Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
1/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.009
SSLS09 - Thin cylinder under actual weight
Summary:
This test from guide VPCS (SSLS 09/89) aims to test a voluminal loading (here the weight
clean), in axisymmetric analysis, by using key word FORCE_INTERN.
One will use for that the two controls: AFFE_CHAR_MECA (modeling A) and AFFE_CHAR_MECA_F
(modeling B).
Modeling C tests the incompressible elements by using the key word GRAVITY on a loading
equivalent.
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
2/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
Average radius: R
= 1m
Thickness
: H
= 0.02 m
Height
: L
= 4 m
1.2
Material properties
Young modulus
: E = 2.1 X 10
11
AP
Poisson's ratio:
= 0.3
Voluminal weight
:
= 7.85 X 10
4
NR/m
3
1.3
Boundary conditions and loadings
·
Axial displacement no one at the low end (U = 0) + conditions of symmetry
·
Actual weight, according to the axis, direction + X
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
3/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
In a point of co-ordinate X:
· radial displacement:
E
X-ray
U
R
-
=
· axial displacement:
E
X
U
X
2
2
=
· rotation of a generator:
E
R
-
=
· axial stress:
X
=
11
· circumferential stress:
0
22
=
2.2
Results of reference
· Axial displacement high end:
X
U
= 2.99 X 10
6
m
· Radial displacement low end:
R
U
= 4.49 X 10
7
m
·
= 1.12 X 10
7
rad
·
11
= 3.14 X 10
5
AP, at the low end
·
0
22
=
. everywhere
2.3
Uncertainty on the solution
Analytical solution.
2.4 Reference
bibliographical
[1]
Guide VPCS Edition 1990 (SSLS 09/89)
[2]
R.J. ROARK and W.C. YOUNG: Formulated for stress and strain, 5
ème
edition, New York,
Mc Graw-Hill, 1975
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
4/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS, T6 meshs and Q8
Position of the points:
·
E, F with middle height
·
G, H, I remote R of the axis
Cutting:
100 elements according to the height
1 element in the thickness
Limiting conditions: DY = 0 on AB
Loading:
Constant voluminal force equalizes with 78500.
Name of the nodes:
Not A = N1
Not C = N452
Not E = N201
Not G = N51
Not I = N503
Not B = N101
Not D = N504
Not F = N203
Not H = N202
3.2
Characteristics of the mesh
A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3
3.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS”
ALL
AFFE_CHAR_MECA DDL_IMPO
FORCE_INTERN
GROUP_NO
CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
5/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Standard localization
of
value Reference Aster
% difference
Points C, D, I
U
X
(m)
2.99 10
6
2.99 10
6
0.
Not G
U
R
(m)
4.49 10
7
4.42 10
7
1.5
Not G
11
(AP)
3.14 10
5
3.14 10
5
0.
Points A, B, G
22
(AP)
0. <
40
-
4.2 Remarks
· Values of
22
data are not significant.
· Taking into account the mesh (1 element in the thickness), the results are completely satisfactory.
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
6/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
5 Modeling
B
5.1
Characteristics of modeling
AXIS, T6 meshs and Q8
Position of the points:
·
E, F with middle height
·
G, H, I remote R of the axis
Cutting:
100 elements according to the height
1 element in the thickness
Limiting conditions: DY = 0 on AB
Loading:
Voluminal force in the form of a constant function defined in y = 0, 3, 6.
Name of the nodes:
Not A = N1
Not C = N452
Not E = N201
Not G = N51
Not I = N503
Not B = N101
Not D = N504
Not F = N203
Not H = N202
5.2
Characteristics of the mesh
A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3
5.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS”
ALL
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
AFFE_CHAR_MECA_F FORCE_INTERN
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
7/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
6
Results of modeling B
6.1 Values
tested
Standard localization
of
value Reference Aster
% difference
Points C, D, I
U
X
(m)
2.99 10
6
2.99 10
6
0.
Not G
U
R
(m)
4.49 10
7
4.42 10
7
1.5
Not G
11
(AP)
3.14 10
5
3.14 10
5
0.
Points A, B, G
22
(AP)
0. <
40
-
6.2 Remarks
· Values of
22
data are not significant.
· The results are identical to those of modeling A.
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
8/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
7 Modeling
C
7.1
Characteristics of modeling
AXIS_INCO, T6 meshs and Q8
Position of the points:
·
E, F with middle height
·
G, H, I remote R of the axis
Cutting:
100 elements according to the height
1 element in the thickness
Limiting conditions: DY = 0 on AB
Loading:
Gravity
Name of the nodes:
Not A = N1
Not C = N452
Not E = N201
Not G = N51
Not I = N503
Not B = N101
Not D = N504
Not F = N203
Not H = N202
7.2
Characteristics of the mesh
A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3
7.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS_INCO” ALL
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
AFFE_CHAR_MECA GRAVITY
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
CALC_ELEM OPTION
“SIEF_ELNO_ELGA”
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
9/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
8
Results of modeling C
8.1 Values
tested
Standard localization
of
value Reference Aster
% difference
Points C, D, I
U
X
(m)
2.99 10
6
2.99 10
6
0.
Not G
U
R
(m)
4.49 10
7
4.42 10
7
1.5
Not G
11
(AP)
3.14 10
5
3.14 10
5
0.
Points A, B, G
22
(AP)
0. <
40
-
8.2 Remarks
· Values of
22
found are not significant.
· The results are identical to those of modeling A and B.
Code_Aster
®
Version
7.4
Titrate:
SSLS09 - Thin cylinder under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES
Key
:
V3.03.009-B
Page:
10/10
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
9
Summary of the results
The use of a function for the definition of a constant density of volume charge is valid: results
are identical, whether one uses one or the other of 2 controls AFFE_CHAR_MECA or
AFFE_CHAR_MECA_F. An equivalent loading gravity gives the same results.
Moreover, the incompressible elements give the same results (modeling C).