Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
1/12
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.100
SSLV100 - Hollow Cylindre in plane deformations
Summary:
This test makes it possible to validate the elements of plane deformation on the following functionalities:
· pressure distributed,
· stamp rigidity,
· imposed displacements:
- by
ddl,
-
by face of element.
It includes/understands 4 modelings.
The 3 first correspond to elements of the different type (linear and quadratic).
The last validates the displacements imposed by face (blocking of the normal component).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
2/12
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
Properties of materials
E = 2.105 Mpa
= 0.3
1.3
Boundary conditions and loadings
Internal pressure: P = 60. MPa
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
3/12
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical
2

has
=
zz
2 P b2 - a2
2

2

has
B
=
1

rr
P b2 - a2 R

2
2

2

has
B

= P
1+

b2 - a2
R

2
=
R
0
P
a2

b2
U
=
(1+ 1 - 2 +
R
) (
)
R
E b2 - a2

R

2
One obtains:
- 5
5
-
for R = 0 1
.
U = 5.72 10
for R = 0.2
U = 3.64 10
R
R
= 60.
-
= 0.
rr
rr
= 100.
= 40.
= 12.
= 12.
zz
zz
= 0.
= 0.
R
R
Passage in the system of Cartesian axes:

=
cos2
+
sin2
-
xx
rr

2 R sin cos

=
sin2
+
cos2
+
yy
rr

2 R sin cos

=
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
Displacements (U, v) and forced (xx, yy
, zz
, xy
) at the points A, B, C, D, E, F.
2.3 References
bibliographical
[1]
Y.C. FUNG. Fundations off solid mechanics. Prentice-hall, Inc. Englewood Cliffs. NJ. 1965
p. 243 to 245.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
4/12
3 Modeling
With
3.1
Characteristics of modeling: D-plan (QUAD4 + TRIA3)
F
Normally blocked face
y
D
Face with imposed pressure
E
C
45°
X
With
B
Face blocked out of Dy
Limiting conditions:
side AB
DDL_IMPO: (GROUP_NO:bordAB
DY: 0. )
side EFF
FACE_IMPO: (GROUP_MA:faceEF
DNOR: 0. )
pressure on face AE
PRES_REP: (GROUP_MA:faceAE
PRES: 60. )
Names of the nodes:
With = N23
B = N1
C = N391
D = N369
E = N451
F = 751
3.2
Characteristics of the grid
A number of nodes: 759
A number of meshs and types: 704 TRIA3, 352 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_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
POST_RELEVE
CHAM_GD
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
5/12
4
Results of modeling A
4.1 Values
tested
Place
Size
Reference
Aster
% difference
tolerance
With
U
5.72 10­5
5.7155 10­5
­ 0.08
10­2
v
0.
eps
-
xx
­ 60.
­ 56.3770
­ 6.04
yy
100.
96.3917
­ 3.61
zz
12.
12.0044
0.04
xy
0.
­ 0.9563
­
C
U
5.28459 10­5
5.2832 10­5
­ 0.03
10­2
v
2.18895 10­5
2.1777 10­5
­ 0.51
xx
­ 36.56854
­ 33.5312
­ 8.31
yy
76.56854
76.9335
0.48
zz
12.
13.0207
8.51
xy
­ 56.56854
­ 53.7445
­ 4.99
E
U
4.04465 10­5
4.0400 10­5
­ 0.11
10­2
v
4.04465 10­5
4.0400 10­5
­ 0.11
xx
20.
23.4926
17.46
yy
20.
25.4141
27.07
zz
12.
14.6720
22.27
xy
­ 80.
­ 78.3081
­ 2.11
B
U
3.640 10­5
3.6405 10­5
0.01
10­2
v
0.
eps
-
xx
0.
­ 0.4064
-
yy
40.
39.8759
­ 0.31
zz
12.
11.8408
­ 1.33
xy
0.
­ 0.4447
­
D
U
3.36292 10­5
3.3603 10­5
­ 0.08
10­2
v
1.39297 10­5
1.3945 10­5
0.11
xx
5.85786
5.2229
­ 10.84
yy
34.14214
33.8961
­ 0.72
zz
12.
11.7357
­ 2.20
xy
­ 14.14214
­ 14.1755
0.24
F
U
2.57387 10­5
2.5710 10­5
­ 0.11
10­2
v
2.57387 10­5
