Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
1/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, INSA LYON
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.105
SSLS105 - Doubly gripped hemisphere
Summary:
One treats the case of the hemisphere doubly gripped in linear elasticity, which makes it possible to evaluate the quality of
plane breakages for the representation of a deep hull.
The values tested are the arrows at the points of application of the forces.
One has 3 modelings:
·
A: elements
DKT
·
B: elements of
COQUE_3D
in QUAD9
·
C: elements SHB8
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
2/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
C
With
B
2KN
2KN
Z
X
y
C
With
B
Z
y
X
Radius
R = 10. m
Thickness
T = 0.04 m
Co-ordinates of the points:
With
B
C
X 10.
0.
0.
y 0.
10.
0.
Z 0.
0.
10.
1.2
Material properties
E = 6.825 10
7
AP,
= 0.3
1.3
Boundary conditions and loadings
On a quarter of the hemisphere:
Not C
no displacement in Z
Side AC
symmetry compared to the xz plan
Side BC
symmetry compared to the yz plan
Side AB
free
Specific force in a: F = 2. KN
Specific force in b: F = +2. KN
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
3/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in the card “Test No LE3” of the tests of reference published
by NAFEMS [bib1].
2.2
Results of reference
Displacement of point A following X.
2.3 References
bibliographical
[1]
A. Morris. Dynamics Working Group - College off Aeronautics, Cranfield, the U.K. Free vibrations
benchmarks. NAFEMS - Test No LE3 - (1986).
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
4/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Element of hull DKT
Modeling of a quarter of the hemisphere in TRIA3.
Names of the nodes:
Not A
N03
Not B
N02
Not C
N01
3.2
Characteristics of the mesh
A number of nodes: 734
A number of meshs and types: 1373 TRIA3
3.3 Functionalities
tested
Controls
AFFE_CARA_ELEM HULL
ALL
AFFE_CHAR_MECA DDL_IMPO
FORCE_NODALE
GROUP_NO
GROUP_NO
“MECHANICAL” AFFE_MODELE “DKT”
ALL
DEFI_MATERIAU ELAS
4
Results of modeling A
4.1 Values
tested
Identification Reference Aster %
difference
Not A
displacement U
0.185 0.1838 0.66
Not B
displacement v
+0.185 +0.1839 0.59
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
5/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling
Element of hull
COQUE_3D
MEC3QU9H
C
B
With
Modeling of a quarter of the hemisphere in QUAD9
Names of the nodes:
Not A
N01
Not B
N021
Not C
N041
5.2
Characteristics of the mesh
A number of nodes: 256
A number of meshs and types: 75 QUAD9
5.3 Functionalities
tested
Controls
AFFE_CARA_ELEM HULL
ALL
AFFE_CHAR_MECA DDL_IMPO
FORCE_NODALE
GROUP_NO
GROUP_NO
AFFE_MATERIAU ALL
“MECHANICAL” AFFE_MODELE “COQUE_3D”
ALL
DEFI_MATERIAU ELAS
6
Results of modeling B
6.1 Values
tested
Identification Reference Aster %
difference
Not A
displacement U
0.185 0.1844
0.32
Not B
displacement v
+0.185 +0.1844
0.32
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
6/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
7 Modeling
C
7.1
Characteristics of modeling
Element of hull
COQUE_MASSIF
SHB8
C1
C2
B1 B2
A1
A2
Modeling of a quarter of the hemisphere in SHB8
7.2
Characteristics of the mesh
Case 1:
A number of nodes: 662
A number of meshs and types: 300 SHB8
Names of the nodes:
Not A1
N40
Not A2
N42
Not B1
N01
Not B2
N02
Not C1
N662
Not C2
N658
Case 2:
A number of nodes: 2522
A number of meshs and types: 1200 SHB8
Names of the nodes:
Not A1
N1239
Not A2
N1241
Not B1
N301
Not B2
N303
Not C1
N602
Not C2
N604
Case 3:
A number of nodes: 5582
A number of meshs and types: 2700 SHB8
Names of the nodes:
Not A1
N329
Not A2
N331
Not B1
N3439
Not B2
N3441
Not C1
N4760
Not C2
N4762
7.3 Functionalities
tested
Controls
MODI_MAILLAGE ORIE_SHB8
GROUP_MA ALL
AFFE_CHAR_MECA DDL_IMPO
FORCE_NODALE
GROUP_NO
GROUP_NO
AFFE_MATERIAU ALL
“MECHANICAL” AFFE_MODELE SHB8
ALL
DEFI_MATERIAU ELAS
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
7/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
8
Results of modeling C
8.1 Values
tested
Identification Reference Aster %
difference
Cas¨ 1
Not A
displacement U
0.185 0.1490
19.44
Not
B
displacement v
+0.185 +0.1490
19.44
Case 2
Not A
displacement U
0.185 0.1822
1.49
Not
B
displacement v
+0.185 +0.1822
1.49
Case 3
Not A
displacement U
0.185 0.1845
0.24
Not
B
displacement v
+0.185 +0.1845
0.24
8.2 Notice
For this modeling, convergence is relatively slower than for the MEC3QU9H, it is necessary in
effect 1200 elements to obtain a relative error of about 1%. But time CPU is not
crippling (12s). This is undoubtedly due to the choice of the law of behavior specific to the element
SHB8: law of plane stresses, and nonnull rigidity in the direction of the normal to the element.
If one chose a law of elasticity in plane stresses, without amendment, one one would obtain then
correct solution (0,2% of variation) as of the 1
Er
case (300 elements). But this law would be then unsuited
for other tests, such that of the sphere under pressure (SSLS123).
Code_Aster
®
Version
7.2
Titrate:
SSLS105 - Doubly gripped hemisphere
Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, S. BAGUET
Key
:
V3.03.105-D
Page:
8/8
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
9
Summary of the results
Severe test which requires a fine mesh, in particular for element DKT. Results with the element
MEC3TR7H were not retained as test because it is necessary to have many elements
(1801) and thus a time of convergence much longer to obtain correct values by
report/ratio with other modelings (> 500 S for a relative error of about 4%).
For element SHB8, convergence is relatively slower than for the MEC3QU9H, it is necessary in
effect 1200 elements to obtain a relative error of about 1%. But time CPU is not
crippling (12s).
Results in conformity with the reference solution.