Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
1/36
Organization (S): EDF-R & D/AMA, CS IF
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
V3.04.004 document
SSLV04 - Hollow Cylindre in plane constraints
Summary:
This test is drawn from Guide VPCS (test SSLV04/89) and has as an aim a hollow roll charged in pressure
intern.
This three-dimensional problem is dealt with with various modelings:
· in 3D: 9 modelings (pentahedral, hexahedrons, tetrahedrons and pyramids, degrees 1 and 2),
· in 2D forced plane: 4 modelings (triangles and quadrangles degrees 1 and 2,
quadrangles with 9 nodes),
· in axisymmetric 2D: 3 modelings (triangles and quadrangles degrees 1 and 2, quadrangles with
9 nodes).
The functionalities tested are:
· pressure distributed,
· basic effect (with fixed or variable pressure),
· imposed displacements,
· matrices of rigidity,
· strains and stresses with the nodes,
· nodal reactions (modeling K).
There are 16 modelings.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
2/36
1
Problem of reference
1.1 Geometry
y
R
E
F
C
45°
D
P
With
B
Z
X
Internal radius
= 0.1 m has
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 = 2.105 MPa
= 0.3
1.3
Boundary conditions and loadings
Internal pressure:
P = 60 MPa
Pressure interns variable (modeling P only):
P varies linearly from 60 MPa with t=1.s with 120 MPa with t=2.s
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
3/36
2
Reference solution
2.1
Method of calculation used for the reference solution
In constraint planes (cylinder on free board at the ends)
zz = 0
2
2
B
has
rr
= P
1
b2 - a2
R 2
2
2
B
has
= P
1+
b2 - a2
R 2
R = 0
P
a2
2
B
ur =
(1) + (1+) R
E b2 - a2
R 2
One obtains:
for
= 0.1
= 59. 10 6
-
for
= 0.2
= 40. 10 6
R
U
R
U
-
R
R
= 60.
-
= 0.
rr
rr
= 100.
= 40.
= = 0.
= = 0.
zz
R
zz
R
Passage in the system of Cartesian axes:
2
2
xx
= rr cos + sin - 2 R sin cos
2
2
yy
= rr sin + cos + 2 R sin cos
2
2
xy
= rr sin cos - sin cos - 2 R (cos - 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
Displacements (U, v) and forced (xx, yy
, zz
, xy
) at the points A, B, C, D, E, F.
2.3 References
bibliographical
[1]
Guide VPCS. SSLV04/89
[2]
Y.C. FUNG. Foundations off solid mechanics. Prentice-hall, Inc. Englewood Cliffs. NJ. 1965
p. 243 to 245.
[3]
J. COURBON. Resistance of the materials p 649
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
4/36
3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (PENTA6 and HEXA8)
Grid obtained by extrusion starting from a grid 2D resembling the grid below (30
elements in the radial direction with déraffinement progressive and 15+15 elements in the direction
circumferential).
F
Normally blocked face
y
E
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Along axis Z:
1 layer of elements
Total thickness:
0.01
Limiting conditions:
node F: uz = 0
face AB blocked out of Dy
normally blocked face EFF
pressure on face AE p = 60.
Names of the nodes:
With = N993
B=N1443
C=N1
D=N31
E=N496
F=N495
3.2
Characteristics of the grid
A number of nodes: 1922
A number of meshs and types: 900 PENTA6, 450 HEXA8 and 90 QUAD4 (faces internal skin).
3.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
POST_RELEVE “EXTRACTION”
MODI_REPERE DEFI_REPERE “USER”
“CYLINDRIQUE”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
5/36
4
Results of modeling A
4.1 Values
tested
Localization Size
Reference
Aster %
difference
With U
5.9
105 5.8950
105 0.08
v
0.
eps
-
xx 60.
59.2225
1.30
yy
100. 100.4159 0.42
zz
0. 0.3093
-
xy
0.
1.0442 -
xx
4.5 104
4.472 104 0.62
yy
5.9 104 5.904
104 0.08
xy
0.
6.788 105 -
B U
4
105 3.9959
105 0.10
v
0.
eps
-
xx 0.
1.7246
-
yy
40. 39.2451
1.89
zz
0.
0.3761 -
xy
0.
0.2659 -
xx
0.6 104
6.692 105 11.54
yy
2. 104 1.994
104 0.31
xy
0.
1.728 106 -
E U
4.17193
105 4.1708
105 0.03
v
4.17193 105 4.1708
105
0.03
xx 20.
19.0824
4.59
yy
20. 21.1394
5.70
zz
0. 0.0870
-
xy
80.
79.8831 0.15
xx
0.7 104 0.636
104 9.18
yy
0.7 104 0.769
104 9.92
xy
5.2 104
5.192 104 0.15
F U
2.82843
105 2.8302
105 0.06
v
2.82843 105 2.8302
105 0.06
xx 20.
18.9528
5.24
yy
20. 19.9104
0.45
zz
0. 0.1198
-
xy
20. 20.1809 0.90
xx
0.7 104 0.647
104 7.54
yy
0.7 104 0.709
104 1.35
xy
1.3 104 1.312
104 0.90
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
6/36
5 Modeling
B
5.1
Characteristics of modeling
Elements 3D (PENTA15 and HEXA20)
Grid obtained by extrusion starting from the grid 2D below (modeling F)
y
B
Face blocked in dx
F
With
Normally blocked face
E
Face with imposed pressure
45°
X
Along axis Z:
2 layers of elements
Total thickness:
0.01
Limiting conditions:
node F = uz = 0
face AB blocked in dx
normally blocked face EFF
pressure on face AE
p = 60.
