Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
1/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN, SAMTECH
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.104
SSLV104 - Beam in rotation
Summary:
This test makes it possible to validate the linear elastic design of a slim beam subjected to a rotation of one of its
ends. Three modelings are tested: elements 3D (HEXA20) and elements of
COQUE_3D
(QUAD9 and
TRIA7). That tests the inertias of rotation, without taking account of the elementary terms of stiffening
centrifuge (cf [V3.04.105]).
The reference solution is analytical (1D). The results coincide perfectly with the reference solution.
Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
2/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
Directed slim beam carried in space by the axis of directing vector (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
A_CIS = 0.8333 (factor of correction of transverse shearing equal to 5/6 for a theory of the type
Thin Reissner hull)
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.
Component 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:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
3/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
In the local reference mark of the beam:
()
()
()
2
2
2
0
0
0
0
U
X
E
X
with U
U
X
L
L
X
X
X
xx
+
=
=
=
=
By integrating the preceding differential equation one obtains, in the reference mark of the beam:
()
U
X
E
X L
X
U
U
X
y
=
-
=
=
2
2
3
2
2
3
0
Displacements of all points of the beam are thus written in the total reference mark:
(
)
(
)
(
)
U
X Y Z
E R L
R
U
X Y Z
E R L
R
U
X Y Z
E R L
R
R
X
Y
Z
X
y
Z
,
,
,
=
-
=
-
=
-
=
+
+
2
2
3
2
2
3
2
2
3
2
2
2
2 3
3
2 3
3
2 3
3
with
2.2
Results of reference
Values of three displacements in the center of the section furthest away from the axis of rotation.
Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
4/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (HEXA20)
Embedded face
0.5 m
0.02 m
Regulated mesh including:
4 elements on the section
50 elements over the length
200 elements on the whole
Z
Y
X
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_MODELE
AFFE
PHENOMENON
MODELING
“MECHANICAL”
“3D”
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
DX, DY, DZ
ROTATION
[U4.25.01]
CALC_MATR_ELEM
OPTION
“RIGI_MECA”
[U4.41.01]
CALC_VECT_ELEM
OPTION
“CHAR_MECA”
[U4.41.02]
RESO_LDLT
MATR_FACT
[U4.51.02]
Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
5/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
DX in L
8.44 10
3
8.44 10
3
0.05
DY in L
8.44 10
3
8.44 10
3
0.04
DZ in L
8.44 10
3
8.44 10
3
0.04
4.2 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
6 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
6/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Elements of hull MEC3QU9H
Z
y
X
Embedded face
0.5 m
0.02
Mesh including:
2 elements according to the dispatcher
4 elements according to the length
8
elements
with
total
5.2
Characteristics of the mesh
A number of nodes: 45
A number of meshs and types: 8 QUAD9
5.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
AFFE
PHENOMENON
MODELING
“MECHANICAL”
“3D”
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
DX, DY, DZ
ROTATION
[U4.25.01]
CALC_MATR_ELEM
OPTION
“RIGI_MECA”
[U4.41.01]
CALC_VECT_ELEM
OPTION
“CHAR_MECA”
[U4.41.02]
RESO_LDLT
MATR_FACT
[U4.51.02]
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
DX in L
8.44 10
3
8.44 E3
0.04
DY in L
8.44 10
3
8.44 E3
0.04
DZ in L
8.44 10
3
8.44 E3
0.04
6.2 Parameters
of execution
Version: 4.00.14
Machine: CRAY C90
Overall dimension memory:
16 MW
Time CPU To use:
4.3 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
7/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
Elements of hull MEC3TR7H
Z
y
X
Embedded face
0.5 m
0.02
Mesh including:
4 elements according to the dispatcher
8 elements according to the length
64
elements
with
total
7.2
Characteristics of the mesh
A number of nodes: 217
A number of meshs and types: 64 TRIA7
7.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
AFFE
PHENOMENON
MODELING
“MECHANICAL”
“3D”
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
DX, DY, DZ
ROTATION
[U4.25.01]
CALC_MATR_ELEM
OPTION
“RIGI_MECA”
[U4.41.01]
CALC_VECT_ELEM
OPTION
“CHAR_MECA”
[U4.41.02]
RESO_LDLT
MATR_FACT
[U4.51.02]
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster
% difference
DX in L
8.44 10
3
8.44 E3
0.08
DY in L
8.44 10
3
8.44 E3
0.02
DZ in L
8.44 10
3
8.44 E3
0.03
8.2 Parameters
of execution
Version: 4.00.14
Machine: CRAY C90
Overall dimension memory:
16 MW
Time CPU To use:
7.6 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV104 Beam in rotation
Date:
07/12/98
Author (S):
J.M. PROIX, P. MASSIN, A. LAULUSA
Key:
V3.04.104-B
Page:
8/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/98/040 - Ind A
9
Summary of the results
The coincidence of the results with the analytical solution makes it possible to validate the loading due to the forces
of inertia of rotation.
Modeling
COQUE_3D
with MEC3QU9H the solution with very few elements gives.
One will refer to test SSLV105 [V3.04.105] to evaluate the effect of the stiffening centrifuges for
the element 3D, HEXA20.