Code_Aster
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
1/24
Organization (S): EDF/IMA/MN
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
V2.07.100 document
SHLV 100 - Harmonic Réponse 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 grid used.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
2/24
1 Problem of reference
1.1 Geometry
y
R
F
E
C
45°
D
P
With
B
Z
face blocked according to Z
X
face blocked according to Z
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/M2
= 0.3
= 35 kg/m3
The very low value of the Young modulus does not have anything physics.
1.3 Boundary conditions and loadings
Pressure interns P = p E jt
with p = 1 Mpa
and
= 0.2 rad/S
1.4 Initial conditions
· without initial conditions,
· direct calculation of the harmonic solution.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
3/24
2 Reference solution
2.1 Method of calculation used for the reference solution
U = A J
+
=
=
R
1 (K
R
L
) B Y1 (K rL)
U
U
Z
0
=
1
1
2 µ K
With
2
2
- 1
-
+
2
2
-
rr
L
(
) J0 (K R
L
)
J1 (K R
L
) B
Y0 (K R
L
)
Y1 (K R
L
)
K R
K R
L
L
=
1
1
2 µ K
With
2
2
- 1
+
+
2
2
+
L
(
) J0 (K R
L
)
J1 (K R
L
) B
Y0 (K R
L
)
Y1 (K R
L
)
K R
K R
L
L
= 2 µ
2
zz
K L (
2
-) 1 [A J0 (kL R) + B Y0 (kL R)]
= = =
R
rz
Z
0
+ µ
1 -
1
with: 2
2
=
=
K
4 µ
2 (
=
=
=
1 -)
L
2
C
+
4
2 µ
L
J, J, Y, Y
: Functions of Bessel.
1
0
1
0
Constant A and B are calculated by solving the linear system obtained while writing:
(A) = - p
(b) =
rr
rr
0
One obtains:
- 3
-
for R = 0.1 U = 7 3398
.
10
for R = 0.2
U =
3
R
R
4 6816
.
10
= 1
=
rr
rr
0.
= 16685
.
= 0 66738
.
= 0 20055
.
=
zz
zz
0 20031
.
Passage in the system of Cartesian axes:
= cos2 + sin2 - 2 sin cos
xx
rr
R
= sin2 + cos2 + 2 sin cos
yy
rr
R
= sin cos - sin cos - 2
cos2
-
2
xy
rr
R (
sin)
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
(,
xx
yy
zz
xy)
Displacements (U, v) and forced
at the points A, B, C, D, E, F.
2.3 Uncertainty on the solution
Precision of the calculation of Fonctions de Bessel.
2.4 Bibliographical references
[1] Mr. BONNET: Methods of the integral equations regularized into elastodynamic - Bulletin
DER - Sery C - N°1/2 - (1987).
[2] ERINGEN - SUHUBI - Elastodynamics, Vol.2: linear theory Academic Press (1975).
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
4/24
3 Modeling A
3.1 Characteristics of modeling
Elements 3D (PENTA6 and HEXA8) (resulting from the grid 2D below).
F
Normally blocked face
y
D
E
C
45°
X
With
B
Face with imposed pressure
Face blocked out of Dy
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 grid
A number of nodes: 513
A number of meshs and types: 400 PENTA6 100 HEXA8 40 QUAD4
3.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[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.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
5/24
4 Results of modeling A
4.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3243 103
0.21
102
With
v
0.
eps
0.2
xx
1.
0.8789
12.1
yy
1.6685
1.6241
2.66
zz
0.20055
0.2235
11.75
0.2
xy
0.
0.0922
U
6.78109 103
6.7670 103
0.21
102
C
v
2.80882 103
2.8012 103
0.27
0.3
0.3
xx
0.60921
0.5121
15.94
yy
1.27771
1.3300
4.09
0.3
0.3
zz
0.20055
0.2454
22.39
xy
0.94346
0.8567
9.20
0.3
U
5.19002 103
5.1784 103
0.22
102
E
v
5.19002 103
5.1784 103
0.22
0.6
0.6
xx
0.33425
0.4319
29.23
yy
0.33425
0.5315
59.04
0.6
0.6
zz
0.20055
0.289
44.50
xy
1.33425
1.269
4.87
U
4.6716 103
4.6641 103
0.16
102
B
v
0.
eps
xx
0.
0.0132
yy
0.66738
0.6724
0.75
2.102
zz
0.20021
0.1977
1.25
xy
0.