Names of the nodes:
With = 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 (faces skin interns)
5.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
“EPSI_ELNO_DEPL”
POST_RELEVE “EXTRACTION”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
7/36
6
Results of modeling B
6.1 Values
tested
Localization Size
Reference
Aster %
difference
With U
0. eps
-
v
5.9 105 5.8944
105
0.09
xx 100.
99.6056
0.39
yy
60.
59.4473
0.92
zz
0. 0.0196
-
xy
0. 0.2481
-
xx
5.9 104 5.87
104
0.48
yy
4.5 104
4.47 104
0.74
xy
0. 1.61
106 -
B U
0. eps
-
v
4 105 3.9974
105
0.07
xx 40.
39.9711
0.07
yy
0. 0.0781
-
zz
0. 5.7992
103 -
xy
0.
0.0182
-
xx
2. 104 1.997
104
0.13
yy
0.6. 104
0.596 104
0.67
xy
0.
1.18107 -
E U
4.17193
105 4.1680
105
0.09
v
4.17193 105 4.1680
105
0.09
xx 20.
20.0515
0.26
yy
20. 20.0264
0.13
zz
0. 0.0155
-
xy
80. 79.7918
0.26
xx
0.7 104 0.702
104 0.34
yy
0.7 104 0.701
104 0.11
xy
5.2 104 5.19
104
0.26
F U
2.82843
105
2.82656 105
0,07
v
2.82843 105 2.82656
105
0.07
xx 20.
20.0099
0.05
yy
20. 19.9980
0.01
zz
0.
3.90 104 -
xy
20. 20.0122
0.06
xx
0.7 104 0.7005
104 0.08
yy
0.7 104 0.6997
104
0.03
xy
1.3 104 1.3008
104 0.06
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
8/36
7 Modeling
C
7.1
Characteristics of modeling
Elements 3D (TETRA4)
AB is on axis OX
Cutting:
21 equidistant nodes on segments AB, CD and EFF
21 equidistant nodes on arcs ACE and BDF
Along axis Z:
1 layer of elements
Total thickness:
0.01
Limiting conditions:
node F: uz = 0
face AB blocked out of Dy
normally blocked face EFF
pressure on face AE
p = 60.
Names of the nodes:
With = N165
B = N4
C = N209
D = N82
E = N244
F = N1068
7.2
Characteristics of the grid
A number of nodes: 1115
A number of meshs and types: 3724 TETRA4 and 1760 TRIA3 (faces skin interns)
7.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
9/36
8
Results of modeling C
8.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.8901
105
0.17
v
0. eps
-
xx
60.
57.2290
4.62
yy
100. 97.8711
2.13
zz
0. 0.0568
-
xy
0.
2.6589 -
xx
4.5 104
4.33 104
3.77
yy
5.9 104 5.75
104
2.52
xy
0.
1.73 105 -
B U
4
105 3.9878
105
0.30
v
0. eps
-
xx 0.
1.5296
-
yy
40. 40.9839
2.46
zz
0.
0.1006 -
xy
0.
0.8513 -
xx
0.6 104
6.897 104 14.95
yy
2. 104 2.074
104 3.68
xy
0.
5.534 105 -
E U
4.17193
105 4.1655
105
0.15
v
4.17193 105 4.1655
105
0.15
xx 20.
17.9096
10.45
yy
20. 21.8929
9.46
zz
0.
0.3679 -
xy
80.
77.6897
2.89
xx
0.7 104 0.573
104
18.20
yy
0.7 104 0.832
104 18.79
xy
5.2 104
5.050
2.89
F U
2.82843
105 2.8251
105
0.12
v
2.82843 105 2.8251
105
0.12
xx 20.
18.4444
7.78
yy
20. 19.8876
0.56
zz
0.
0.3910 -
xy
20.
20.1631
0.81
xx
0.7 104 0.630
104
10.05
yy
0.7 104 0.723
104 3.35
xy
1.3 104 1.311
104 0.81
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
10/36
9 Modeling
D
9.1
Characteristics of modeling
Element 3D (TETRA10)
AB is on axis OX
Cutting:
11 equidistant nodes on segments AB, CD and EFF
11 equidistant nodes on arcs ACE and BDF
Along axis Z:
1 layer of elements
Total thickness:
0.01
Limiting conditions:
node F: uz = 0
face AB blocked out of Dy
normally blocked face EFF
pressure on face AE
p = 60.
Names of the nodes:
With = N184
B = N4
C = N207
D = N50
E = N22
F = N726
9.2
Characteristics of the grid
A number of nodes: 1395
A number of meshs and types: 652 TETRA10 and 480 TRIA6 (faces skin interns)
9.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
11/36
10 Results of modeling D
10.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.8974
105
0.04
v
0. eps
-
xx
60.
60.3816
0.64
yy
100. 99.1907
0.81
zz
0.
0.9707
-
xy
0.
0.2979
-
xx
4.5 104
4.49 104
0.17
yy
5.9 104 5.88
104
0.34
xy
0.
1.94 106 -
B U
4
105 3.9989
105
0.03
v
0. eps
-
xx 0.
0.0388
-
yy
40. 40.0725
0.18
zz
0.
0.0046
-
xy
0. 0.1634
-
xx
0.6 104
0.599 104
0.15
yy
2. 104 2.003
104 0.16
xy
0. 1.062
106 -
E U
4.17193
105 4.17021
105 0.04
v
4.17193 105 4.17021
105 0.04
xx 20.
