Code_Aster
®
Version
4.0
Titrate:
Dynamometric SSLL402 Rings
Date:
01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A
Page:
1/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A
Organization (S)
: EDF/IMA/MN, IAT St CYR
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.402
SSLL402 - Dynamometric ring
Summary:
This test makes it possible to check in linear elasticity the calculation of the interior efforts and the stresses on a beam
curve.
A modeling makes it possible to test the curved elements of Timoshenko (
POU_C_T
).
The reference solution is analytical and the results obtained are of very good quality.
Code_Aster
®
Version
4.0
Titrate:
Dynamometric SSLL402 Rings
Date:
01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A
Page:
2/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
Circular ring
F
F
With
B
C
D
0
y
G
Y
X
R
X
Appear 1.1-a
R = 2 m
The section (full) is a circle of radius 0,01 Mr.
1.2
Properties of materials
Young modulus:
E = 2. 10
11
AP
Poisson's ratio:
= 0.3
1.3
Boundary conditions and loading
Boundary condition:
DX = DY = DZ = DRX = 0 on point A
DY = DZ = 0 on the point C
Loading:
on B, F = 1 NR,
on D, F = - 1 NR.
Code_Aster
®
Version
4.0
Titrate:
Dynamometric SSLL402 Rings
Date:
01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A
Page:
3/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A
2
Reference solutions
2.1 Method of calculation used for the reference solutions
:
analytical
On the section
()
WITH B
,
0
2
< <
, we have:
(
)
NR
F
Vy
F
M
FR
Z
=
= -
= -
-
2
2
2 1
cos
,
sin
,
cos
+
.
On the section
()
B C
,
2
< <
, we have:
(
)
NR
F
Vy
F
M
FR
Z
= -
=
= -
+
2
2
2 1
cos
,
sin
,
cos
+
.
By the use of the law of behavior connecting M to the rotation of the normal and given that this
last is null in A and out of B, we have:
O
2
M D = 0
,
from where:
=
=
2
2
=
-
M
M
F R
With
C
2.2
Results of reference
Interior efforts for
= 0°et 90°.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Report/ratio n° 2314/A of the Institute Aerotechnics “Proposal and realization for new cases
tests missing with the validation beams
Aster
”
Code_Aster
®
Version
4.0
Titrate:
Dynamometric SSLL402 Rings
Date:
01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A
Page:
4/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
The model is composed of 4 elements curved beam of Timoshenko.
3.2
Characteristics of the mesh
It consists of 4 elements
POU_C_T
.
3.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
BEAM
SECTION
RING
[U4.24.01]
CALC_ELEM
OPTION
EFGE_ELNO_DEPL
[U4.31.01]
SIGM_ELNO_DEPL
AFFE_CHAR_MECA
FORCE_NODALE
FY
[U4.25.01]
Code_Aster
®
Version
4.0
Titrate:
Dynamometric SSLL402 Rings
Date:
01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A
Page:
5/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
4.1.1 Interior effort with
= 0°
Reference
Aster
Variation %
NR
5.000E01
5.000E01
0.0000
Vy
0.0000
0.0000
0.0000 *
MFz
3.6338E01
3.6338E01
0.0000
* Absolute deviation
4.1.2 Interior effort with
= 90°
Reference
Aster
Variation %
NR
0.0000
0.0000
0.0000 *
Vy
5.0000E01
5.000E01
0.0000
MFz
6.3662E01
6.3662E01
0.0000
* Absolute deviation
4.1.3 Stress
with
= 0°
Reference
Aster
Variation %
SIXX
4.6426E+05
4.6426E+05
0.0000
SIXY
0.0000
0.0000 *
0.0000
* Absolute deviation
4.1.4 Stress
with
= 90°
Reference
Aster
Variation %
SIXX
8.1056E+05
8.1056E+05
0.0000
SIXY
1.7683E+03
1.7683E+03
0.0000
4.2 Remarks
Symmetry compared to axis (A, C) implies the nullity of the shearing action T in A and C. balance
according to OY of the half-ring (A, B, C) imposes in A and C a normal effort equal to
F
2
. Symmetry by
report/ratio with the axis (B, D) implies that the moments in A and C are equal in absolute value and of direction
opposites.
4.3 Parameters
of execution
Version: 4.02.13
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU to use:
4 seconds
Code_Aster
®
Version
4.0
Titrate:
Dynamometric SSLL402 Rings
Date:
01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A
Page:
6/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A
5
Summary of the results
The results agree with the analytical solution and make it possible to validate the calculation of the efforts
interns (
EFGE_ELNO_DEPL
) and of the stresses (
SIGM_ELNO_DEPL
) by the elements of beams
curves (
POU_C_T
).