0.0219
U
4.32523 103
4.3084 103
0.39
102
D
v
1.79157 103
1.7854 103
0.34
0.3
xx
0.09774
0.0739
24.39
0.3
yy
0.56964
0.5728
0.56
0.3
zz
0.20021
0.1941
3.05
0.3
xy
0.23595
0.2348
0.49
0.3
U
3.31039 103
3.2974 103
0.39
102
F
v
3.31039 103
3.2974 103
0.39
0.2
xx
0.33369
0.2977
10.78
0.2
yy
0.33369
0.3245
2.75
0.2
zz
0.20021
0.1866
6.80
0.2
0.2
xy
0.33369
0.3415
2.34
4.2 Remarks
The grid is insufficient for linear elements.
4.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 10.23 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
6/24
5 Modeling B
5.1 Characteristics of modeling
Elements 3D (PENTA15 and HEXA20) (resulting from the grid 2D below).
y
B
D
Face blocked in dx
F
With
Normally blocked face
C
E
45°
Face with imposed pressure
X
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 grid
A number of nodes: 2115
A number of meshs and types: 400 PENTA15 100 HEXA20 40 QUAD8
5.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[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.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
7/24
6 Results of modeling B
6.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
0.
eps
With
v
7.3398 103
7.3326 103
0.10
102
xx
1.6685
1.6669
0.09
102
yy
1.
0.9959
0.41
102
zz
0.20055
0.2013
0.37
102
xy
0.
3.3234 103
102
U
2.80882 103
2.8063 103
0.09
102
C
v
6.78109 103
6.7745 103
0.10
102
xx
1.27771
1.278
0.02
102
yy
0.60921
0.6078
0.23
102
zz
0.20055
0.20107
0.26
102
xy
0.94346
0.94027
0.34
102
U
5.19002 103
5.1851 103
0.09
102
E
v
5.19002 103
5.1851 103
0.10
102
xx
0.33425
0.3346
0.10
102
yy
0.33425
0.3340
0.07
102
zz
0.20055
0.2006
0.02
102
xy
1.33425
1.331
0.24
102
U
0.
eps
B
v
4.6716 103
4.6682 103
0.07
102
xx
0.66738
0.6675
0.02
102
yy
0.
3.2779 104
102
zz
0.20021
0.2003
0.04
102
xy
0.
5.0918 104
102
U
1.79157 103
1.7864 103
0.29
102
D
v
4.32523 103
4.3129 103
0.29
102
xx
0.56964
0.56957
0.01
102
yy
0.09774
0.09803
0.30
102
zz
0.20021
0.20027
0.03
102
xy
0.23595
0.23623
0.12
102
U
3.31039 103
3.3009 103
0.29
102
F
v
3.31039 103
3.3009 103
0.29
102
xx
0.33369
0.3337
0.003
103
yy
0.33369
0.3337
0.003
103
zz
0.20021
0.2002
0.
103
xy
0.33369
0.3339
0.06
103
6.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 94.09 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
8/24
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 grid
A number of nodes: 423
A number of meshs and types: 1416 TETRA4 72 TRIA3
7.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[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.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
9/24
8 Results of modeling C
8.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3331 103
0.10
102
With
v
0.
eps
-
xx
1.
0.9000
+10.00
0.02
yy
1.6685
1.6809
0.74
0.02
zz
0.20055
0.2343
16.83
0.02
xy
0.
0.1016
-
0.02
U
6.78109 103
6.7783 103
0.04
102
C
v
2.80882 103
2.8077 103
0.04
0.04
xx
0.60921
0.5061
16.92
yy
1.27771
1.3184
3.18
0.04
0.04
zz
0.20055
0.2437
21.51
xy
0.94346
0.9123
3.30
0.04
U
5.19002 103
5.1853 103
0.09
102
E
v
5.19002 103
5.1853 103
0.09
0.5
xx
0.33425
0.2888
13.60
yy
0.33425
0.4920
47.19
0.5
0.5
zz
0.20055
0.2343
16.83
xy
1.33425
1.2905
3.28
0.5
U
4.6716 103
4.6634 103
0.18
102
B
v
0.
eps
-
xx
0.
0.0146
-
yy
0.66738
0.6570
1.55
5.102
zz
0.20021
0.1976
1.30
5.102
xy
0.