19.1178
4.41
yy
20. 19.6399
1.80
zz
0.
1.0206
-
xy
80.
79.7804
0.27
xx
0.7 104 0.677
104
3.34
yy
0.7 104 0.711
104 1.50
xy
5.2 104
5.186 104
0.27
F U
2.82843
105 2.82718
105
0.04
v
2.82843 105 2.82718
105
0.04
xx 20.
20.1903
0.95
yy
20. 19.9023
0.49
zz
0.
0.0016
-
xy
20.
20.0570
0.28
xx
0.7 104 0.711
104 1.57
yy
0.7 104 0.692
104
1.10
xy
1.3 104
1.304 104 0.28
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
12/36
11 Modeling
E
11.1 Characteristics of modeling
C_plan elements (TRIA3 + QUAD4)
Grid 2D resembling the grid below (30 elements in the radial direction with
déraffinement progressive and 15+15 elements in the circumferential direction).
F
Normally blocked face
y
E
D
C
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Limiting conditions:
side AB blocked out of Dy
normally blocked side EFF
pressure on AE p = 60.
Names of the nodes:
With = N1
B = N451
C = N496
D = N495
E = N990
F = N989
11.2 Characteristics of the grid
A number of nodes: 961
A number of meshs and types: 900 TRIA3, 450 QUAD4
11.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “C_PLAN” ALL
DEFI_MATERIAU ELAS
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
“CYLINDRICAL” MODI_REPERE DEFI_REPERE
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
13/36
12 Results of modeling E
12.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.8957
105
0.07
v
0. eps
-
xx
60.
59.3645
1.06
yy
100. 100.2653 0.26
zz
0. 0. -
xy
0.
1.0472 -
xx
4.5 104
4.472 104
0.62
yy
5.9 104 5.904
104 0.06
xy
0.
6.807 106 -
B U
4.
105 3.9965
105
0.09
v
0. eps
-
xx 0.
1.4986
-
yy
40. 39.4415
1.40
zz
0. 0. -
xy
0.
0.2658 -
xx
0.6 104
0.667 105 11.09
yy
2. 104 1.995
104
0.27
xy
0.
1.728 106 -
E U
4.17193
105 4.17101
105
0.02
v
4.17193 105 4.17101
105
0.02
xx 20.
19.0706
4.65
yy
20. 21.1354
5.68
zz
0. 0. -
xy
80.
79.8720
0.16
xx
0.7 104 0.636
104
9.07
yy
0.7 104 0.771
104 10.10
xy
5.2 104
5.192 104
0.16
F U
2.82843
105 2.82996
105 0.05
v
2.82843 105 2.82996
105 0.05
xx 20.
18.9626
5.19
yy
20. 19.8483
0.76
zz
0. 0. -
xy
20.
20.2466
1.23
xx
0.7 104 0.650
104
7.08
yy
0.7 104 0.708
104 1.14
xy
1.3 104
1.316 104 1.23
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
14/36
13 Modeling
F
13.1 Characteristics of modeling
C_plan elements (QUAD8 + TRIA6)
y
B
D
Face blocked in dx
F
With
Normally blocked face
C
E
Face with imposed pressure
45°
X
Limiting conditions:
side AB blocked in dx
normally blocked side EFF
pressure on AE p = 60.
Names of the nodes:
With = 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
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “C_PLAN”
TOUT
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
POST_RELEVE “EXTRACTION”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
15/36
14 Results of modeling F
14.1 Values
tested
Localization Size Reference
Aster %
difference
With U
0.
0.
-
v
5.9
105 5.8945
105
0.09
xx 100.
99.6095
0.39
yy
60.
59.4620
0.90
zz
0. 0. -
xy
0. 0.2441
-
xx
5.9 104 5.872
104
0.47
yy
4.5 104
4.467 104
0.73
xy
0. 1.586
106 -
B U
0. eps
-
v
4
105 3.9974
105
0.07
xx 40.
39.9774
0.06
yy
0. 0.0786
-
zz
0. 0. -
xy
0.
0.0181
-
xx
2. 104 1.998
104
0.11
yy
0.6 104
0.596 104
0.67
xy
0.
1.176 107 -
E U
4.17193
105
4.16814 105
0.09
v
4.17193 105 4.16814
105
0.09
xx 20.
20.0024
0.01
yy
20. 20.0045
0.02
zz
0. 0. -
xy
80. 79.8164
0.23
xx
0.7 104 0.7001
104 0.01
yy
0.7 104 0.7002
104 0.03
xy
5.2 104 5.188
104
0.23
F
U
2.82843 105
2.82655 105
0.07
v
2.82843 105 2.82655
105
0.07
xx 20.
20.0083
0.04
yy
20. 19.9915
0.04
zz
0. 0. -
xy
20. 20.0138
0.07
xx
0.7 104 0.7005
104 0.08
yy
0.7 104 0.6995
104
0.08
xy
1.3 104 1.3009
104 0.07
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
16/36
15 Modeling
G
15.1 Characteristics of modeling
C_plan (QUAD9)
F
Normally blocked face
y
E
D
C
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Limiting conditions:
side AB blocked out of Dy
normally blocked side EFF
pressure on AE p = 60.
Names of the nodes:
With = 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
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “C_PLAN”
TOUT
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
17/36
16 Results of modeling G
16.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.9000
105 0.00
v
0. eps
-
xx
60.
