Code_Aster ®
Version
5.0
Titrate:
SDNL103 - Dynamique of a gantry modelled by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Key Mr. AUFAURE
:
V5.02.103-B Page:
1/6

Organization (S): EDF/IMA/MN
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
Document: V5.02.103

SDNL103 - Dynamique of a modelled 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 the command
DYNA_NON_LINE [U4.32.02].
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SDNL103 - Dynamique of a gantry modelled by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Key Mr. AUFAURE
:
V5.02.103-B Page:
2/6

1
Problem of reference

1.1 Geometry
2 m
F
Z
12 m
X
y


1.2
Material properties

For the span:
E = 7. E10 Pa;
= 0.3;
= 2700 kg/m3
For the posts:
E = 5. E10 Pa;
= 0.3;
= 2500 kg/m3

1.3
Boundary conditions and loadings

Embedding in foot of posts.

Evolution of the force F:

F (NR)
500
T (S)
0
0.1
0.2


1.4 Conditions
initial

Static position of balance; null speed.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SDNL103 - Dynamique of a gantry modelled by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Key Mr. AUFAURE
:
V5.02.103-B Page:
3/6

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.

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SDNL103 - Dynamique of a gantry modelled by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Key Mr. AUFAURE
:
V5.02.103-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

Characteristics of the span:

To = 2.24 E3 m2; Iy = Iz = 3.7 E6 m4; Jx = 7.4 E6 m4;
Ay = Az = 1.2

Characteristics of the posts:

To = 3.14 E2 m2; Iy = Iz = 4.5 E5 m4; Jx = 9.0 E5 m4;
Ay = Az = 1.2

The analysis relates to 0.5 S in 100 steps of equal times.

3.2
Characteristics of the grid

The span is modelled by 12 elements of beam; each post by 2 elements. All these
elements have 1m of longor.

3.3 Functionalities
tested

Commands
Key word factor
Key word
Argument
Keys
AFFE_MODELE AFFE
MODELISATION
POU_D_T_GD [U4.22.01]
DYNA_NON_LINE
COMP_ELAS RELATION ELAS_POUTRE_GD
[U4.32.02]
DEFORMATION
GREEN


Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SDNL103 - Dynamique of a gantry modelled by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Key Mr. AUFAURE
:
V5.02.103-B Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification
POU_D_T
POU_D_T_GD
% difference
Aster
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



Obstruction memory:
8 MW
Time CPU To use:
183 seconds

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SDNL103 - Dynamique of a gantry modelled by elements
Date:
17/12/01
Author (S):
J.M. PROIX, Key Mr. AUFAURE
:
V5.02.103-B Page:
6/6

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 elements POU_D_T, in small displacements, this variation is
thus explainable and remains weak in the course of time.

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HI-75/01/010/A

Outline document