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
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.105
SSLV105 - Raidissement centrifuges of a beam
in rotation
Summary:
Test of Mécanique 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.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

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
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).
0.5 m
Z
Y
0.02 m
X
Embedded face
Square section of surface: 4.0 10­4 m2
Length of the beam: 0.5 m
1.2
Material properties
E = 2. 1011 Pa
= 0
= 7800 kg/m3
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).
Disk speed: = 3000 rd/S.
The important value disk speed does not have anything physics.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

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
2
Reference solution
2.1
Method of calculation used for the reference solution
In local reference mark of the beam: the equation relating to Ux displacement (without neglecting lengthening) is:
2Ux
+ 2 X + U = 0
2
(
X)
X
E
With the boundary conditions U () =
X 0
0
Ux (L) = (L) = 0
X
xx

2

One poses: =
E
By integrating the preceding differential equation one obtains, in the reference mark of the beam:
(
sin X)
U (X) = cos (
- X
U = U =
X
y

2
0
L)
The displacement of any points of the beam is thus written in the total reference mark:
1 sin R

U
=

-
X (X, Y, Z)
()
3 cos

(
R
L)
1 sin R

U
=

-
y (X, Y, Z)
()
3 cos

(
R
L)
1 sin R

U
=

-
Z (X, Y, Z)
()
3 cos

(
R
L)
with R
=
X 2 + Y 2 + Z2
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).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

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
3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (HEXA20)
Regulated grid including:
4 elements on the section
50
elements
on

length
200
elements
with
total
0.5 m
Z
Y
0.02 m
X
Embedded face
3.2
Characteristics of the grid
A number of nodes: 1521
A number of meshs and types: 200 HEXA20
3.3 Functionalities
tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
ROTATION
CALC_MATR_ELEM
RIGI_ROTA
[U4.41.01]
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

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
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
DX in L
8.75 10­3
8.75 10­3
0
DY in L
8.75 10­3
8.75 10­3
0
DZ in L
8.75 10­3
8.75 10­3
0
4.2 Parameters
of execution
Version: 3.5.27
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
7 seconds
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

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
5
Summary of the results
Correct operation of option RIGI_ROTA. To note the increase in axial displacement by report/ratio
with the case without stiffening (SSLV104 [V3.04.104]).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A