59.8354
0.27
yy
100. 99.8409
0.16
zz
0. 0. -
xy
0. 0.0283
-
xx
4.5 104
4.489 104 - 0.24
yy
5.9 104 5.890
104
0.18
xy
0.
1.839 107 -
B U
4
105 3.9999
105
0.001
v
0. eps
-
xx 0.
- 0.0189
-
yy
40. 40.0182
0.05
zz
0. 0. -
xy
0.
3.6815 103 -
xx
0.6 104
0.601 104 0.20
yy
2. 104 2.001
104 0.06
xy
0.
2.393 108 -
E U
4.17193
105 4.17195
105 0.00
v
4.17193 105 4.17195
105
0.00
xx 20.
19.9745
0.13
yy
20. 20.0311
0.16
zz
0. 0. -
xy
80.
79.8382
0.20
xx
0.7 104 0.698
104
0.25
yy
0.7 104 0.702
104 0.28
xy
5.2 104
5.189 104
0.20
F U
2.82843
105 2.82839
105
0.001
v
2.82843 105 2.82839
105
0.001
xx 20.
19.9960
0.02
yy
20. 20.0034
0.02
zz
0. 0. -
xy
20.
20.0185
0.09
xx
0.7 104 0.6997
104
0.04
yy
0.7 104 0.7002
104 0.03
xy
1.3 104
1.301 104 0.09
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
18/36
17 Modeling
H
17.1 Characteristics of modeling
Elements axis (TRIA3 + QUAD4)
Center cylinder
Node blocked out of Dy
y
E
F
C
0.01m
D
X
With
B
Face with imposed pressure
Limiting conditions:
node F blocked out of Dy
pressure on AE p = 60.
Names of the nodes:
With = 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
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “AXIS” ALL
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
CREA_RESU EVOL_ELAS DEPL
CALC_ELEM “SIGM_ELNO_DEPL”
INTE_MAIL_2D
POST_RCCM
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
19/36
18 Results of modeling H
18.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.8992
105
0.01
v
0. -
-
xx
60.
56.6060
5.66
yy
0. 1.0383 -
zz
100. 101.2924
1.29
xy
0.
1.1635
-
xx
4.5 104
4.36 104
2.99
yy
0.
6.18 105 -
zz
5.9 104 5.898
104
0.03
xy
0.
1.06 106 -
B U
4
105 3.9997
105
0.01
v
0. -
-
xx 0.
0.8951
-
yy
0.
0.4106
-
zz
40. 39.6001
1.00
xy
0.
0.1281
-
xx
0.6 104
0.632 104 5.43
yy
0.
6.011 105 -
zz
2. 104 1.999
104
0.02
xy
0.
8.325 107 -
E U
5.9
105 5.8992
105
0.01
v
0. -
-
xx
60.
56.6060
5.66
yy
0. 1.0383 -
zz
100. 101.2924
1.29
xy
0. 1.1635 -
xx
4.5 104
4.365 104
2.99
yy
0.
6.184 105 -
zz
5.9 104 5.898
104
0.03
xy
0. 1.063
106 -
F U
4
105 3.9997
105
0.01
v
0. -
-
xx 0.
0.4221
-
yy
0.
0.2280
-
zz
40. 39.8015
0.50
xy
0.
0.0020
-
xx
0.6 104
0.615 104 2.45
yy
0.
6.021 105 -
zz
2. 104 1.9998
104
0.01
xy
0.
1.280 108 -
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
20/36
19 Modeling
I
19.1 Characteristics of modeling
Elements axis (TRIA6 + QUAD8)
Center cylinder
Node blocked out of Dy
y
E
F
0.01m
C
D
X
With
B
Face with imposed pressure
Limiting conditions:
Node F blocked out of Dy
pressure on AE p = 60.
Names of the nodes:
With = 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
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “AXIS” ALL
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
POST_RELEVE “EXTRACTION”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
21/36
20 Results of modeling I
20.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.9000
105 0.00
v
0. -
-
xx
60.
59.8976
0.17
yy
0.
0.0024
-
zz
100. 99.9089
0.09
xy
0.
0.0137
-
xx
4.5 104
4.493 104
0.14
yy
0.
6.003 105 -
zz
5.9 104 5.894
104
0.10
xy
0.
8.895 108 -
B U
4
105 4.0000
105 0.00
v
0. -
-
xx 0.
0.0308
-
yy
0.
0.0020
-
zz
40. 39.9738
0.07
xy
0. 0.0131 -
xx
0.6 104
0.598 104
0.33
yy
0.
6.002 105 -
zz
2. 104 1.998
104
0.09
xy
0. 8.495
108 -
E U
5.9
105 5.9000
105 0.00
v
0. -
-
xx
60.
59.8976
0.17
yy
0.
0.0024
-
zz
100. 99.9089
0.09
xy
0. 0.0137 -
xx
4.5 104
4.493 104
0.14
yy
0.
6.003 105 -
zz
5.9 104 5.894
104
0.10
xy
0. 8.895
108 -
F U
4
105 4.0000
105 0.00
v
0. -
-
xx 0.
0.0308
-
yy
0.
0.0020
-
zz
40. 39.9738
0.07
xy
0.
0.0131
-
xx
0.6 104
0.598 104
0.33
yy
0.
6.002 105 -
zz
2. 104 1.998
104
0.09
xy
0.