0.0159
-
5.102
U
4.32523 103
4.2960 103
0.68
102
D
v
1.79157 103
1.7795 103
0.67
xx
0.09774
0.0824
15.69
0.2
0.2
yy
0.56964
0.5809
1.97
0.2
zz
0.20021
0.1921
4.05
xy
0.23595
0.2378
7.84
0.2
U
3.31039 103
3.2976 103
0.39
102
F
v
3.31039 103
3.2975 103
0.39
0.1
xx
0.33369
0.3052
8.54
0.1
yy
0.33369
0.3371
1.02
0.1
zz
0.20021
0.1921
4.05
0.1
xy
0.33369
0.3358
0.63
8.2 Remarks
One notes a variation (< 0.24%) displacements for the points of the z=0.005 plan.
The grid is insufficient for linear elements.
8.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 18.55 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
10/24
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 grid
A number of nodes: 703
A number of meshs and types: 356 TETRA10 36 TRIA6
9.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[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.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
11/24
10 Results of modeling D
10.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3522 103
0.10
102
With
v
0.
eps
-
102
xx
1.
0.9925
0.75
5.102
yy
1.6685
1.6725
0.24
5.102
zz
0.20055
0.2040
1.72
5.102
xy
0.
0.0365
-
5.102
U
6.78109 103
6.7836 103
0.04
102
C
v
2.80882 103
2.8099 103
0.04
102
xx
0.60921
0.5977
1.89
5.102
yy
1.27771
1.294
1.28
5.102
zz
0.20055
0.2088
4.11
5.102
xy
0.94346
0.9457
0.24
5.102
U
5.19002 103
5.1988 103
0.17
102
E
v
5.19002 103
5.1988 103
0.17
102
0.15
xx
0.33425
0.3035
9.20
yy
0.33425
0.3766
12.67
0.15
0.15
zz
0.20055
0.2040
1.72
xy
1.33425
1.332
0.17
0.15
U
4.6716 103
4.6711 103
0.01
102
B
v
0.
eps
-
102
xx
0.
8.597 104
-
102
yy
0.66738
0.6679
0.08
102
zz
0.20021
0.2006
0.19
102
xy
0.
1.0181 103
-
102
U
4.32523 103
4.3134 103
0.28
102
D
v
1.79157 103
1.7867 103
0.28
102
xx
0.09774
0.09418
3.64
5.102
yy
0.56964
0.5652
0.78
5.102
zz
0.20021
0.1978
1.20
5.102
xy
0.23595
0.2355
0.19
5.102
U
3.31039 103
3.3029 103
0.23
102
F
v
3.31039 103
3.3029 103
0.23
102
xx
0.33369
0.3357
0.60
102
yy
0.33369
0.3334
0.09
102
zz
0.20021
0.2007
0.24
102
xy
0.33369
0.3336
-
102
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
Obstruction memory:
8 megawords
Time CPU To use: 21.05 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
12/24
11 Modeling E
11.1 Characteristics of modeling
Elements D_PLAN (TRIA3 + QUAD4)
F
Normally blocked face
y
D
E
C
45°
X
With
B
Face with imposed pressure
Face blocked out of Dy
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 grid
A number of nodes: 171
A number of meshs and types: 200 TRIA3 50 QUAD4
11.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
13/24
12 Results of modeling E
12.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3243 103
0.21
102
With
v
0.
eps
-
0.15
xx
1.
0.8790
12.10
yy
1.6685
1.6241
2.66
0.15
0.15
zz
0.20055
0.2235
11.44
0.15
xy
0.
0.0922
-
U
6.78109 103
6.7670 103
0.21
102
C
v
2.80882 103
2.8012 103
0.27
0.3
xx
0.60921
0.5122
15.92
yy
1.27771
1.3302
4.11
0.3
0.3
zz
0.20055
0.2454
22.36
xy
0.94346
0.8567
9.19
0.3
U
5.19002 103
5.1784 103
0.22
102
E
v
5.19002 103
5.1784 103
0.22
0.6
xx
0.33425
0.4318
29.18
yy
0.33425
0.5315
59.01
0.6
0.6
zz
0.20055
0.2890
44.10
xy
1.33425
1.2686
4.92
0.6
U
4.6716 103
4.6641 103
0.16
102
B
v
0.
eps
-
xx
0.
1.3198 102
-
0.05
0.05
yy
0.66738
0.6723
0.74
0.05
zz
0.20021
0.1977
1.25
xy
0.