2.5710 10­5
­ 0.11
xx
20.
19.1238
­ 4.38
yy
20.
19.6156
­ 1.92
zz
12.
11.6218
­ 3.15
xy
­ 20.
­ 20.1797
0.90
4.2 Remarks
The increase in the error, when one passes from AB to CD then EFF, is ascribable with the grid (density in
elements QUAD4 lower than that in TRIA3).
4.3 Parameters
of execution
Version: 3.03.32
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
8.54 seconds
5 Modeling
B
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
6/12
5.1
Characteristics of modeling: D-plan (QUAD8 + TRIA6)
y
B
D
Face blocked in dx
F
With
Normally blocked face
C
Face with imposed pressure
E
45°
X
Limiting conditions:
side AB
DDL_IMPO: (GROUP_NO:bordAB
DY: 0. )
side EFF
FACE_IMPO: (GROUP_MA:faceEF
DNOR: 0. )
pressure on AE
PRES_REP: (GROUP_MA:faceAE
PRES: 60. )
Names of the nodes:
With = N2
B = N48
C = N401
D = N424
E = N606
F = N494
5.2
Characteristics of the grid
A number of nodes: 729
A number of meshs and types: 192 TRIA6, 96 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_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
POST_RELEVE
CHAM_GD
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
7/12
6
Results of modeling B
6.1 Values
tested
Place
Size
Reference
Aster
% difference
tolerance
With
U
0.
eps
-
10­2
v
5.72 10­5
5.7155 10­5
­ 0.04
xx
100.
99.7100
­ 0.29
yy
­ 60.
­ 59.7725
­ 0.38
zz
12.
11.9813
­ 0.16
xy
0.
0.2643
-
C
U
­ 2.18895 10­5
­ 2.1881 10­5
­ 0.04
10­2
v
5.28459 10­5
5.2826 10­5
­ 0.04
xx
76.56854
76.7005
0.17
yy
­ 36.56854
­ 36.4500
­ 0.32
zz
12.
12.0751
0.63
xy
­ 56.56854
56.2844
­ 0.50
E
U
­ 4.04465 10­5
­ 4.0432 10­5
­ 0.04
10­2
v
4.04465 10­5
4.0432 10­5
­ 0.04
xx
20.
20.0083
4.10­4
yy
20.
19.9988
­ 6.10­5
zz
12.
12.0021
2.10­4
xy
80.
79.8176
­ 0.23
B
U
0.
eps
-
10­2
v
3.640 10­5
3.6390 10­5
­ 0.03
xx
40.
39.9924
­ 0.02
yy
0.
­ 0.001338
-
zz
12.
11.9973
­ 0.02
xy
0.
­ 0.04083
-
D
U
­ 1.39297 10­5
­ 1.3926 10­5
­ 0.03
10­2
v
3.36292 10­5
3.3619 10­5
­ 0.03
xx
34.14214
34.1361
­ 0.02
yy
5.85786
5.8948
0.63
zz
12.
12.0093
0.08
xy
14.14214
14.1596
0.12
F
U
­ 2.57387 10­5
­ 2.5731 10­5
­ 0.03
10­2
v
2.57387 10­5
2.5731 10­5
­ 0.03
xx
20.
20.0000
3.10­6
yy
20.
19.9996
­ 2.10­5
zz
12.
11.9999
­ 7.10­6
xy
20.
19.9975
­ 1.10­4
6.2 Remarks
The evolution of the error induced by the grid according to AB, CD or EFF, is clearly attenuated by report/ratio
with modeling A.
6.3 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
6.11 seconds
7 Modeling
C
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
8/12
7.1
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:bordAB DY: 0. )
side EFF
FACE_IMPO: (GROUP_MA:faceEF DNOR: 0. )
pressure on AE
PRES_REP: (GROUP_MA:faceAE PRES: 60. )
Names of the nodes:
With = N1
B = N47
C = N351
D = N374
E = N569
F = N423
7.2
Characteristics of the grid
A number of nodes: 725
A number of meshs and types: 168 QUAD9
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_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
POST_RELEVE
CHAM_GD
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
9/12
8
Results of modeling C
8.1 Values
tested
Place
Size
Reference
Aster
% difference
tolerance
With
U
5.72 10­5
5.7173 10­5
­ 0.05
10­2
v
0.
eps
-
xx
­ 60.
­ 56.8334
­ 0.27
yy
100.
99.84
­ 0.16
zz
12.
12.0023
0.02
xy
0.
­ 0.00272
-
C
U
5.28459 10­5
5.2821 10­5
­ 0.05
10­2
v
2.18895 10­5
2.1879 10­5
­ 0.05
xx
