Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
1/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.307
SSLV307 - Cylinder obliques under load
axial uniform
Summary:
The purpose of the test is to validate the various types of linear relations, defined by the key words
LIAISON_DDL
,
LIAISON_OBLIQUE
,
LIAISON_GROUP
.
It also makes it possible to test the option “symmetries cyclic” starting from the modeling of a sector of the cylinder.
The analysis is carried out in 3D.
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
2/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Average radius: R
O
= 1 m
Thickness:
H = 0.02 m
Height:
L = 4 m
Cosine Directors of the axis of the cylinder: (0.0, 0,5,
2
3
)
Center local X parallel with the total axis X.
1.2
Material properties
E = 2.1 X 10
11
AP
v = 0.3
1.3
Boundary conditions and loadings
·
Axial displacement no one at the low end (W = 0)
For the other boundary conditions (linear relations), to see paragraph [§3].
·
Uniform axial loading per unit of length Q = 10000 NR/m, applied at the high end.
1.4 Conditions
initial
Without object for the static analysis.
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
3/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
·
Radial displacement in local reference mark
(
)
Z
y
X
,
,
:
Eh
qvRo
U
R
=
= -
2
/
1
2
2
5
.
0
2
3
-
+
W
V
U
where
W
V
U
,
,
= component of displacement in the total reference mark
(
)
Z
Y
X
,
,
.
·
If
11
,
=
zz
yy
xx
are the stresses in the local reference mark, the stresses expressed in
the total reference mark are worth:
11
11
11
11
4
3
4
3
4
/
3
4
/
1
/
4
/
1
4
/
3
+
-
=
+
=
=
+
=
=
yy
yz
yy
zz
yy
xx
xx
H
Q
In the local plan
()
0
,
,
=
yy
Z
X
(circumferential stress),
from where
11
11
4
/
3
,
4
/
1
=
zz
yy
2.2
Results of reference
·
Raidal displacement:
R
U
= 7.14 X 10
7
m
·
In the local plan
()
=
yy
Z
X
,
,
1.25 X 10
5
AP,
zz
= 3.75 X 10
5
AP
2.3
Uncertainty on the solution
·
Analytical solution
2.4 References
bibliographical
[1]
R.J. ROARK and W.C. YOUNG: Formulated for stress and strain, 5
E
edition. New York,
Mc Graw-Hill, 1975
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
4/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (PENTA15 + HEXA20)
Modeling:
1/4 of the cylinder following the circumference
2 areas:
area 1 = left lower
(0
Z
L/2)
area 2 = left higher (L/2
Z
L)
Cutting:
20 elements according to the length
16 elements according to the circumference
2 elements in the thickness
Co-ordinates of the points (R,
, Z)
WITH G B E
G1
F
A2
A'2
H
H'
B2
B'2
E2
E'2
H1
H'1
F2
F'2
A3 I B 3E3 I1 F3
R IH R Re IH R Re IH R Re IH R Re IH R Re IH R Re
0. 0. 0. 90. 90. 90. 0. 0 .0. 90. 90. 90. 0. 0. 0. 90. 90. 90.
Z 0. 0. 0. 0. 0. 0. L/2 L/2
L/2
L/2
L/2
L/2 L L L L L L
IH = interior radius
Re = external radius
the points A2, H, B2, E2, H2, F2 are in the section Z = L/2 of area 1
the points A'2, H', B'2, E'2, H'2, F'2 are opposite respective in area 2
Z, W
y, v
X, U
y
F
E
With
B X
Section of the cylinder
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
5/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Boundary conditions:
·
Conditions of support W = 0 at the base (section Z = 0.) introduced by the key word
LIAISON_OBLIQUE
·
Conditions of symmetry v = 0. on face AB introduced by the key word
LIAISON_OBLIQUE
·
Conditions of symmetry U = 0. on face EFF introduced by the key word
LIAISON_OBLIQUE
·
Identification of the nodes common to the 2 areas (section Z = L/2) by the key word
LIAISON_GROUP
.
Loading:
Density of surface charge p = Q/H = 500000 NR/m2, along the axis, is in total reference mark:
Fx = 0.
Fy = p/2
Fz = p
3
2
Name of the nodes:
plan Z = 0.
