Code_Aster
®
Version
5.0
Titrate:
SDNL103 - Dynamics of a gantry modelized by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Mr. AUFAURE
Key
:
V5.02.103-B
Page:
1/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
Document: V5.02.103
SDNL103 - Dynamics of a modelized gantry
by elements of beam in great rotation.
Comparison with an analysis in small rotation
Summary:
One analyzes the response of a gantry, embedded in feet and subjected to a dynamic force applied to the medium
of its span and perpendicular to its plan. Displacements are small. One compares two modelings of
beams:
POU_D_T_GD
and
POU_D_T
.
Interest: to test the element of beam in great rotation
MECA_POU_D_T_GD
and orders it
DYNA_NON_LINE
[U4.32.02].
Code_Aster
®
Version
5.0
Titrate:
SDNL103 - Dynamics of a gantry modelized by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Mr. AUFAURE
Key
:
V5.02.103-B
Page:
2/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
2 m
12 m
F
X
y
Z
1.2
Material properties
For the span:
E = 7. E10 AP;
= 0.3;
= 2700 kg/m
3
For the posts:
E = 5. E10 AP;
= 0.3;
= 2500 kg/m
3
1.3
Boundary conditions and loadings
Embedding in foot of posts.
Evolution of the force F:
F (NR)
500
0
0.1
0.2
T (S)
1.4 Conditions
initial
Static position of balance; null speed.
Code_Aster
®
Version
5.0
Titrate:
SDNL103 - Dynamics of a gantry modelized by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Mr. AUFAURE
Key
:
V5.02.103-B
Page:
3/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
This problem does not have an analytical solution. But, as displacements are small, one takes for
reference modeling by elements of beam
POU_D_T
.
2.2
Results of reference
Displacement of the medium of the span, in direction X at the moments:
0.14
S; 0.26
S; 0.36
S and 0.47
S.
Code_Aster
®
Version
5.0
Titrate:
SDNL103 - Dynamics of a gantry modelized by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Mr. AUFAURE
Key
:
V5.02.103-B
Page:
4/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Characteristics of the span:
To = 2.24 E3 m
2
; I
y
= I
Z
= 3.7 E6 m
4
; J
X
= 7.4 E6 m
4
;
With
y
= A
Z
= 1.2
Characteristics of the posts:
To = 3.14 E2 m
2
; I
y
= I
Z
= 4.5 E5 m
4
; J
X
= 9.0 E5 m
4
;
With
y
= A
Z
= 1.2
The analysis relates to 0.5 S in 100 pitches of equal times.
3.2
Characteristics of the mesh
The span is modelized by 12 elements of beam; each post by 2 elements. All these
elements have 1m of longor.
3.3 Functionalities
tested
Controls
Key word factor
Key word
Argument
Keys
AFFE_MODELE AFFE
MODELING
POU_D_T_GD
[U4.22.01]
DYNA_NON_LINE
COMP_ELAS RELATION ELAS_POUTRE_GD
[U4.32.02]
DEFORMATION
GREEN
Code_Aster
®
Version
5.0
Titrate:
SDNL103 - Dynamics of a gantry modelized by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Mr. AUFAURE
Key
:
V5.02.103-B
Page:
5/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Identification
POU_D_T
POU_D_T_GD
Aster
% difference
DX in T = 1.4 E1
2.9706 E2
2.9069 E2
2.1
DX in T = 2.6 E1
2.6290 E2
2.5376 E2
3.5
DX in T = 3.6 E1
2.5126 E2
2.5147 E2
0.08
DX in T = 4.7 E1
2.5488 E2
2.5390 E2
0.4
4.2 Parameters
of execution
Version: 4.1
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
183 seconds
Code_Aster
®
Version
5.0
Titrate:
SDNL103 - Dynamics of a gantry modelized by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Mr. AUFAURE
Key
:
V5.02.103-B
Page:
6/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A
5
Summary of the results
The variation compared to the reference solution is to the maximum of 3,5% during the transient.
reference solution being obtained with the elements
POU_D_T
, in small displacements, this variation is
thus explainable and remains weak in the course of time.