Code_Aster
®
Version
5.0
Titrate:
SSLP305 - Thin disc in support under concentrated loading
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.305-A
Page:
1/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.305
SSLP305 - Thin disc in support under load
concentrated
Summary:
The purpose of the test is to validate the calculation of the potential energy in linear elasticity.
Only one axisymmetric modeling is presented.
The reference solution is analytical.
Code_Aster
®
Version
5.0
Titrate:
SSLP305 - Thin disc in support under concentrated loading
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.305-A
Page:
2/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Diameter:
= 0.5 m
Thickness: H = 0.005 m
1.2
Material properties
Young modulus: E = 2.1 X 10
11
AP
Poisson's ratio: v = 0.3
1.3
Boundary conditions and loadings
·
Support on the edge (W = 0)
·
Charge concentrated at point a: P = 350 NR
1.4 Conditions
initial
Without object for the static analysis.
Z
H
With
X
B
C
Code_Aster
®
Version
5.0
Titrate:
SSLP305 - Thin disc in support under concentrated loading
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.305-A
Page:
3/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
·
The value of axial displacement in the center of disc (not A) is given by:
W
With
=
P
D X
v
v
2
64
3
1
+
+
where D =
Eh
v
3
2
12 1
(
)
-
·
The value of the potential energy (with balance) is given by:
E
p
=
1
2
PW
has
·
The absolute value of the potential energy by radian is:
E
p
=
1
2
2
has
PW
2.2
Results of reference
·
Displacement at point a:
W
With
= 0.4596 X 10
3
m
·
Potential energy by radian:
E
p
= 0.012799 Nm/rd
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
R.J. ROARK and W.C. YOUNG Formulated for stress and strain, 5
ème
edition, New York,
Mc Graw-Hill, 1975
Code_Aster
®
Version
5.0
Titrate:
SSLP305 - Thin disc in support under concentrated loading
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.305-A
Page:
4/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
It is an axisymmetric modeling.
Y
With
D
X
G
B
Limiting conditions:
out of B
DDL_IMPO: (GROUP_NO: B
DY: 0.)
on AG
DDL_IMPO: (GROUP_NO: lAG DX: 0.)
Loading:
in A
FORCE_NODALE: (GROUP_NO: With
FY:
- 55.704)
Name of the nodes:
A=N1
B = N755
D = N858
G = N201
Cutting:
100 elements according to the radius
2 elements according to the thickness
3.2
Characteristics of the mesh
A number of nodes: 905
A number of meshs and types: 100 QUAD 8, 200 SORTED 6, 208 SEG 3
3.3 Functionalities
tested
Controls
AFFE_MODELE
“MECHANICAL”
“AXIS”
ALL
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
FORCE_NODALE
GROUP_NO
POST_ELEM
ENER_POT
Code_Aster
®
Version
5.0
Titrate:
SSLP305 - Thin disc in support under concentrated loading
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.305-A
Page:
5/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Localization
Type of value
Reference
Aster
% difference
Not A
W
With
(m)
0.4596 10
3
0.4617 10
3
0.46
E
p
(Nm/rd)
1.2799 10
2
1.2859 10
2
0.47
4.2 Remarks
·
The value of the load required is brought back to a sector of 1 radian. Consequently, the value
potential energy given on the file result corresponds to the deformation of this sector
(with the sign near).
·
Option ENERPOT calculates in fact a deformation energy:
KU
U
E
T
D
2
1
=
who is identical to the potential energy with the sign near:
(
)
F
KU
KU
U
F
U
F
U
KU
U
E
T
T
T
T
p
=
-
=
-
=
-
=
because
2
1
2
1
2
1
Code_Aster
®
Version
5.0
Titrate:
SSLP305 - Thin disc in support under concentrated loading
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.305-A
Page:
6/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
5
Summary of the results
These good results on the displacement and the deformation energy (variation similar of 0,5% with
analytical reference solution) show that the calculation of this energy is correct. To approach
still better the value of reference, it would be necessary to discretize the mesh more.