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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
1/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.104
SSNV104 - Contact of two phères
Summary:
Calculation consists in crushing two quarters of spheres one on the other to test the algorithm of unilateral contact
in statics. The solution is compared with the analytical result of Hertz. This functionality re-enters within the framework
mechanics of the structures having a nonlinear behavior.
Three axisymmetric modelings suggested differ by the type of finite elements used (modeling
AXIS
, meshs
TRIA3
,
QUAD4
and
QUAD8
).
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
2/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
1
Problem of reference
1.1 Geometry
Two half-spheres: axisymmetric model
With
B
C
D
H
I
G
G'
Z1
Z2
radius R = 50 mm
y
X
Taking into account the differences in mesh, positions of the nodes H and I, indicated here in manner
approximate, are different in 3 modelings (one will note the nodes H
With
, I
With
, H
B
, I
B
, H
C
, I
C
).
1.2
Material properties
E
= 20.000. MPa
= 0.3
1.3
Boundary conditions and loadings
DX
locked on the axis AC
DY
imposed ­ 2 mm for the nodes of AB
+2 mm for the CD nodes
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
3/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical method for calculation of
yy
in G (and G'): it is the solution of a problem of Hertz
yy
E
H
R
= -
-
1
1
2
2
where
H
is imposed crushing
()
(
)
H
= - - =
2
2
4
mm
.
2.2
Results of reference
yy
at the point G (analytical solution).
Displacements in three points of the edge (of which G).
xx
,
yy
and
zz
in a mesh being pressed on AG.
2.3 Reference
bibliographical
[1]
G. DUMONT
: “Method of the active stresses applied to the unilateral contact”
Note HI-75/93/016.
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
4/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
3.2
Characteristics of the mesh
Nodes: 110 nodes.
Meshs: 170 TRIA3 and 53 SEG2.
3.3 Functionalities
tested
AFFE_CHAR_MECA
LIAISON_UNIL_NO
STAT_NON_LINE
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Code_Aster
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Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
5/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
Tolerance
yy
net M1 node N110 (G)
­ 2798.3
­ 2636.5
5.8%
7%
yy
net M8 node N110 (G)
­ 2798.3
­ 2976.7
6.4%
7%
DX node N110 (G)
0.
1.14 10
­ 17
10
­ 17
(ABS)
10
­ 13
DY node N110 (G)
0.
­ 2.63 10
­ 4
10
­ 14
(ABS)
10
­ 13
DX node N100 (H
With
)
­ 1.23616 10
­ 1
DY node N100 (H
With
)
­ 1.43310 10
­ 1
DX node N92 (I
With
)
­ 1.76462 10
­ 1
DY node N92 (I
With
)
­ 6.94980 10
­ 1
4.2 Remarks
The node G belongs to 2 meshs (M1 and M8): one can make the average of both
yy
corresponding
to compare with the theoretical value, from where an error of 0.3%.
4.3 Parameters
of execution
Version: 3.02.24
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
5 seconds
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
6/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
5.2
Characteristics of the mesh
Nodes: 410.
Meshs: 30 TRIA3, 324 QUAD4, 93 SEG2.
5.3 Functionalities
tested
AFFE_CHAR_MECA
LIAISON_UNIL_NO
STAT_NON_LINE
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
7/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
Tolerance
yy
net M31 node N291 (G)
­ 2798.3
­ 2477.
11.5%
12%
DX node N291 (G)
0
­ 2. 10
­ 17
10
­ 17
(ABS)
10
­ 13
DY node N291 (G)
0
­ 5.8. 10
­ 17
10
­ 17
(ABS)
10
­ 13
DX node N287 (H
B
)
­ 1.22920 10
­ 1
DY node N287 (H
B
)
­ 1.62911 10
­ 1
DX node N285 (I
B
)
­ 1.89036 10
­ 1
DY node N285 (I
B
)
­ 6.29666 10
­ 1
6.2 Parameters
of execution
Version: 3.02.24
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
6 seconds
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
8/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
7.2
Characteristics of the mesh
Nodes: 660.
Meshs: 176
QUAD8
and 80
SEG3
.
7.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
LIAISON_UNIL_NO
[U4.25.01]
STAT_NON_LINE
[U4.32.01]
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
9/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster
% difference
Tolerance
yy
net M1 node N660 (G)
­ 2 798.3
­ 2419.8
13.5%
14%
DX node N660 (G)
0
­ 3.4 10
­ 17
10
­ 17
(ABS)
10
­ 13
DY node N660 (G)
0
­ 3.4 10
­ 14
10
­ 14
(ABS)
10
­ 13
DX node N644 (H
C
)
­ 1.10481 10
­ 1
DY node N644 (H
C
)
­ 1.11082 10
­ 1
DX node N606 (I
C
)
­ 2.10057 10
­ 1
DY node N606 (I
C
)
­ 7.37809 10
­ 1
8.2 Parameters
of execution
Version: 3.02.24
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
6 seconds
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Code_Aster
®
Version
4.0
Titrate:
SSNV104 Contact of two spheres
Date:
04/02/98
Author (S):
I. VAUTIER
Key:
V6.04.104-A
Page:
10/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
9
Summary of the results
The comparison of each of 3 modelings to the analytical reference (limited to the point G) is
satisfactory for modeling A, less for modelings B and C.
The comparison of 3 modelings between them shows that:
·
the deformations are superposable,
·
the stress fields have marked enough local differences, in particular in
areas Z1 and Z2. The phase of independent validation should make it possible to include/understand
why.
In the command files, one ensures oneself of the not-degradation of the results by testing them
displacements in two nodes of the edge, H and I. These nodes occupying of the positions slightly
different according to modelings', one should not seek to compare the values of the cases A, B, C.