WITH = NR 1
B = NR 321
E = NR 1740 F = NR 1541 G = NR 1540
plan Z = 2
(area 1)
A2 = NR 961
B2 = NR 993
E2 = NR 2141 F2 = NR 2122 H = NR 962
H1 = NR 2121
plan Z = 2
(area 2)
A'2 = NR 3361 B'2 = NR 3364 E'2 = NR 2159 F'2 = NR 2155
H' = NR 3360
H'1 = NR 2156
plan Z = 4
A3 = NR 3359 B3 = NR 3355 I = NR 3356
E3 = NR 2151 F3 = NR 2154
I1 = NR 2150
3.2
Characteristics of the mesh
A number of nodes: 4298
A number of meshs and types: 160 HEXA20, 320 PENTA15
3.3 Functionalities
tested
Controls
AFFE-MODELE
“MECHANICAL”
“3D”
AFFE_CHAR_MECA
FORCE_CONTOUR
LIAISON_OBLIQUE
LIAISON_GROUP
AFFE_CHAR_MECA_F
LIAISON_DDL
CALC-CHAM-ELEM
OPTION
“SIGM_ENLO-DEPL”
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
6/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Values of displacements U, V, W read on file
Standard localization
of
value
Reference
Aster
% difference
Not G
U (m)
7.143 X 10
7
7.13895 X 10
7
0.057
V
(m)
0.
10
- 22
-
W
(m)
0.
10
- 23
-
Not H, H'
U (m)
7.143 X 10
7
7.13859 X 10
7
0.062
Not I
U (m)
7.143 X 10
7
7.13739 X 10
7
0.078
Not G1
U (m)
0.
10
- 23
Points H1, H'1
U (m)
0.
10
- 22
Values of displacements U, v, U
R
in local reference mark calculated starting from U, V, W
Standard localization
of
value
Reference
Aster
% difference
Not G
U
R
(m)
7.143 X 10
7
7.13895 X 10
7
0.057
v
(m)
0.
10
- 22
-
Not H, H'
U
R
(m)
7.143 X 10
7
7.13859 X 10
7
0.062
v
(m)
0.
10
- 12
-
Not I
U
R
(m)
7.143 X 10
7
7.13739 X 10
7
0.078
v
(m)
0.
10
12
-
Not A2, A'2
Points B2, B'2
v (m)
0.
10
12
-
-
Not G1
U (m)
0.
10
23
U
R
(m)
7.143 X 10
7
7.14676 X 10
7
0.053
Points H1, H'1
U (m)
0.
10
22
-
U
R
(m)
7.143 X 10
7
7.14708 X 10
7
0.057
Not I1
U (m)
0.
10
22
-
U
R
(m)
7.143 X 10
7
7.14796 X 10
7
0.069
Points E2, E'2
U (m)
0.
10
21
-
Points F2, F'2
U (m)
0.
10
22
Points A, B, G
A2, B2, H
A'2, B'2, H'
A3, B3, I
YY
(AP)
1.25 X 10
5
1.2500 X 10
5
0.
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
7/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Points A, B, G
A2, B2, H
A'2, B'2, H'
A3, B3, I
ZZ
(AP)
3.75 X 10
5
3.700 X 10
5
0.
4.2 Remarks
·
Radial displacement ur is obtained with a good precision.
·
The conditions of symmetry on face AB (v = 0 locally, are
3
2
V 05 W = 0) are checked
at the points A2, A'2, G, B2, B'2, H, H', I considered.
In the same way, the conditions of symmetry on face EFF (U = U = 0) are checked at the points E2, E'2,
F2, F'2, G1, H1, H'1, I1 considered.
The key word
LIAISON_OBLIQUE
is thus validated.
·
Identification of the nodes common to the 2 areas by the key word
LIAISON_GROUP
is also
validated: displacements U, V, W are identical to the points A'2, B'2, H', E'2, F'2, H'1 in
comparison of displacements to opposite respective A2, B2, H, E2, F2, H1.
Code_Aster
®
Version
5.0
Titrate:
SSLV307 - Cylinder obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES
Key
:
V3.04.307-A
Page:
8/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Intentionally white left page.