Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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
V5.02.105 document
SDNL105 - Under-structuring transitory
nonlinear: shock of 3 beams between them
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 3 beams in bending with shocks to the center of the beams.
The beams are modelized by elements of the type “
POU_D_E
“(model 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 between mobile structures.
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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
Play
F
X
y
K
C
X
X
X
The length of the beams is worth: L = 1 m
The beams are of circular section:
·
of radius: R = 0.1 m
·
of thickness: ep = 0.01 m
The play between the beams is worth: Play = 1 10
3
m
1.2
Material properties
E = 1 10
10
AP
= 0.3
= 1 10
8
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 = DRX = DRY = 0.
With the superior ends and inferior of the beams: DY = DRZ = 0.
In the middle of the beam of left: as from the moment T = 0 S, Fy = 1 10
6
NR
1.4 Conditions
initial
Structure initially at rest.
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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 superposition
(modeling A).
2.2
Results of reference
Value of displacements and speed of the nodes of the 3 beams according to the direction Y and at the moment T = 1 S.
Displacement
(m)
Speed
(Mr. S
1
)
Diagram of integration of Euler
Beam of left
1.64 10
2
2.54 10
2
Beam medium
1.12 10
2
4.49 10
2
Beam of straight line
5.90 10
3
1.05 10
1
Diagram of integration of Devogelaere
Beam of left
1.64 10
2
2.54 10
2
Beam medium
1.12 10
2
4.41 10
2
Beam of straight line
5.89 10
3
1.05 10
1
Diagram of integration to pitch of adaptive time
Beam of left
1.64 10
2
2.55 10
2
Beam medium
1.12 10
2
4.41 10
2
Beam of straight line
5.91 10
3
1.05 10
1
2.3
Uncertainty on the solution
Numerical solution.
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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 15 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: 41
A number of meshs and types: 42 SEG2
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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: reference for modeling B
Identification
Aster
Diagram of integration of Euler
Beam of left: Displacement (m)
1.64 10
2
Speed (Mr. S
1
)
2.54 10
2
Beam of medium: Displacement (m)
1.12 10
2
Speed (Mr. S
1
)
4.43 10
2
Beam of straight line: Displacement (m)
5.90 10
3
Speed (Mr. S
1
)
1.05 10
1
Diagram of integration of Devogelaere
Beam of left: Displacement (m)
1.64 10
2
Speed (Mr. S
1
)
2.54 10
2
Beam of medium: Displacement (m)
1.12 10
2
Speed (Mr. S
1
)
4.41 10
2
Beam of straight line: Displacement (m)
5.89 10
3
Speed (Mr. S
1
)
1.05 10
1
Diagram of integration to pitch of time
adaptive
Beam of left: Displacement (m)
1.64 10
2
Speed (Mr. S
1
)
2.55 10
2
Beam of medium: Displacement (m)
1.12 10
2
Speed (Mr. S
1
)
4.41 10
2
Beam of straight line: Displacement (m)
5.91 10
3
Speed (Mr. S
1
)
1.05 10
1
4.2 Parameters
of execution
Version: 3.05.32
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
29.61 seconds
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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
=
X 3
The dynamic under-structuring makes it possible to calculate the vibratory behavior of the 3 beams to be left
dynamic characteristics of only one beam. The aforementioned is with a grid in segments to which are
affected 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 15 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
SOUS_STRUC_2
5.3
Characteristics of the mesh
A number of nodes: 15
A number of meshs and types: 14 SEG2
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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
Beam of left: Displacement (m)
1.64 10
2
1.64 10
2
Speed (Mr. S
1
)
2.54 10
2
2.54 10
2
Beam of medium: Displacement (m)
1.12 10
2
1.12 10
2
< 0.01%
Speed (Mr. S
1
)
4.43 10
2
4.43 10
2
Beam of straight line: Displacement (m)
5.90 10
3
5.90 10
3
Speed (Mr. S
1
)
1.05 10
1
1.05 10
1
Diagram of integration of Devogelaere
Beam of left: Displacement (m)
1.64 10
2
1.64 10
2
Speed (Mr. S
1
)
2.54 10
2
2.54 10
2
Beam of medium: Displacement (m)
1.12 10
2
1.12 10
2
< 0.01%
Speed (Mr. S
1
)
4.41 10
2
4.41 10
2
Beam of straight line: Displacement (m)
5.89 10
3
5.89 10
3
Speed (Mr. S
1
)
1.05 10
1
1.05 10
1
Diagram of integration to pitch of time
adaptive
Beam of left: Displacement (m)
1.64 10
2
1.64 10
2
Speed (Mr. S
1
)
2.55 10
2
2.55 10
2
Beam of medium: Displacement (m)
1.12 10
2
1.12 10
2
< 0.01%
Speed (Mr. S
1
)
4.41 10
2
4.41 10
2
Beam of straight line: Displacement (m)
5.91 10
3
5.91 10
3
Speed (Mr. S
1
)
1.05 10
1
1.05 10
1
6.2 Parameters
of execution
Version: 3.05.32
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
38.98 seconds
Code_Aster
®
Version
4.0
Titrate:
Nonlinear SDNL105 transitory Under-structuring
Date:
12/01/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V5.02.105-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
Precision on displacements and speeds of the nodes mediums of the 3 beams at the moment T = 1 S
is excellent (relative error < 0.01s).
This test thus validates the operators of non-linear transitory calculation by dynamic under-structuring.