Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
1/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
V5.02.104 document
SDNL104 - Under-structuring transitory
nonlinear: shock of a beam on 1 support
Summary:
The applicability of this test relates to the dynamics of the structures, and more particularly the calculation of
nonlinear transitory response by dynamic under-structuring.
It is a question of calculating the nonlinear transitory response of a beam in bending with shock on an elastic support and
subjected to a constant force as from the initial moment. The beam is modelized by elements of the type
POU_D_E
(model beam of Euler).
The results of reference result from a direct transitory calculation by modal recombination. This test allows
thus to validate the computational tools of response transitory per under-structuring, in the case of the catch in
count non-linearities of the shock type on a fixed obstacle.
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
2/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
1
Problem of reference
1.1 Geometry
With
F
K
C
Play
y
X
The length of the beam is worth: L = 1 m
The section of the beam is full circular of radius: R = 0.1 m
The play between the beam and the elastic support is worth: J = 1 10
4
m
1.2
Material properties
E = 1 10
10
AP
= 0.3
= 1 10
6
kg/m
3
The stiffness within the competence of contact is worth: K
C
= 1 10
8
NR/m
1.3
Boundary conditions and loadings
On all the structure: DX = DZ = DRY = DRX = 0.
At point a: DY = DRZ = 0.
At the loose lead of the beam: as from the moment T = 0 S, Fy = 1000. NR
1.4 Conditions
initial
Structure initially at rest.
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
3/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is given by a direct transitory calculation by modal recombination
(modeling A).
2.2
Results of reference
Value of displacements, speed and acceleration of the loose lead of the beam according to the direction Y and
at the moment T = 1 S.
Displacement
(m)
Speed
(Mr. S
1
)
Acceleration
(Mr. S
2
)
Diagram of integration of Euler
1.255 10
4
8.352 10
4
3.640 10
1
Diagram of integration of Devogelaere
1.254 10
4
8.410 10
4
2.855 10
1
Diagram of integration to pitch of time
adaptive
1.255 10
4
8.480 10
4
3.620 10
1
2.3
Uncertainty on the solution
Numerical solution.
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
4/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
The beam is with a grid in segments to which are affected of the elements of the type “
POU_D_E
“.
The dealt with transitory problem, projected on the basis of clean mode the first 5 of the structure, is
solved directly by the transitory operator of calculation by modal recombination (
DYNA_TRAN_MODAL
[U4.54.03]).
3.2 Functionalities
tested
This modeling is used as reference of the case test. It does not have thus as an aim to test them
functionalities of
Code_Aster
.
3.3
Characteristics of the mesh
A number of nodes: 11
A number of meshs and types: 10 SEG2
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
5/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
4
Results of modeling A
4.1
Actual values: references for modeling B
Identification
Aster
Diagram of integration of Euler
Displacement (m)
1.255 10
4
Speed (Mr. S
1
)
8.352 10
4
Acceleration (Mr. S
2
)
3.640 10
1
Diagram of integration of
Devogelaere
Displacement (m)
1.254 10
4
Speed (Mr. S
1
)
8.410 10
4
Acceleration (Mr. S
2
)
2.855 10
1
Diagram of integration to pitch of
adaptive time
Displacement (m)
1.255 10
4
Speed (Mr. S
1
)
8.480 10
4
Acceleration (Mr. S
2
)
3.620 10
1
4.2 Parameters
of execution
Version: 3.05.23
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
16.43 seconds
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
6/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
The beam is cut out in 2 parts of equal size. Each substructure considered is
with a grid in segments to which are affected of the elements of the type “
POU_D_E
“.
=
+
The structure is studied using the method of under-structuring with interfaces of the type
“Craig-Bampton” (locked interfaces).
The base of the first 5 clean modes of the complete structure is calculated by under-structuring.
Then, the transitory problem, projected on this basis, is solved by the transitory operator of calculation by
modal recombination (
DYNA_TRAN_MODAL
).
5.2 Functionalities
tested
Order
Keys
DYNA_TRAN_MODAL
METHOD
“EULER”
[U4.54.03]
“DEVOGE”
“ADAPT”
SHOCK
SOUS_STRUC_1
IDENTIFY
5.3
Characteristics of the mesh
A number of nodes: 6
A number of meshs and types: 5 SEG2
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
7/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
Diagram of integration of Euler
Displacement (m)
1.255 10
4
1.255 10
4
0.043
Speed (Mr. S
1
)
8.352 10
4
8.289 10
4
0.75
Acceleration (Mr. S
2
)
3.640 10
1
3.870 10
1
6.32
Diagram of integration of
Devogelaere
Displacement (m)
1.254 10
4
1.255 10
4
0.042
Speed (Mr. S
1
)
8.410 10
4
8.320 10
4
1.076
Acceleration (Mr. S
2
)
2.855 10
1
3.079 10
1
7.85
Diagram of integration to pitch of
adaptive time
Displacement (m)
1.255 10
4
1.255 10
4
0.028
Speed (Mr. S
1
)
8.480 10
4
8.508 10
4
0.328
Acceleration (Mr. S
2
)
3.620 10
1
3.926 10
1
8.448
6.2 Remarks
In the case of a nonlinear transitory calculation, it is not abnormal to obtain uncertainties
important on not realized sizes. The variation from 6 to 8% between the reference solution and
solution obtained by under-structuring for acceleration thus does not invalidate the method tested,
more especially as the results in displacements are excellent (variation < 0.1%).
6.3 Parameters
of execution
Version: 3.05.23
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
20.7 seconds
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL104 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.104-A
Page:
8/8
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
7
Summary of the results
The precision on displacements of the loose lead of the beam at the moment T = 1. S is excellent
(relative error < 0.1%).
This test thus validates the operators of non-linear transitory calculation by dynamic under-structuring.
The values of acceleration with the diagram of Devogelaere are to be analyzed.