0.0219
-
0.05
U
4.32523 103
4.3084 103
0.39
102
D
v
1.79157 103
1.7854 103
0.39
xx
0.09774
0.07393
24.36
0.3
0.3
yy
0.56964
0.5728
0.55
0.3
zz
0.20021
0.1940
3.10
xy
0.23595
0.2347
0.53
0.3
U
3.31039 103
3.2974 103
0.39
102
F
v
3.31039 103
3.2974 103
0.39
0.15
xx
0.33369
0.2976
10.81
0.15
yy
0.33369
0.3245
2.75
0.15
zz
0.20021
0.1866
6.80
0.15
xy
0.33369
0.3415
2.34
12.2 Remarks
The grid is insufficient for linear elements.
12.3 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 5.87 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
14/24
13 Modeling F
13.1 Characteristics of modeling
Elements D_PLAN (QUAD8 + TRIA6)
y
B
D
Face blocked in dx
F
With
Normally blocked face
C
E
45°
Face with imposed pressure
X
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 grid
A number of nodes: 591
A number of meshs and types: 200 TRIA6 50 QUAD8
13.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
15/24
14 Results of modeling F
14.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
0.
0.
-
102
With
v
7.3398 103
7.3326 103
0.10
102
xx
1.6685
1.6669
0.09
102
yy
1.
0.9959
0.41
102
zz
0.20055
0.20129
0.37
102
xy
0.
0.00332
-
102
U
2.80882 103
2.8063 103
0.09
102
C
v
6.78109 103
6.7745 103
0.10
102
xx
1.27771
1.27799
0.02
102
yy
0.60921
0.60779
0.23
102
zz
0.20055
0.20106
0.25
102
xy
0.94346
0.94027
0.34
102
U
5.19002 103
5.1851 103
0.09
102
E
v
5.19002 103
5.1851 103
0.09
102
xx
0.33425
0.33462
0.11
102
yy
0.33425
0.33403
0.066
102
zz
0.20055
0.20059
0.02
102
xy
1.33425
1.33117
0.23
102
U
0.
eps
-
102
B
v
4.6716 103
4.6682 103
0.07
102
xx
0.66738
0.66758
0.03
102
yy
0.
0.00033
-
102
zz
0.20021
0.20037
0.08
102
xy
0.
5.1132 104
-
102
U
1.79157 103
1.7865 103
0.28
102
D
v
4.32523 103
4.3129 103
0.28
102
xx
0.56964
0.56962
0.003
102
yy
0.09774
0.09805
0.32
102
zz
0.20021
0.200298
0.044
102
xy
0.23595
0.23623
0.12
102
U
3.31039 103
3.3009 103
0.29
102
F
v
3.31039 103
3.3009 103
0.29
102
xx
0.33369
0.33371
0.006
102
yy
0.33369
0.33366
0.009
102
zz
0.20021
0.20021
0.
102
xy
0.33369
0.33392
0.069
102
14.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 6.05 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
16/24
15 Modeling G
15.1 Characteristics of modeling
D_PLAN (QUAD9)
F
Normally blocked face
y
D
E
C
45°
X
With
B
Face with imposed pressure
Face blocked out of Dy
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 grid
A number of nodes: 441
A number of meshs and types: 100 QUAD9
15.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
17/24
16 Results of modeling G
16.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3329 103
0.09
102
With
v
0.
eps
-
102
xx
1.
0.9968
0.32
102
yy
1.6685
1.6655
0.18
102
zz
0.20055
0.20059
0.02
102
xy
0.
2.97 104
-
102
U
6.78109 103
6.7747 103
0.09
102
C
v
2.80882 103
2.8062 103
0.09
102
xx
0.60921
0.60695
0.37
102
yy
1.27771
1.27563
0.16
102
zz
0.20055
0.20060
0.02
102
xy
0.94346
0.94128
0.23
102
U
5.19002 103
5.1851 103
0.09
102
E
v
5.19002 103
5.1851 103
0.09
102
xx
0.33425
0.33403
0.06
102
yy
0.33425
0.33463
0.11
102
zz
0.20055
0.20059
0.02
102
xy
1.33425
1.33117
0.23
102
U
4.6716 103
4.6682 103
0.07
102
B
v
0.
eps
-
102
xx
0.
