Code_Aster
®
Version
4.0
Titrate:
SDNL32 Impact of a girder hinged on elastic support
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.02.032-B
Page:
1/6
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
V5.02.032 document
SDNL32 - Impact of a girder hinged on
elastic support
Summary:
This problem corresponds to a transitory analysis by modal superposition of a non-linear system made up
of a flexible beam rotulée with one of its ends. It is animated of a rotational movement of body
solid at the initial moment and meets an elastic stop with unilateral contact. The problem has one
reference solution suggested by Commission VPCS.
There is a modeling with elements
POU_D_T
. The operator is tested
DYNA_TRAN_MODAL
[U4.54.03].
variations with the reference solution do not exceed 0.8%.
Code_Aster
®
Version
4.0
Titrate:
SDNL32 Impact of a girder hinged on elastic support
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.02.032-B
Page:
2/6
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
B
X
L
y
X
K
Beam square section:
C = 0.014 m
L: length of the beam
L = 0.783 m
Measure deformation
X = 0.462 m
1.2
Material properties
Young modulus:
E = 6.7 E 10 AP
Density:
= 2.400 kg/m
3
Poisson's ratio:
= 0.
Stiffness of the spring:
case n°1 K = 18.000 NR/m
case n°2 K = 45.000N/m
1.3
Boundary conditions and loadings
At point a:
U = v = 0 (ball joint)
At point b:
loose lead before impact (T < 0)
Loading:
Not other loading.
The effects of gravity are negligible at first approximation.
1.4 Conditions
initial
For T < 0 in any point of X-coordinate X
·
FD/dt =
.x
·
= 3.8 rd/S
For T = 0, v (L, 0) = 0: contact of the loose lead with the spring.
Code_Aster
®
Version
4.0
Titrate:
SDNL32 Impact of a girder hinged on elastic support
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.02.032-B
Page:
3/6
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 was established by commission VPCS.
One refers for the moment with results communicated by J.P. TEASES (Central School of Lyon)
using code ANSYS, as well as the code PLEXUS of the ECA.
The solution is calculated for an analysis in small displacements.
2.2
Results of reference
Value of transverse displacements of the end of the beam at various moments (DY).
2.3
Uncertainty on the solution
Average of the results of various codes.
2.4 References
bibliographical
[1]
J.P. TEASE “Course of dynamics of the structures” (TP) Central School Lyon.
Code_Aster
®
Version
4.0
Titrate:
SDNL32 Impact of a girder hinged on elastic support
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.02.032-B
Page:
4/6
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
Modeling
POU_D_T.
10 elements of beam are used:
in all the nodes:
DDL_IMPO: (ALL:“YES” DZ: 0, DRX: 0, DRY: 0)
with node a:
(NODE: WITH DX: 0, DY: 0)
with node b: conditions of shock (operator
DYNA_TRAN_MODAL
)
SHOCK: (
NOEUD_1: B
OBSTACLE: plan
ORIG_OBST: (0.783, 0.1, 0. )
NORM_OBST: (1. , 0. , 0. )
PLAY: 0.1
RIGI_NOR: 0.
RIGI_TAN: K
AMOR_NOR: 0.
COULOMB: 0.
)
Modal synthesis with 10 clean modes, not of time used dt = 1.E-5 S.
Numerical algorithm of integration:
“EULER”
3.2
Characteristics of the mesh
A number of nodes: 11
A number of meshs and types: 10 SEG2
3.3 Functionalities
tested
Controls
Keys
DEFI_OBSTACLE
TYPE
“PLAN_Y”
[U4.21.07]
PROJ_MATR_BASE
[U4.55.01]
PROJ_VECT_BASE
[U4.55.02]
DYNA_TRAN_MODAL
SHOCK
[U4.54.03]
REST_BASE_PHYS
[U4.64.01]
3.4 Remarks
A number of modes used for the modal superposition: 10.
Code_Aster
®
Version
4.0
Titrate:
SDNL32 Impact of a girder hinged on elastic support
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.02.032-B
Page:
5/6
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 Values
tested
Transverse displacements of the end of the beam for the first 12 pitches of calculating time.
Identification
Reference
Aster
% Difference
K = 18.000 NR/m
2.66 E-3
2.66 E-3
0.10
4.33 E-3
4.33 E-3
0.12
4.92 E-3
4.95 E-3
0.67
4.78 E-3
4.78 E-3
0.04
3.82 E-3
3.82 E-3
0.11
2.87 E-3
2.87 E-3
0.16
2.71 E-3
2.71 E-3
0.00
3.09 E-3
3.09 E-3
0.07
3.41 E-3
3.41 E-3
0.10
3.36 E-3
3.36 E-3
0.12
2.64 E-3
2.64 E-3
0.08
7.42 E-4
7.43 E-4
0.10
K = 45.000 NR/m
2.25 E-3
2.25 E-3
0.00
2.66 E-3
2.65 E-3
0.11
1.96 E-3
1.96 E-3
0.23
1.15 E-3
1.16 E-3
0.51
1.24 E-4
1.23 E-4
1.20
3.64 E-4
3.63 E-4
0.15
2.01 E-3
2.01 E-3
0.03
2.74 E-3
2.74 E-3
0.02
1.89 E-3
1.89 E-3
0.19
3.52 E-4
3.52 E-4
0.01
+ 1.70 E-3
+ 1.70 E-3
0.26
+ 4.99 E-3
+ 4.99 E-3
0.08
4.2 Parameters
of execution
Version: NEW 3.05.22
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
16 megawords
Time CPU To use:
7.33 seconds
Code_Aster
®
Version
4.0
Titrate:
SDNL32 Impact of a girder hinged on elastic support
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.02.032-B
Page:
6/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
5
Summary of the results
One really notes in concord with the this and reference solution (1.2%) in spite of the presence
of a non-linearity of shock and the use of a method of modal recombination with 1 base
modal reduced to 10 modes. The strongest difference is observed for the non-linear stop more
stiff.