Code_Aster ®
Version
7.2
Titrate:
SSLS123 - Sphère under uniform external pressure


Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A Page:
1/6

Organization (S): EDF-R & D/AMA, INSA-LYON

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.123

SSLS123 - Sphère 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

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS123 - Sphère under uniform external pressure


Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A Page:
2/6

1
Problem of reference

1.1 Geometry

Z
Z
C
P
C
y
B
B
y
With
With
X
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 = 6.825 107 Pa, = 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

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS123 - Sphère under uniform external pressure


Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A Page:
3/6

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:
C
U =.
B R +

R
2
R
With
1 - 2
R 3
1+
R 3r 3
B
E
=
.
P
. and C
I
E
=
.
P
.
E
R 3 - R 3
2nd R 3 - R 3
I
E
I
E

T
T
where R = R -
and R = R +

I
2
E
2

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.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS123 - Sphère under uniform external pressure


Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

Element hull SHB8
C2
C1
A1
B1
A2
B2


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 grid

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

Commands



MODI_MAILLAGE ORIE_SHB8
GROUP_MA
TOUT
MODI_MAILLAGE ORIE_PEAU_3D GROUP_MA
SEXT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE
SHB8 TOUT
DEFI_MATERIAU ELAS



4
Results of modeling A

4.1 Values
tested

Identification Reference Aster %
difference
Not A2
­ 1.28279.10­5 ­ 1.27928.10­5
0.27
displacement U
Not B2
­ 1.28279.10­5 ­ 1.27929.10­5
0.27
displacement v
Not C2
­ 1.28279.10­5 ­ 1.3034.10­5
1.7
displacement W
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS123 - Sphère under uniform external pressure


Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A Page:
5/6

5 Modeling
B

5.1
Characteristics of modeling

Voluminal element 3D HEXA8
C2
C1
A1
B1
A2
B2


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 grid

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

Commands




MODI_MAILLAGE ORIE_PEAU_3D
SEXT


AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


PRES_REP
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
TOUT

DEFI_MATERIAU ELAS




6
Results of modeling B

6.1 Values
tested

Identification Reference Aster %
difference
Not A2
­ 1.28279.10­5 ­ 1.28298.10­5
0.015
displacement U
Not B2
­ 1.28279.10­5 ­ 1.28298.10­5
0.015
displacement v
Not C2
­ 1.28279.10­5 ­ 1.28662.10­5
0.30
displacement W
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS123 - Sphère under uniform external pressure


Date:
03/11/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.123-A Page:
6/6

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 grid. The grid 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.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Outline document