8.495 108 -
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
22/36
21 Modeling
J
21.1 Characteristics of modeling
Elements axis (QUAD9)
Center cylinder
Node blocked out of Dy
y
E
F
0.01m
C
D
X
With
B
Face with imposed pressure
Limiting conditions:
node F blocked out of Dy
pressure on AE p = 60.
Names of the nodes:
With = 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
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “AXIS” ALL
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
POST_RELEVE “EXTRACTION”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
23/36
22 Results of modeling J
22.1 Values
tested
Localization Size Reference
Aster %
difference
With U
5.9
105 5.9000
105 0.00
v
0.
-
-
xx
60.
59.8997
0.17
yy
0.
0.0035
-
zz
100. 99.9080
0.09
xy
0.
0.0141
-
xx
4.5 104
4.494 104
0.14
yy
0.
6.003 105 -
zz
5.9 104 5.894
104
0.10
xy
0.
9.156 108 -
B U
4.
105 4.0000
105 0.00
v
0.
-
-
xx 0.
0.0070
-
yy
0.
0.0001
-
zz
40. 39.9936
0.02
xy
0. 0.0010 -
xx
0.6 104
0.5996 104
0.07
yy
0.
6.000 105 -
zz
2. 104 1.9996
104
0.02
xy
0. 6.748
109 -
E U
5.9
105 5.9000
105 0.00
v
0.
-
-
xx
60.
59.8997
0.17
yy
0.
0.0035
-
zz
100. 99.9080
0.09
xy
0. 0.0141 -
xx
4.5 104
4.494 104
0.14
yy
0.
6.003 105 -
zz
5.9 104 5.894
104
0.10
xy
0.
9.156 108 -
F U
4.
105 4.0000
105 0.00
v
0.
-
-
xx 0. 0.0070
-
yy
0.
0.0001
-
zz
40. 39.9936
0.02
xy
0.
0.0010
-
xx
0.6 104
0.5996 104
0.07
yy
0.
6.000 105 -
zz
2. 104 1.9996
104
0.02
xy
0.
6.748 109 -
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
24/36
23 Modeling
K
23.1 Characteristics of modeling
Elements 3D (PENTA6 and HEXA8)
Grid obtained by extrusion starting from the grid 2D below (modeling E)
F
Normally blocked face
y
E
G
45°
H
With
B
X
Face with displacement
radial imposed
Face blocked out of Dy
Along axis Z:
2 layers of elements
Total thickness:
0.01
Limiting conditions:
node F: uz = 0
face AB blocked out of Dy
normally blocked face EFF
face AE
radial displacement imposed on 5.9 E-5 m
Names of the nodes:
With = No1
C = No36
D = No166
plan Z = 0.005
A2 = No172
C2 = No242
D2 = No5025
plan Z = 0.01
A3 = No173
C3 = No243
D3 = No503
Names of the nodes:
E = No41
H = No9
G = No38
plan Z = 0.005
E2 = No252
H2 = No188
G2 = No246
plan Z = 0.01
E3 = No253
H3 = No189
G3 = No247
23.2 Characteristics of the grid
A number of nodes: 513
A number of meshs and types: 400 PENTA6, 100 HEXA8 40 QUAD4 (faces skin interns)
23.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_NO “REAC_NODA”
MODI_MAILLAGE ORIE_PEAU_3D
23.4 Remarks
The loading is here in imposed displacement, contrary to other modelings. They are tested
reactions.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
25/36
24 Results of modeling K
24.1 Values
tested
Localization Size Reference
Aster %
difference
C Fx
1.0884 E3 1.0953 E3 0.64
Fy
4.5084 E4 4.5836 E4 1.67
C2 Fx
2.1768 E3 2.1571 E3
0.91
Fy
9.0170 E4 9.1304 E4 1.26
C3 Fx
1.0884 E3 1.0953
E3 0.64
Fy
4.5084 E4 4.5836 E4 1.67
H Fx
1.1636 E3 1.1709
E3 0.63
Fy
1.8429 E4 1.8527
E4 0.53
G Fx
1.0045 E3 1.0144
E3 0.99
Fy
6.1550 E4 6.2117
E4 0.92
H2 Fx
2.3272 E3 2.3173
E3
0.43
Fy
3.6858 E4 3.6669 E4
0.51
G2 Fx
2.0090 E3 1.9951
E3
0.69
Fy
1.2310 E3 1.2214
E3
0.78
24.2 Remarks
One checks that the nodal forces of reactions are null in all the nodes, except on the nodes of
surface AE and surfaces EFF and AB.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
26/36
25 Modeling
L
25.1 Characteristics of modeling
Elements 3D (PYRAM5)
F
Normally blocked face
y
E
D
C
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Along axis Z:
each parallélipipède is cut out in 6 pyramids
Total thickness:
0.01
Limiting conditions:
node F: uz = 0
face AB blocked out of Dy
normally blocked face EFF
pressure on face AE
p = 60.
Names of the nodes:
With = N267
B = N142
E = N29
F = N1
25.2 Characteristics of the grid
A number of nodes: 342
A number of meshs and types: 600 PYRAM5 620 QUAD4 (faces skin interns)
25.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
“EPSI_ELNO_DEPL”
“SIEF_ELGA_DEPL”
“ENDO_ELNO_SIGM”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
27/36
26 Results of modeling L
26.1 Values
tested
Identification Reference Aster %
difference
U-node (A)
5.9 105 5.8873
105
0.21
v-node (A)
0.
eps
-
xx - node (A)
60.
52.9567
11.74
yy - node (A)
100. 91.7830
8.22
zz - node (A)
0.
1.1206 -
xy - node (A)
0.
