Code_Aster
®
Version
7.2
Titrate:
SSLS123 - Sphere under uniform external pressure
Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A
Page:
1/6
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: V3.03.123
SSLS123 - Sphere under uniform external pressure
Summary:
One treats the case of the sphere under uniform pressure external in linear elasticity, which makes it possible to evaluate
quality of the modeling of the compressive forces.
The values tested are radial displacements at the points of intersection with the axes.
One has 2 modelings:
·
A: elements
3D
in HEXA8
·
B: elements SHB8
Code_Aster
®
Version
7.2
Titrate:
SSLS123 - Sphere under uniform external pressure
Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A
Page:
2/6
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
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:
Side AC
symmetry compared to the xz plan
Side BC
symmetry compared to the yz plan
Side AB
symmetry compared to the xy plan
External pressure uniform P=1.Pa
C
With
B
Z
X
y
C
With
B
Z
y
X
Radius
R = 10. m
Thickness
T = 0.04 m
P
Code_Aster
®
Version
7.2
Titrate:
SSLS123 - Sphere under uniform external pressure
Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A
Page:
3/6
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
Radial displacement in any node of the sphere under external pressure is given by:
2
.
R
C
R
B
U
R
+
=
With
P
R
R
R
E
B
E
I
E
.
.
2
1
3
3
3
-
-
=
and
P
R
R
R
R
E
C
E
I
E
I
.
.
2
1
3
3
3
3
-
+
=
where
2
T
R
R
I
-
=
and
2
T
R
R
E
+
=
2.2
Results of reference
Displacement of point A following X, displacement of the point B following y, displacement of the point C following
z.
Code_Aster
®
Version
7.2
Titrate:
SSLS123 - Sphere under uniform external pressure
Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A
Page:
4/6
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 hull SHB8
C1
C2
B1 B2
A1
A2
Modeling of a quarter of the sphere in SHB8.
Names of the nodes:
Not A1
N40
Not A2
N42
Not B1
N01
Not B2
N02
Not C1
N662
Not C2
N658
3.2
Characteristics of the mesh
A number of nodes: 662
A number of meshs and types: 300 SHB8 for the sphere and 300 QUAD4 for external surface.
3.3 Functionalities
tested
Controls
MODI_MAILLAGE ORIE_SHB8
GROUP_MA
ALL
MODI_MAILLAGE ORIE_PEAU_3D GROUP_MA
SEXT
AFFE_CHAR_MECA DDL_IMPO
PRES_REP
GROUP_NO
GROUP_MA
“MECHANICAL” AFFE_MODELE
SHB8 ALL
DEFI_MATERIAU ELAS
4
Results of modeling A
4.1 Values
tested
Identification Reference Aster %
difference
Not A2
displacement U
1.28279.10
5
1.27928.10
5
0.27
Not B2
displacement v
1.28279.10
5
1.27929.10
5
0.27
Not C2
displacement W
1.28279.10
5
1.3034.10
5
1.7
Code_Aster
®
Version
7.2
Titrate:
SSLS123 - Sphere under uniform external pressure
Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A
Page:
5/6
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
Voluminal element 3D HEXA8
C1
C2
B1 B2
A1
A2
Modeling of a quarter of the sphere in HEXA8.
Names of the nodes:
Not A1
N40
Not A2
N42
Not B1
N01
Not B2
N02
Not C1
N662
Not C2
N658
5.2
Characteristics of the mesh
A number of nodes: 662
A number of meshs and types: 300 HEXA8 for the sphere and 300 QUAD4 for external surface.
5.3 Functionalities
tested
Controls
MODI_MAILLAGE ORIE_PEAU_3D
SEXT
AFFE_CHAR_MECA DDL_IMPO
PRES_REP
GROUP_NO
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
ALL
DEFI_MATERIAU ELAS
6
Results of modeling B
6.1 Values
tested
Identification Reference Aster %
difference
Not A2
displacement U
1.28279.10
5
1.28298.10
5
0.015
Not B2
displacement v
1.28279.10
5
1.28298.10
5
0.015
Not C2
displacement W
1.28279.10
5
1.28662.10
5
0.30
Code_Aster
®
Version
7.2
Titrate:
SSLS123 - Sphere under uniform external pressure
Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A
Page:
6/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
7
Summary of the results
Results in conformity with the reference solution.
One could expect to find exactly same displacement to the three point A, B and C.
difference at the point C comes from not-symmetry from the mesh. The mesh is slightly more
distorted around this point, which explains the fall of precision, which remains nevertheless very good,
as well for element HEXA8 for the SHB8.