2.394 103
-
102
yy
0.66738
0.66759
0.03
102
zz
0.20021
0.200207
0.001
102
xy
0.
2.65 105
-
102
U
4.32523 103
4.3128 103
0.29
102
D
v
1.79157 103
1.7864 103
0.29
102
xx
0.09774
0.09756
0.18
102
yy
0.56964
0.56979
0.02
102
zz
0.20021
0.200206
0.002
102
xy
0.23595
0.23611
0.07
102
U
3.31039 103
3.3009 103
0.29
102
F
v
3.31039 103
3.3009 103
0.29
102
xx
0.33369
0.33366
0.009
102
yy
0.33369
0.33371
0.006
102
zz
0.20021
0.20021
0.
102
xy
0.33369
0.33392
0.07
102
16.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 5.38 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
18/24
17 Modeling H
17.1 Characteristics of modeling
Elements axis (TRIA3 + QUAD4)
Center cylinder
Face blocked out of Dy
y
E
F
C
0.01m
D
X
With
B
Face with imposed pressure
Face blocked out of Dy
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 grid
A number of nodes: 113
A number of meshs and types: 40 QUAD4 80 TRIA3
17.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“AXIS”
TOUT
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
19/24
18 Results of modeling H
18.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3390 103
0.01
102
With
v
0.
eps
-
0.2
xx
1.
0.9430
5.72
yy
0.20055
0.2248
12.19
0.2
0.2
zz
1.6685
1.6923
1.46
0.2
xy
0.
eps
-
U
7.3398 103
7.3390 103
0.01
102
C
v
0.
eps
-
0.2
xx
1.
0.9430
5.72
yy
0.20055
0.2248
12.19
0.2
0.2
zz
1.6685
1.6923
1.46
xy
0.
eps
-
0.2
U
7.3398 103
7.3390 103
0.01
102
E
v
0.
0.
-
0.2
xx
1.
0.9430
5.72
yy
0.20055
0.2248
12.19
0.2
0.2
zz
1.6685
1.6923
1.46
xy
0.
eps
-
0.2
U
4.6716 103
4.6713 103
0.01
102
B
v
0.
eps
-
xx
0.
0.0110
-
0.05
0.05
yy
0.20021
0.1954
2.35
0.05
zz
0.66738
0.6625
0.72
xy
0.
0.0011
-
0.05
U
4.6716 103
4.6713 103
0.01
102
D
v
0.
eps
-
xx
0.
0.0110
-
0.05
0.05
yy
0.20021
0.1954
2.35
0.05
zz
0.66738
0.6625
0.72
xy
0.
eps
-
0.05
U
4.6716 103
4.6713 103
0.01
102
F
v
0.
eps
-
0.05
xx
0.
0.0110
-
0.05
yy
0.20021
0.1954
2.35
0.05
zz
0.66738
0.6625
0.72
0.05
xy
0.
+0.0011
-
18.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 5.60 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
20/24
19 Modeling I
19.1 Characteristics of modeling
Elements axis (TRIA6 + QUAD8)
Center cylinder
Face blocked out of Dy
y
E
F
0.01m
C
D
X
With
B
Face with imposed pressure
Face blocked out of Dy
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 grid
A number of nodes: 175
A number of meshs and types: 20 QUAD8 40 TRIA6
19.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“AXIS”
TOUT
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
21/24
20 Results of modeling I
20.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3397 103
0.00
102
With
v
0.
eps
-
102
xx
1.
0.9984
0.16
102
yy
0.20055
0.20055
-
102
zz
1.6685
1.669
0.57
102
xy
0.
eps
-
102
U
7.3398 103
7.3397 103
0.00
102
C
v
0.
eps
-
102
xx
1.
0.9984
0.16
102
yy
0.20055
0.20055
-
102
zz
1.6685
1.669
0.57
102
xy
0.
eps
-
102
U
7.3398 103
7.3397 103
0.00
102
E
v
0.
eps
-
102
xx
1.
0.9984
0.16
102
yy
0.20055
0.20055
-
102
zz
1.6685
1.669
0.57
102
xy
0.
eps
-
102
U
4.6716 103
4.6716 103
0.00
102
B
v
0.
eps
-
102
xx
0.
3.8 104
-
102
yy
0.20021
0.2002
-
102
zz
0.66738
0.66716 105
0.03
102
xy
0.
-
102
U
4.6716 103
4.6716 103
0.00
102
D
v
0.
eps
-
102
xx
0.