­ 36.56854
­ 36.45
0.32
yy
76.56854
76.46
­ 0.14
zz
12.
12.003
0.02
xy
­ 56.56854
­ 56.45
0.2
E
U
4.04465 10­5
4.0427 10­5
­ 0.05
10­2
v
4.04465 10­5
4.0427 10­5
­ 0.05
xx
20.
19.996
­ 2. 10­4
yy
20.
20.011
5.5 10­4
zz
12.
12.002
2. 10­4
xy
­ 80.
­ 79.837
0.2
B
U
3.640 10­5
3.6386 10­5
0.04
10­2
v
0.
eps
-
xx
0.
­ 2.7 10­3
-
yy
40.
40.0011
­ 4. 10­4
zz
12.
11.9995
­ 4. 10­4
xy
0.
­ 4.8 10­4
-
D
U
3.36292 10­5
3.3617 10­5
­ 0.04
10­2
v
1.39297 10­5
1.3924 10­5
­ 0.04
xx
5.85786
5.8557
­ 0.03
yy
34.14214
34.143
2.5 10­5
zz
12.
11.9996
3. 10­5
xy
­ 14.14214
­ 14.1435
­ 1. 10­4
F
U
2.57387 10­5
2.5729 10­5
­ 0.04
10­2
v
2.57387 10­5
2.5729 10­5
­ 0.04
xx
20.
19.999
­ 3. 10­5
yy
20.
20.0002
1. 10­5
zz
12.
11.9999
­ 9. 10­6
xy
­ 20.
­ 20.0025
­ 0.01
8.2 Remarks
The evolution of the error induced by the grid according to AB, CD or EFF, is clearly attenuated by report/ratio
with modeling A.
8.3 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
5.67 seconds
9 Modeling
D
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
10/12
9.1
Characteristics of modeling: D-plan (QUAD4 + TRIA3)
F
Normally blocked face
y
E
D
G
Face with displacement
normal imposed
C
H
45°
X
With
B
Face blocked out of Dy
Limiting conditions:
side AB
DDL_IMPO: (GROUP_NO:bordAB DY: 0. )
side EFF
FACE_IMPO: (GROUP_MA:faceEF DNOR: 0. )
on AE
normal displacement imposed on 5.72 E-5m
FACE_IMPO: (GROUP_MA:faceAE DNOR: - 5.72 E-5)
Names of the nodes:
With = N23
B = N1
C = N391
D = N369
E = N451
F = N751
H = N92
G = N447
9.2
Characteristics of the grid
A number of nodes: 759
A number of meshs and types: 704 TRIA3, 352 QUAD4
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_MODELE
“MECANIQUE”
“D_PLAN”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
[U4.61.01]
POST_RELEVE
CHAM_GD
“EXTRACTION”
[U4.74.03]
CALC_NO
“REAC_NODA”
[U4.61.03]
10
Results of modeling D
10.1 Values
tested
Localization
Size
Reference
Aster
% difference
C
Fx
0.1360
0.14069
3.45
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
11/12
Fy
0.056
0.05827
4.06
H
Fx
0.14686
0.13608
7.34
Fy
0.0108
0.0100
7.04
G
Fx
0.1138
0.114
0.19
Fy
0.093
0.0936
0.61
10.2 Remarks
One checks that the nodal forces of reaction are null in all the nodes, except on the nodes of
line AE, EFF and AB.
10.3 Parameters
of execution
Version: 2.03.04
Machine: CRAY C90
System:
UNICOS 6.0
Obstruction memory:
6 megawords
Time CPU To use:
10.17 seconds
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
3
Titrate:
SSLV100 hollow Cylindre in plane deformations
Date:
24/08/99
Author (S):
X. DESROCHES
Key:
V3.04.100-D Page:
12/12
11
Summary of the results
D_plan
modeling
Summary of the errors
With
B
C
max in %
Displacements
WITH, B
0.08
0.04
0.05
C, D
0.51
0.04
0.05
E, F
0.11
0.04
0.05
Constraints
WITH, B
6.04
0.29
0.27

C, D
10.84
0.17
0.32
xx
E, F
17.46
4.10­4
2.10­4
Constraints
WITH, B
3.61
0.38
0.16

C, D
0.72
0.63
0.14
yy
E, F
27.07
2.10­5
5.5.10­4
Constraints
WITH, B
1.33
0.16
0.02

C, D
8.51
0.63
0.02
zz
E, F
22.27
2.10­4
2.10­4
Constraints
WITH, B
-
-
-

C, D
4.99
0.50
0.2
xy
E, F
2.11
0.23
0.2
These 3 modelings appreciably have the same number of nodes; results obtained with
elements of command 1 (modeling A in Tria3 and Quad4) are definitely less precise, in particular on
internal wall.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A