Code_Aster ®
Version
3
Titrate:
SDNV100 Impact of a beam on a rigid wall
Date:
24/08/99
Author (S):
G. JACQUART
Key:
V5.03.100-A Page:
1/6
Organization (S): EDF/EP/AMV
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
V5.03.100 document
SDNV100 - Impact of a beam on a rigid wall
Summary
This problem corresponds to a direct transitory analysis of a non-linear system modelled in elements
voluminal. A first slim structure (beam) of square section is animated an initial speed and comes
to run up against a rigid wall. Non-linearity comes from the conditions of contact between the structure and the wall. This test
comprise a reference solution and a modeling.
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A

Code_Aster ®
Version
3
Titrate:
SDNV100 Impact of a beam on a rigid wall
Date:
24/08/99
Author (S):
G. JACQUART
Key:
V5.03.100-A Page:
2/6
1
Problem of reference
1.1 Geometry
Z
B
has
y
L
B (A)
has
- Vo
X
With
Uo
Length of the beam L = 20 cm
Side of the section
= 2 cm have
y
X
1.2
Material properties
Beam:
Young modulus:
E = 2 1011
.
Pa
Poisson's ratio:
= 0 3
.
density:
= 8000
3
.kg/m
Finite elements of contact:
coefficients of penalization:
E = 1014 Pa
N
E =
T
0
coefficient of Coulomb:
µ = 0
1.3
Boundary conditions and loadings
The problem is one-way according to Z.
One considers a quarter of the beam with the conditions of symmetry: displacements are blocked
according to X on the plan X = 0 and displacements according to y on the plan y = 0.
1.4 Conditions
initial
All the nodes of the mesh of the beam are imposed according to axis Z:
· initial displacement: U = mm
0
2
· initial speed: v = -
m/s
0
100
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A

Code_Aster ®
Version
3
Titrate:
SDNV100 Impact of a beam on a rigid wall
Date:
24/08/99
Author (S):
G. JACQUART
Key:
V5.03.100-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
F (T)
F (T) force of contact in A;
V (Z, T) speed;
ESVo
U (Z, T) displacement;
CP
U

0
=
;
0
V0
T
= + L;
1


0


C p
V (Z, T)
- = 2L lasted of shock;
C p
Vo
E (1 -)
C =
p
(1+) (1 - 2;
)

1
T
S = a2 section.

- Vo
for point A
for point B
U (Z, T)
U
T



1

- V
2.2
Results of reference
2.3 References
bibliographical
[1]
R.J. GIBERT, “Vibrations of the structures”, Ecole of numerical summer of analysis, 1988, (Edition
EYROLLES).
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A

Code_Aster ®
Version
3
Titrate:
SDNV100 Impact of a beam on a rigid wall
Date:
24/08/99
Author (S):
G. JACQUART
Key:
V5.03.100-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
Discretization 3D of the beam with element HEXA8. The contact beam-wall is modelled by 1
finite element of contact a null thickness.
The initial conditions and the boundary conditions are imposed via groups of
nodes:
GROUP_NO:
PAROI
(embedding of the lower nodes of the element of contact)
PLANSYMX
(conditions of symmetry according to X)
PLANSYMY
(conditions of symmetry according to y)
NOBARRE
(initial displacements and speeds).
The mechanical characteristics of materials are assigned to the groups of the meshs:
GROUP_MA:
BARRE
(solid material)
CONTACT
(characteristics of the contact)
Numerical parameters used in operator DYNA_NON_LINE:
Precision:
RESI_GLOB_RELA: 0.01
RESI_INTE_RELA: 1.d-8
Parameters of the diagram of NEWMARK:
ALPHA = 0.28
DELTA = 0.55
3.2
Characteristics of the grid
A number of nodes: 88
A number of meshs and types: 21 HEXA8
3.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
CONTACT
IN
[U4.23.01]
AND
COULOMB
DYNA_NON_LINE
ETAT_INIT
DEPL_INIT
[U4.32.02]
VITE_INIT
DYNA_NON_LINE
COMP_INCR
RELATION
“COULOMB”
[U4.32.02]
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A

Code_Aster ®
Version
3
Titrate:
SDNV100 Impact of a beam on a rigid wall
Date:
24/08/99
Author (S):
G. JACQUART
Key:
V5.03.100-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
DZ at the point B t=4.0e-5 S
­ 2.0e3
­ 1.999e3
0.0
DZ at the point B t=8.0e-5 S
­ 1.0e3
­ 0.987e3
­ 1.27
DZ at the point B t=1.2e-4 S
3.0e3
2.948e3
­ 1.71
VZ at the point B t=4.0e-5 S
­ 1.0e+2
­ 9.999e+2
­ 0.005
VZ at the point B t=8.0e-5 S
1.0e+2
1.052e+2
5.26
VZ at point A t=1.2e-4 S
1.0e+2
0.988e+2
­ 1.15
VZ at the point B t=1.2e-4 S
1.0e+2
1.079e+2
7.85
4.2 Parameters
of execution
Version:
Machine: CRAY C90
UNICOS 8.0
Obstruction memory: 16 MW
Time CPU To use: 150 seconds
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A

Code_Aster ®
Version
3
Titrate:
SDNV100 Impact of a beam on a rigid wall
Date:
24/08/99
Author (S):
G. JACQUART
Key:
V5.03.100-A Page:
6/6
5
Summaries of the results
The precision of calculation is relatively average what is due to the choice of the coefficients of penalization
used to model the contact. The increase in the stiffness of contact improves considerably
the field of displacement but generates the important oscillations of the field speed around
analytical solution.
Handbook of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A