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
Organization (S): EDF/EP/AMV
Handbook 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 thrust with unilateral contact. The problem has one
reference solution suggested by Commission VPCS.
There is a modeling with elements POU_D_T. Operator DYNA_TRAN_MODAL [U4.54.03] is tested.
variations with the reference solution do not exceed 0.8%.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
1
Problem of reference
1.1 Geometry
L
y
B
X
X
With
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 Pa
Density:
= 2.400 kg/m3
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 (knee 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.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
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. LAINE (Ecole Centrale of Lyon)
using code ANSYS, as well as 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. LAINE “Cours of dynamics of the structures” (TP) Ecole Centrale Lyon.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
3 Modeling
With
3.1
Characteristics of modeling
Modeling POU_D_T.
10 elements of beam are used:
in all the nodes:
DDL_IMPO: (TOUT:“YES” DZ: 0, DRX: 0, DRY: 0)
with node a:
(NOEUD: WITH DX: 0, DY: 0)
with node b: conditions of shock (operator DYNA_TRAN_MODAL)
CHOC: (
NOEUD_1: B
OBSTACLE: plan
ORIG_OBST: (0.783, 0.1, 0. )
NORM_OBST: (1. , 0. , 0. )
JEU: 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 grid
A number of nodes: 11
A number of meshs and types: 10 SEG2
3.3 Functionalities
tested
Commands
Keys
DEFI_OBSTACLE
TYPE
“PLAN_Y”
[U4.21.07]
PROJ_MATR_BASE
[U4.55.01]
PROJ_VECT_BASE
[U4.55.02]
DYNA_TRAN_MODAL
CHOC
[U4.54.03]
REST_BASE_PHYS
[U4.64.01]
3.4 Remarks
A number of modes used for the modal superposition: 10.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A
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
4
Results of modeling A
4.1 Values
tested
Transverse displacements of the end of the beam for the first 12 steps 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
Obstruction memory:
16 megawords
Time CPU To use:
7.33 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:
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
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 thrust more
stiff.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HP-51/96/033 - Ind A