4.5121 -
xx - node (A)
4.5 104
4.008 104
10.94
yy - node (A)
5.9 104 5.400
104
8.47
xy - node (A)
0.
2.933 105 -
U-node (B)
4. 105 3.9936
105
0.16
v-node (B)
0.
eps
-
xx - node (B)
0.
0.7670
-
yy - node (B)
40. 39.5319
1.17
zz - node (B)
0.
0.3115 -
xy - node (B)
0.
1.5858 -
xx - node (B)
0.6 104
0.627 104 4.44
yy - node (B)
2. 104 1.993
104
0.36
xy - node (B)
0.
1.031 105 -
U-node (E)
4.17193 105 4.16293
105
0.21
v-node (E)
4.17193 105 4.16293
105
0.21
xx - node (E)
20.
19.3586
3.21
yy - node (E)
20. 31.5151
57.57
zz - node (E)
0. 2.5686
-
xy - node (E)
80.
77.2309
3.46
xx - node (E)
0.7 104 0.457
104
34.76
yy - node (E)
0.7 104 1.247
104 78.12
xy - node (E)
5.2 104
5.020 104
3.46
U-node (F)
2.82843 105 2.82393
105
0.16
v-node (F)
2.82843 105 2.82393
105
0.16
xx - node (F)
20.
18.9523
5.24
yy - node (F)
20. 20.9510
4.75
zz - node (F)
0. 0.0035
-
xy - node (F)
20.
20.9897
4.95
xx - node (F)
0.7 104 0.633
104
9.60
yy - node (F)
0.7 104 0.763
104 8.96
xy - node (F)
1.3 104
1.364 104 4.95
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
28/36
27 Modeling
M
27.1 Characteristics of modeling
Elements 3D (PYRAM13)
F
Normally blocked face
y
E
D
C
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Along axis Z:
each parallélipipède is cut out in 6 pyramids
Total thickness:
0.01
Limiting conditions:
node F: uz = 0
face AB blocked out of Dy
normally blocked face EFF
pressure on face AE
p = 60.
Names of the nodes:
With = N1403
B = N734
E = N152
F = N4
27.2 Characteristics of the grid
A number of nodes: 1703
A number of meshs and types: 600 PYRAM13 620 QUAD8 (faces skin interns)
27.3 Functionalities
tested
Commands
MODI_MAILLAGE ORIE_PEAU_3D
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_CHAM_ELEM “SIGM_ELNO_DEPL”
“EPSI_ELNO_DEPL”
“SIEF_ELGA_DEPL”
“ENDO_ELNO_SIGM”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
29/36
28 Results of modeling M
28.1 Values
tested
Identification Reference Aster %
difference
U-node (A)
5.9 105 5.8999
105
0.002
v-node (A)
0.
eps
-
xx - node (A)
60.
59.9880
0.02
yy - node (A)
100. 100.1277 0.13
zz - node (A)
0. 0.0425
-
xy - node (A)
0.
0.0913 -
xx - node (A)
4.5 104
4.502 104 0.04
yy - node (A)
5.9 104 5.906
104 0.09
xy - node (A)
0.
5.934 107 -
U-node (B)
4. 105 4.0000
105 0.00
v-node (B)
0.
eps
-
xx - node (B)
0.
0.0276
-
yy - node (B)
40. 40.0331
0.08
zz - node (B)
0. 0.0024
-
xy - node (B)
0. 0.0126
-
xx - node (B)
0.6 104
0.602 104 0.32
yy - node (B)
2. 104 2.002
104 0.10
xy - node (B)
0. 8.177
108 -
U-node (E)
4.17193 105 4.17183
105
0.002
v-node (E)
4.17193 105 4.17183
105
0.002
xx - node (E)
20.
19.9787
- 0.11
yy - node (E)
20. 20.1612
0.81
zz - node (E)
0. 0.0425
-
xy - node (E)
80.
80.0580
0.07
xx - node (E)
0.7 104 0.696
104
0.59
yy - node (E)
0.7 104 0.708
104 1.11
xy - node (E)
5.2 104
5.204 104 0.07
U-node (F)
2.82843 105 2.82844
105 0.00
v-node (F)
2.82843 105 2.82844
105 0.00
xx - node (F)
20.
20.0224
0.11
yy - node (F)
20. 19.9901
0.05
zz - node (F)
0. 0.0031
-
xy - node (F)
20.
19.9818
0.09
xx - node (F)
0.7 104 0.701
105 0.17
yy - node (F)
0.7 104 0.699
105
0.13
xy - node (F)
1.3 104
1.299 105
0.09
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
30/36
29 Modeling
NR
29.1 Characteristics of modeling
Elements 3D (PENTA15 and HEXA20)
Grid obtained by extrusion starting from a grid 2D resembling the grid below
(8 elements in the radial direction, 4+4 elements in the circumferential direction) and duplicated for
to have a complete section of the cylinder (on 360°).
F
Normally blocked face
y
E
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Along axis Z:
1 layer of elements
Total thickness:
0.01
Limiting conditions:
face AB blocked out of Dy
normally blocked face EFF
pressure on face AE
p = 60.
basic effect on the sections p = 60.
Names of the nodes:
With = N5349
B = N6092
C = N433
D = N441
E = N2180
F = N1632
29.2 Characteristics of the grid
A number of nodes: 8832
A number of meshs and types: 1024 PENTA15, 512 HEXA20, 1176 QUAD8 and 2048 TRIA6.
