Code_Aster
®
Version
4.0
Titrate:
SSLV105 Raidissement centrifuges of a beam in rotation
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.04.105-A
Page:
1/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.105
SSLV105 - Stiffening centrifuges of a beam
in rotation
Summary:
Test of Mechanics of the structures in linear static analysis.
The geometry is that of a slim beam subjected to a rotation around one of its ends. Only one
modeling: elements 3D (HEXA20). One tests here the inertias of rotation (like test SSLV104)
with taking into account of the centrifugal stiffening.
The reference solution (analytical) takes into account the term of additional rigidity due to rotation.
results are identical to the reference solution.
Code_Aster
®
Version
4.0
Titrate:
SSLV105 Raidissement centrifuges of a beam in rotation
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.04.105-A
Page:
2/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
1
Problem of reference
1.1 Geometry
The structure is made up of a directed slim beam carried in space by the axis of vector
Director (1, 1, 1).
Z
Y
X
Embedded face
0.5 m
0.02 m
Square section of surface: 4.0 10
4
m
2
Length of the beam: 0.5 m
1.2
Material properties
E = 2. 10
11
AP
= 0
= 7800 kg/m
3
1.3
Boundary conditions and loadings
Free beam fixed in rotation around an axis perpendicular to its greater dimension and
passing by the center of the embedded face.
Co-ordinates of the vector rotation: (1, 0, 1).
Rotational speed:
= 3000 rd/S.
The important value rotational speed does not have anything physics.
Code_Aster
®
Version
4.0
Titrate:
SSLV105 Raidissement centrifuges of a beam in rotation
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.04.105-A
Page:
3/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
In local reference mark of the beam: the equation relating to displacement
U
X
(without neglecting lengthening) is:
(
)
2
2
2
0
U
X
E
X U
X
X
+
+
=
()
()
()
With the boundary conditions
One poses:
=
U
U
X
L
L
E
X
X
xx
0
0
0
2
=
=
=
By integrating the preceding differential equation one obtains, in the reference mark of the beam:
()
()
()
U
X
X
L
X
U
U
X
y
=
-
=
=
sin
cos
2
0
The displacement of any points of the beam is thus written in the total reference mark:
(
)
()
()
(
)
()
()
(
)
()
()
U
X Y Z
R
L
R
U
X Y Z
R
L
R
U X Y Z
R
L
R
R
X
Y
Z
X
y
Z
,
sin
cos
,
sin
cos
,
sin
cos
=
-
=
-
=
-
=
+
+
1
3
1
3
1
3
2
2
2
with
2.2
Results of reference
Values of three displacements in the center of the section furthest away from the axis of rotation.
2.3
Uncertainty on the solution
Without object (analytical solution).
Code_Aster
®
Version
4.0
Titrate:
SSLV105 Raidissement centrifuges of a beam in rotation
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.04.105-A
Page:
4/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (HEXA20)
Z
Y
X
Embedded face
0.5 m
0.02 m
Regulated mesh including:
4 elements on the section
50
elements
on
length
200
elements
with
total
3.2
Characteristics of the mesh
A number of nodes: 1521
A number of meshs and types: 200 HEXA20
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
ROTATION
CALC_MATR_ELEM
RIGI_ROTA
[U4.41.01]
Code_Aster
®
Version
4.0
Titrate:
SSLV105 Raidissement centrifuges of a beam in rotation
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.04.105-A
Page:
5/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
DX in L
8.75 10
3
8.75 10
3
0
DY in L
8.75 10
3
8.75 10
3
0
DZ in L
8.75 10
3
8.75 10
3
0
4.2 Parameters
of execution
Version: 3.5.27
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
7 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV105 Raidissement centrifuges of a beam in rotation
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.04.105-A
Page:
6/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
5
Summary of the results
Correct operation of the option
RIGI_ROTA
. To note the increase in axial displacement by report/ratio
with the case without stiffening (SSLV104 [V3.04.104]).