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Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
1/8
Organization (S): EDF/AMA
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.307
SSLV307 - Cylindre obliques under load
axial uniform
Summary:
The purpose of the test is to validate the various types of linear relations, defined by 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.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
2/8
1
Problem of reference
1.1 Geometry
Average radius: Ro = 1 m
Thickness:
H = 0.02 m
Height:
L = 4 m
3
Cosine directors of the axis of the cylinder: (0.0, 0,5,
)
2
Center local X parallel with the total axis X.
1.2
Material properties
E = 2.1 X 1011 Pa
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.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
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2
Reference solution
2.1
Method of calculation used for the reference solution
· Radial displacement in local reference mark (X, y, Z):
1/2
2
qvRo
3
U
2
U +
V -
W
R =
= -
5
.
0
Eh
2
where U, V, W = component of displacement in the total reference mark (X, Y, Z).
· If,
xx yy zz = 11 is the constraints in the local reference mark, the constraints expressed in
the total reference mark are worth:
xx = xx
= 3/4 yy +1/411
11 = Q/H
zz = 1/4 yy + 3/411
3
3
yz = -
yy +
11
4
4
In the local plan (X, Z), yy = 0 (circumferential constraint),
from where 1/4
yy
11, zz = 3/4 11
2.2
Results of reference
· Raidal displacement: ur = 7.14 X 107 m
· In the local plan (X, Z), yy = 1.25 X 105 Pa, zz = 3.75 X 105 Pa
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, 5th edition. New York,
Mc Graw-Hill, 1975
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
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3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (PENTA15 + HEXA20)
Z, W
y
F
E
X, U
With
B X
Section of the cylinder
y, v
Modeling:
1/4 of the cylinder following the circumference
2 zones:
zone 1 = left lower
(0
Z L/2)
zone 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 points (R, Z)
WITH G B E
G1
F
A2
H
B2
E2 H1
F2
A3 I B 3E3 I1 F3
A'2
H'
B' 2e'2 H'1 F'2
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 zone 1
the points A'2, H', B'2, E'2, H'2, F'2 are opposite respective in zone 2
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
5/8
Boundary conditions:
· Conditions of support W = 0 at the base (section Z = 0.) introduced by key word LIAISON_OBLIQUE
· Conditions of symmetry v = 0. on face AB introduced by key word LIAISON_OBLIQUE
· Conditions of symmetry U = 0. on face EFF introduced by key word LIAISON_OBLIQUE
· Identification of the nodes common to the 2 zones (section Z = L/2) by 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
3
Fz = p
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
A2 = NR 961
B2 = NR 993
E2 = NR 2141 F2 = NR 2122 H = NR 962
H1 = NR 2121
(zone 1)
plan Z = 2
A'2 = NR 3361 B'2 = NR 3364 E'2 = NR 2159 F'2 = NR 2155
H' = NR 3360
H'1 = NR 2156
(zone 2)
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 grid
A number of nodes: 4298
A number of meshs and types: 160 HEXA20, 320 PENTA15
3.3 Functionalities
tested
Commands
AFFE-MODELE
“MECANIQUE”
“3D”
AFFE_CHAR_MECA
FORCE_CONTOUR
LIAISON_OBLIQUE
LIAISON_GROUP
AFFE_CHAR_MECA_F
LIAISON_DDL
CALC-CHAM-ELEM
OPTION
“SIGM_ENLO-DEPL”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
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4
Results of modeling A
4.1 Values
tested
Values of displacements U, V, W read on file
Standard localization
of Référence
Aster
% difference
value
Not G
U (m)
7.143 X 107
7.13895 X 107
0.057
V
(m)
0. 10-22
-
W
(m)
0. 10-23
-
Not H, H'
U (m)
7.143 X 107
7.13859 X 107
0.062
Not I
U (m)
7.143 X 107
7.13739 X 107
0.078
Not G1
U (m)
0.
10-23
Points H1, H'1
U (m)
0.
10-22
Values of displacements U, v, ur in local reference mark calculated starting from U, V, W
Standard localization
of Référence
Aster
% difference
value
Not G
ur (m)
7.143 X 107
7.13895 X 107
0.057
v
(m)
0. 10-22
-
Not H, H'
ur (m)
7.143 X 107
7.13859 X 107
0.062
v
(m)
0. 10-12
-
Not I
ur (m)
7.143 X 107
7.13739 X 107
0.078
v
(m)
0. 1012
-
Not A2, A'2
v (m)
0.
1012
-
Points B2, B'2
-
Not G1
U (m)
0.
1023
ur (m)
7.143 X 107
7.14676 X 107
0.053
Points H1, H'1
U (m)
0.
1022
-
ur (m)
7.143 X 107
7.14708 X 107
0.057
Not I1
U (m)
0.
1022
-
ur (m)
7.143 X 107
7.14796 X 107
0.069
Points E2, E'2
U (m)
0.
1021
-
Points F2, F'2
U (m)
0.
1022
Points A, B, G
A2, B2, H
YY (Pa)
1.25 X 105
1.2500 X 105
0.
A'2, B'2, H'
A3, B3, I
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
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Points A, B, G
A2, B2, H
ZZ (Pa)
3.75 X 105
3.700 X 105
0.
A'2, B'2, H'
A3, B3, I
4.2 Remarks
· Radial displacement ur is obtained with a good precision.
3
· The conditions of symmetry on face AB (v = 0 locally, are
V 05 W = 0) are checked
2
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.
Key word LIAISON_OBLIQUE is thus validated.
· The identification of the nodes common to the 2 zones by 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.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV307 - Cylindre obliques under uniform axial loading
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.307-A Page:
8/8
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Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
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