29.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
EFFE_FOND
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
29.4 Remarks
Contrary to preceding modelings, one takes into account the basic effect here applying to
sections at the ends of the cylinder.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
31/36
30 Results of modeling NR
30.1 Values
tested
Identification Reference Aster %
difference
U-node (A)
5.6 105 5.6000
10-5
0.00
v-node (A)
0.
eps
-
xx - node (A)
60.
- 59.5972
0.67
yy - node (A)
100. 99.5187
0.48
zz - node (A)
20. 19.9584
0.21
xy - node (A)
0. eps
-
U-node (B)
3.4 105 3.4000
10-5
0.00
v-node (B)
0.
eps
-
xx - node (B)
0.
2.0877 10-2
-
yy - node (B)
40. 39.9685
0.08
zz - node (B)
20. 19.9946
0.03
xy - node (B)
0. eps
-
xx - node (E)
20.
20.3287
1.64
yy - node (E)
20. 20.3287
1.64
zz - node (E)
20. 20.1739
0.87
xy - node (E)
80. - 79.9775
0.03
xx - node (F)
20.
20.0176
0.09
yy - node (F)
20. 20.0176
0.09
zz - node (F)
20. 20.0072
0.04
xy - node (F)
20. - 20.0027 0.01
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
32/36
31 Modeling
O
31.1 Characteristics of modeling
C_plan elements (QUAD8 + TRIA6)
Grid 2D resembling the grid below (8 elements in the radial direction, 4+4 elements
in the circumferential direction) and duplicated to have a complete section of the cylinder (on 360°).
y
B
D
Face blocked in dx
F
With
Normally blocked face
C
E
Face with imposed pressure
45°
X
Limiting conditions:
side AB blocked in dx
normally blocked side EFF
pressure on AE p = 60.
Names of the nodes:
With = N249
B = N992
C = N1667
D = N1588
E = N3776
F = N3228
31.2 Characteristics of the grid
A number of nodes: 3840
A number of meshs and types: 1026 TRIA6, 512 QUAD8
31.3 Functionalities
tested
Commands
MODI_MAILLAGE ORIE_PEAU_2D
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “C_PLAN”
TOUT
DEFI_MATERIAU ELAS
CALC_ELEM “SIEF_ELGA_DEPL”
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
33/36
32 Results of modeling O
32.1 Values
tested
Identification Reference Aster %
difference
U-node (A)
5.9 105 5.8999
10-5
0.002
v-node (A)
0.
eps
-
xx - node (A)
60.
- 59.5340
0.78
yy - node (A)
100. 99.5453
0.45
zz - node (A)
0. 0.
-
xy - node (A)
0. eps
-
U-node (B)
4. 105 3.99996
10-5
0.00
v-node (B)
0.
0.
-
xx - node (B)
0.
2.6874 10-2
-
yy - node (B)
40. 39.9716
0.07
zz - node (B)
0. 0.
-
xy - node (B)
0. eps
-
U-node (E)
4.17193 105 4.17215
10-5
0.005
v-node (E)
4.17193 105 4.17215
10-5
0.005
xx - node (E)
20.
20.2875
1.44
yy - node (E)
20. 20.2875
1.44
zz - node (E)
0. 0.
-
xy - node (E)
80. - 79.9196
0.10
U-node (F)
2.82843 105 2.82841
10-5
0.001
v-node (F)
2.82843 105 2.82841
10-5
0.001
xx - node (F)
20.
20.0167
0.08
yy - node (F)
20. 20.0167
0.08
zz - node (F)
0. 0.
-
xy - node (F)
20. - 19.9993
0.004
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
34/36
33 Modeling
P
33.1 Characteristics of modeling
Elements 3D (PENTA15 and HEXA20) even grid that modeling NR
Grid obtained by extrusion starting from a grid 2D resembling the grid below
(8 elements in the radial direction, 4+4 elements in the circumferential direction) and duplicated for
to have a complete section of the cylinder (on 360°).
F
Normally blocked face
y
E
45°
With
B
X
Face with imposed pressure
Face blocked out of Dy
Along axis Z:
1 layer of elements
Total thickness:
0.01
Limiting conditions:
normally blocked face EFF
face AB blocked out of Dy
pressure on face AE
FP
basic effect on sections FP
With FP: linear pressure function of time being worth 60. to t=1s and 120. with t=2s
Names of the nodes:
With = N5349
B = N6092
C = N433
D = N441
E = N2180
F = N1632
33.2 Characteristics of the grid
A number of nodes: 8832
A number of meshs and types: 1024 PENTA15, 512 HEXA20, 1176 QUAD8 and 2048 TRIA6.
33.3 Functionalities
tested
Commands
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FACE_IMPO
GROUP_MA
DNOR
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA
EFFE_FOND
“MECHANICAL” AFFE_MODELE “3D”
TOUT
DEFI_MATERIAU ELAS
CALC_NO “EPSI_NOEU_DEPL”
“SIGM_NOEU_DEPL”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
35/36
33.4 Remarks
Contrary to modeling NR, one tests here a basic pressure and effect variables in function
time. A linear variation of the pressure involves a linear variation of the constraints.
34 Results of modeling P
34.1 Values
tested
Identification Reference Aster %
difference
U-node (A) with t=1. S
5.6 105 5.6000
10-5
0.00
v-node (A) with t=1. S
0.
eps
-
xx - node (A) with t=1. S
60.
