Code_Aster ®
Version
4.0
Titrate:
Dynamometric SSLL402 Anneaux
Date: 01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A Page:
1/6
Organization (S): EDF/IMA/MN, IAT St CYR
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.402
SSLL402 - Dynamometric Anneau
Summary:
This test makes it possible to check in linear elasticity the calculation of the interior efforts and the constraints 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.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Dynamometric SSLL402 Anneaux
Date: 01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A Page:
2/6
1
Problem of reference
1.1 Geometry
Circular ring
F
B
X
y
G
Y
R
C
With

0
X
D
­ F
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. 1011 Pa
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.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Dynamometric SSLL402 Anneaux
Date: 01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A Page:
3/6
2
Reference solutions
2.1 Method of calculation used for the reference solutions
:
analytical


On the section (A, B) 0 < <


, we have:
2
F
F
FR
NR =
cos, Vy = -
sin, M = -
1 -


+

Z
(cos)
.
2
2
2

On the section (B, C)
< <



2

, we have:
F
F
FR
NR = -
cos, Vy =
sin, M = -
1 +


+

Z
(cos)
.
2
2
2
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:

2

M D = 0,
O
- 2
from where:
= M =
M
=

F R
With
C
2
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 Institut Aérotechnique “Proposition and realization of new cases
tests missing with the validation Aster beams “
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Dynamometric SSLL402 Anneaux
Date: 01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
The model is composed of 4 elements curved beam of Timoshenko.
3.2
Characteristics of the grid
It consists of 4 elements POU_C_T.
3.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
POUTRE
SECTION
CERCLE
[U4.24.01]
CALC_ELEM
OPTION
EFGE_ELNO_DEPL
[U4.31.01]
SIGM_ELNO_DEPL
AFFE_CHAR_MECA
FORCE_NODALE
FY
[U4.25.01]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Dynamometric SSLL402 Anneaux
Date: 01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A Page:
5/6
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 Constraint
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 Constraint
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
F
according to OY of the half-ring (A, B, C) imposes in A and C a normal effort equal to
. Symmetry by
2
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
Obstruction memory:
8 MW
Time CPU to use:
4 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Dynamometric SSLL402 Anneaux
Date: 01/12/98
Author (S)
:
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK
Key:
V3.01.402-A Page:
6/6
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 constraints (SIGM_ELNO_DEPL) by the elements of beams
curves (POU_C_T).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/98/040 - Ind A