
0.66716
10
5
0.00
-
-
-
0.03
-
10
2
10
2
10
2
10
2
10
2
10
2
20.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 5.06 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
22/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
21 Modeling J
21.1 Characteristics of modeling
Elements axis (QUAD9)
0.01m
y
X
With
B
C
E
D
F
Face locked out of Dy
Face locked out of Dy
Face with imposed pressure
Center cylinder
Limiting conditions:
side AB
DDL_IMPO:
(Group_no:GRNM11
Dy: 0. )
side EFF
FACE_IMPO:
(Group_ma:GRMA12
Dnor: 0. )
pressure on AE
PRES_REP:
(Group_ma:GRMA13
Near: 1. )
Names of the nodes:
A=N196
B=N1
C=N200
D=N5
E=N202
F=N7
21.2 Characteristics of the mesh
A number of nodes: 205
A number of meshs and types: 40 QUAD9
21.3 Functionalities tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“AXIS”
ALL
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
23/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
22 Results of modeling J
22.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
With
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3397 10
3
eps
0.9984
0.2005
1.667
eps
0.00
-
+0.16
-
0.57
-
10
2
10
2
10
2
10
2
10
2
10
2
C
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3397 10
3
eps
0.9984
0.2005
1.667
eps
0.00
-
+0.16
-
0.57
-
10
2
10
2
10
2
10
2
10
2
10
2
E
U
v
xx
yy
zz
xy
7.3398 10
3
0.
1.
0.20055
1.6685
0.
7.3397 10
3
eps
0.9984
0.2005
1.667
eps
0.00
-
+0.16
-
0.57
-
10
2
10
2
10
2
10
2
10
2
10
2
B
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6716 10
3
eps
1.1 10
4
0.20021
0.66727
eps
0.00
-
-
-
0.04
-
10
2
10
2
10
2
10
2
10
2
10
2
D
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6716 10
3
eps
1.1 10
4
0.20021
0.66727
eps
0.00
-
-
-
0.04
-
10
2
10
2
10
2
10
2
10
2
10
2
F
U
v
xx
yy
zz
xy
4.6716 10
3
0.
0.
0.20021
0.66738
0.
4.6716 10
3
eps
1.1 10
4
0.20021
0.66727
eps
0.00
-
-
0.02
0.04
-
10
2
10
2
10
2
10
2
10
2
10
2
22.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use: 4.84 seconds
Code_Aster
®
Version
3
Titrate:
Harmonic SHLV100 Response of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C
Page:
24/24
Manual of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
23 Summary of the results
Summary
errors
3D
D_PLAN
Axis
max in %
MOD A
MOD B
MOD C
MOD D
MOD E
MOD F
MOD G
MOD H
MOD I
MOD J
Displacements
WITH, C, E
B, D, F
0.27
0.39
0.10
0.02
0.10
0.68
0.17
0.28
0.27
0.39
0.10
0.29
0.09
0.29
0.01
0.01
0.00
0.00
0.00
0.00
Stresses
xx
WITH, C, E
B, D, F
29.23
24.39
0.10
0.02
16.92
15.69
9.20
3.64
29.18
24.36
0.11
0.03
0.37
0.18
5.72
-
0.27
-
0.27
-
Stresses
yy
WITH, C, E
B, D, F
59.04
2.75
0.41
0.30
47.19
1.97
12.67
0.78
59.01
2.75
0.41
0.32
0.18
0.03
12.19
2.35
0.09
0.09
0.09
0.02
Stresses
zz
WITH, C, E
B, D, F
44.50
6.80
0.37
0.04
21.51
4.05
4.11
1.20
44.10
6.80
0.37
0.08
0.02
0.001
1.46
0.72
0.57
0.03
0.57
0.04
Stresses
xy
WITH, C, E
B, D, F
9.20
2.34
0.34
0.12
3.30
7.84
0.24
0.19
9.19
2.34
0.34
0.12
0.23
0.07
-
-
-
-
-
-
·
The mesh for the elements of command 1 is not fine enough.
·
The results are more precise with elements of command 2.
·
The problem is adapted more to an axisymmetric modeling (H, I, J) - > better results.
·
Results of the elements 3D and the plane elements having spaces of interpolation in
correspondence are identical.
·
The results of axisymmetric elements QUAD8 and QUAD9 are identical.