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
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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