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:
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:
3/8

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:
4/8

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:
6/8

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:
7/8
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

Intentionally white left page.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A

Outline document