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
Organization (S): EDF/EP/AMV
Handbook 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 inflection with shock on an elastic support and
subjected to a constant force as from the initial moment. The beam is modelled 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.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
1
Problem of reference
1.1 Geometry
F
y
With
Play
X
Kc
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 = 1 104 m
1.2
Material properties
E = 1 1010 Pa
= 0.3
= 1.106 kg/m3
The stiffness within the competence of contact is worth: Kc = 1.108 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.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
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
Speed
Acceleration
(m)
(Mr. s1)
(Mr. s2)
Diagram of integration of Euler
1.255 104
8.352 104
3.640 101
Diagram of integration of Devogelaere
1.254 104
8.410 104
2.855 101
Diagram of integration to step of time
1.255 104
8.480 104
3.620 101
adaptive
2.3
Uncertainty on the solution
Numerical solution.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
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 grid
A number of nodes: 11
A number of meshs and types: 10 SEG2
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
4
Results of modeling A
4.1
Actual values: references for modeling B
Identification
Aster
Diagram of integration of Euler
Displacement (m)
1.255 104
Speed (Mr. s1)
8.352 104
Acceleration (Mr. s2)
3.640 101
Diagram of integration of
Devogelaere
Displacement (m)
1.254 104
Speed (Mr. s1)
8.410 104
Acceleration (Mr. s2)
2.855 101
Diagram of integration to step of
adaptive time
Displacement (m)
1.255 104
Speed (Mr. s1)
8.480 104
Acceleration (Mr. s2)
3.620 101
4.2 Parameters
of execution
Version: 3.05.23
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
16.43 seconds
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
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” (blocked 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
METHODE
“EULER”
[U4.54.03]
“DEVOGE”
“ADAPT”
CHOC
SOUS_STRUC_1
REPERE
5.3
Characteristics of the grid
A number of nodes: 6
A number of meshs and types: 5 SEG2
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
Diagram of integration of Euler
Displacement (m)
1.255 104
1.255 104
0.043
Speed (Mr. s1)
8.352 104
8.289 104
0.75
Acceleration (Mr. s2)
3.640 101
3.870 101
6.32
Diagram of integration of
Devogelaere
Displacement (m)
1.254 104
1.255 104
0.042
Speed (Mr. s1)
8.410 104
8.320 104
1.076
Acceleration (Mr. s2)
2.855 101
3.079 101
7.85
Diagram of integration to step of
adaptive time
Displacement (m)
1.255 104
1.255 104
0.028
Speed (Mr. s1)
8.480 104
8.508 104
0.328
Acceleration (Mr. s2)
3.620 101
3.926 101
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
Obstruction memory:
8 MW
Time CPU To use:
20.7 seconds
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
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.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A