3.8 104
-
102
yy
0.20021
0.2002
-
102
zz
0.66738
0.66716
0.03
102
xy
0.
eps
-
102
U
4.6716 103
4.6716 103
0.00
102
F
v
0.
eps
-
102
xx
0.
3.8 104
-
102
yy
0.20021
0.2002
-
102
zz
0.66738
0.66716
0.03
102
xy
0.
105
-
102
20.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 5.06 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
22/24
21 Modeling J
21.1 Characteristics of modeling
Elements axis (QUAD9)
Center cylinder
Face blocked out of Dy
y
E
F
0.01m
C
D
X
With
B
Face with imposed pressure
Face blocked out of Dy
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 grid
A number of nodes: 205
A number of meshs and types: 40 QUAD9
21.3 Functionalities tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“AXIS”
TOUT
[U4.22.01]
COMB_MATR_ASSE
[U4.53.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
23/24
22 Results of modeling J
22.1 Values tested
Localization
Sizes
Reference
Aster
% difference
tolerance
U
7.3398 103
7.3397 103
0.00
102
With
v
0.
eps
-
102
xx
1.
0.9984
+0.16
102
yy
0.20055
0.2005
-
102
zz
1.6685
1.667
0.57
102
xy
0.
eps
-
102
U
7.3398 103
7.3397 103
0.00
102
C
v
0.
eps
-
102
xx
1.
0.9984
+0.16
102
yy
0.20055
0.2005
-
102
zz
1.6685
1.667
0.57
102
xy
0.
eps
-
102
U
7.3398 103
7.3397 103
0.00
102
E
v
0.
eps
-
102
xx
1.
0.9984
+0.16
102
yy
0.20055
0.2005
-
102
zz
1.6685
1.667
0.57
102
xy
0.
eps
-
102
U
4.6716 103
4.6716 103
0.00
102
B
v
0.
eps
-
102
xx
0.
1.1 104
-
102
yy
0.20021
0.20021
-
102
zz
0.66738
0.66727
0.04
102
xy
0.
eps
-
102
U
4.6716 103
4.6716 103
0.00
102
D
v
0.
eps
-
102
xx
0.
1.1 104
-
102
yy
0.20021
0.20021
-
102
zz
0.66738
0.66727
0.04
102
xy
0.
eps
-
102
U
4.6716 103
4.6716 103
0.00
102
F
v
0.
eps
-
102
xx
0.
1.1 104
-
102
yy
0.20021
0.20021
0.02
102
zz
0.66738
0.66727
0.04
102
xy
0.
eps
-
102
22.2 Parameters of execution
Version: 3.02
Machine: CRAY C90
System: UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use: 4.84 seconds
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A
Code_Aster ®
Version
3
Titrate:
Harmonic SHLV100 Réponse of a hollow roll
Date:
20/09/99
Author (S):
X. DESROCHES
Key:
V2.07.100-C Page:
24/24
23 Summary of the results
Summary
3D
D_PLAN
Axis
errors
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
0.27
0.10
0.10
0.17
0.27
0.10
0.09
0.01
0.00
0.00
B, D, F
0.39
0.02
0.68
0.28
0.39
0.29
0.29
0.01
0.00
0.00
Constraints
xx
WITH, C, E
29.23
0.10
16.92
9.20
29.18
0.11
0.37
5.72
0.27
0.27
B, D, F
24.39
0.02
15.69
3.64
24.36
0.03
0.18
-
-
-
Constraints
yy
WITH, C, E
59.04
0.41
47.19
12.67
59.01
0.41
0.18
12.19
0.09
0.09
B, D, F
2.75
0.30
1.97
0.78
2.75
0.32
0.03
2.35
0.09
0.02
Constraints
zz
WITH, C, E
44.50
0.37
21.51
4.11
44.10
0.37
0.02
1.46
0.57
0.57
B, D, F
6.80
0.04
4.05
1.20
6.80
0.08
0.001
0.72
0.03
0.04
Constraints
xy
WITH, C, E
9.20
0.34
3.30
0.24
9.19
0.34
0.23
-
-
-
B, D, F
2.34
0.12
7.84
0.19
2.34
0.12
0.07
-
-
-
· The grids for the elements of command 1 are 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.
Handbook of Validation
V2.07 booklet: Harmonic response of the voluminal structures
HI-75/96/005 - Ind A