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7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
1/10
Organization (S): EDF-R & D/AMA
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.009
SSLS09 - Thin Cylindre 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 commands: AFFE_CHAR_MECA (modeling A) and AFFE_CHAR_MECA_F
(modeling B).
Modeling C tests the incompressible elements by using key word PESANTEUR on a loading
equivalent.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
2/10
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 1011 Pa
Poisson's ratio: = 0.3
Voluminal weight
: = 7.85 X 104 NR/m3
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
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
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Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
In a point of co-ordinate X:
- X-ray
· radial displacement: U R =
E
x2
· axial displacement: U X =
2nd
R
· rotation of a generator:
-
=
E
· axial stress:
= X
11
· circumferential constraint:
0
22 =
2.2
Results of reference
· Axial displacement high end: U X = 2.99 X 106 m
· Radial displacement low end: U R = 4.49 X 107 m
· = 1.12 X 107 rad
· 11 = 3.14 X 105 Pa, 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, 5th edition, New York,
Mc Graw-Hill, 1975
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
4/10
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 grid
A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3
3.3 Functionalities
tested
Commands
“MECHANICAL” AFFE_MODELE “AXIS”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FORCE_INTERN
CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
5/10
4
Results of modeling A
4.1 Values
tested
Standard localization
of
value Référence Aster
% difference
Points C, D, I
ux (m)
2.99 106
2.99 106 0.
Not G
ur (m)
4.49 107
4.42 107 1.5
Not G
11 (Pa)
3.14 105
3.14 105 0.
Points A, B, G
22 (Pa)
0. <
40
-
4.2 Remarks
· The values of 22 data are not significant.
· Taking into account the grid (1 element in the thickness), the results are completely satisfactory.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
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Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
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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 grid
A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3
5.3 Functionalities
tested
Commands
“MECHANICAL” AFFE_MODELE “AXIS”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
AFFE_CHAR_MECA_F FORCE_INTERN
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
7/10
6
Results of modeling B
6.1 Values
tested
Standard localization
of
value Référence Aster
% difference
Points C, D, I
ux (m)
2.99 106
2.99 106 0.
Not G
ur (m)
4.49 107
4.42 107 1.5
Not G
11 (Pa)
3.14 105
3.14 105 0.
Points A, B, G
22 (Pa)
0. <
40
-
6.2 Remarks
· The values of 22 data are not significant.
· The results are identical to those of modeling A.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
8/10
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 grid
A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3
7.3 Functionalities
tested
Commands
“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”
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
9/10
8
Results of modeling C
8.1 Values
tested
Standard localization
of
value Référence Aster
% difference
Points C, D, I
ux (m)
2.99 106
2.99 106 0.
Not G
ur (m)
4.49 107
4.42 107 1.5
Not G
11 (Pa)
3.14 105
3.14 105 0.
Points A, B, G
22 (Pa)
0. <
40
-
8.2 Remarks
· The found values of 22 are not significant.
· The results are identical to those of modeling A and B.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
:
02/11/05
Author (S):
X. DESROCHES Key
:
V3.03.009-B Page:
10/10
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 commands 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).
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Outline document