- 59.5414
0.76
yy - node (A) with t=1. S
100. 99.6183
0.38
zz - node (A) with t=1. S
20. 19.9976
0.01
xy - node (A) with t=1. S
0. eps
-
xx - node (A) with t=2. S
120.
- 119.0829
0.76
yy - node (A) with t=2. S
200. 199.2366
0.38
zz - node (A) with t=2. S
40. 39.9952
0.01
xy - node (A) with t=2. S
0. eps
-
U-node (B) with t=1. S
3.4 105 3.4000
10-5
0.00
v-node (B) with t=1. S
0.
eps
-
xx - node (B) with t=1. S
0.
2.6761 10-2
-
yy - node (B) with t=1. S
40. 39.9740
0.06
zz - node (B) with t=1. S
20. 19.9973
0.01
xy - node (B) with t=1. S
0. eps
-
xx - node (B) with t=2. S
0.
5.3523 10-2
-
yy - node (B) with t=2. S
80. 79.9480
0.06
zz - node (B) with t=2. S
40. 39.9946
0.01
xy - node (B) with t=2. S
0. eps
-
xx - node (E) with t=1. S
20.
20.3287
1.64
yy - node (E) with t=1. S
20. 20.3287 1.64
zz - node (E) with t=1. S
20. 20.1739 0.87
xy - node (E) with t=1. S
80. - 79.9775
0.03
xx - node (E) with t=2. S
40.
40.6575
1.64
yy - node (E) with t=2. S
40. 40.6575 1.64
zz - node (E) with t=2. S
40. 40.3479 0.87
xy - node (E) with t=2. S
160. - 159.9550
0.03
xx - node (F) with t=1. S
20.
20.0176
0.09
yy - node (F) with t=1. S
20. 20.0176 0.09
zz - node (F) with t=1. S
20. 20.0072 0.04
xy - node (F) with t=1. S
20. 20.0027 0.01
xx - node (F) with t=2. S
20.
40.0351
0.09
yy - node (F) with t=2. S
20. 40.0351 0.09
zz - node (F) with t=2. S
0. 40.0144 0.04
xy - node (F) with t=2. S
20. 40.0054 0.01
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
6.4
Titrate:
SSLV04 - Hollow Cylindre in plane constraints
Date:
17/06/03
Author (S):
X. DESROCHES, P. Key HERMANN
:
V3.04.004-E Page:
36/36
35 Summary of the results
Summary of the errors max in %
3D
Localization MOD A MOD B MOD C MOD D MOD L MOD M MOD NR MOD P
elem pe6, h8
pe15, h20
te4 te10 py5 py13
pe15, h20 pe15, h20
geom
45° 45° 45° 45° 45° 45° 360° 360°
Nb
1922 2115 1115 1395 342 1703 8832 8832
No
Dépl. With,
E 0.08
0.09
0.17
0.04
0.21
0.00
0.00
0.00
B, F
0.10
0.07
0.30
0.04
0.16
0.00
0.00
0.00
xx A,
E 4.59
0.39
10.45
4.41
11.74
0.11
1.64
1.64
B, F
5.24
0.07
7.78
0.95
5.24
0.11
0.09
0.09
yy
WITH, E
5.70
0.92
9.46
1.80
57.57
0.81
1.64
1.64
B, F
1.89
0.01
2.46
0.49
4.75
0.08
0.09
0.09
zz
WITH, E
Good
Good
Good
Good
Good
Good
0.87
0.87
B, F
Good
Good
Good
Good
Good
Good
0.04
0.04
xy
WITH, E
0.15
0.26
2.89
0.27
3.46
0.07
0.03
0.03
B, F
0.90
0.06
0.81
0.28
4.95
0.09
0.01
0.01
C_plan
Localization
MOD E
MOD F
MOD G
MOD O
Type of elements
tria3, quad4
tria6, quad8
quad9
tria6, quad8
Modelled geometry
45° 45° 45°
360°
A number of nodes
961
591
441
384
Displacements A,
E
0.07
0.09
0.00
0.01
B, F
0.09
0.07
0.00
0.00
Constraints
4.65
0.39
0.27
1.44
xx
WITH, E
B, F
5.19
0.06
0.02
0.08
Constraints
WITH, E
5.68
0.90
0.16
1.44
yy
B, F
1.40
0.04
0.05
0.08
Constraints
WITH, E
Good
Good
Good
Good
zz
B, F
Good
Good
Good
Good
Constraints
WITH, E
0.16
0.23
0.20
0.10
xy
B, F
1.23
0.07
0.09
0.00
Axis
Localization
MOD H
MOD I
MOD J
Type of elements
tria3, quad4
tria6, quad8
quad9
A number of nodes
113
175
205
Displacements A,
E
0.01
0.00
0.00
B, F
0.01
0.00
0.00
Constraints
5.66
0.17
0.17
xx
WITH, E
B, F
Good
Good
Good
Constraints
WITH, E
Good
Good
Good
yy
B, F
Good
Good
Good
Constraints
WITH, E
1.29
0.09
0.09
zz
B, F
1.00
0.07
0.02
Constraints
WITH, E
Good
Good
Good
xy
B, F
Good
Good
Good
· The results are more precise with elements of command 2.
· The problem is adapted more to an axisymmetric modeling. The results are better.
· The grids remain insufficient for the elements 3D of command 1: constraints and deformations
modelings A, C, E and L (especially for modeling L in PYRAM5).
· The pyramids give results similar to the other elements 3D, with equivalent grid.
· Modelings NR and P with basic effect and pressure constant or variables give of good
results.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/03/008/A
Outline document