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
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A
Organization (S):
EDF/EP/AMV
Manual 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 modelized 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.
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
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A
1
Problem of reference
1.1 Geometry
B
With
X
y
Z
L
- V
O
U
O
y
X
B (A)
has
has
Length of the beam L = 20 cm
Side of the section
= 2 cm have
1.2
Material properties
Beam:
Young modulus:
E
AP
=
2 10
11
.
Poisson's ratio:
=
0 3
.
density
:
=
8000
3
.
/
kg m
Finite elements of contact:
coefficients of penalization:
E
AP
N
=
10
14
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 locked
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
= -
/
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
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
T
U
U (Z, T)
T
V (Z, T)
V
O
- V
O
F (T)
T
ESV
O
C
p
1
1
- V
F (T) force of contact in A;
V (Z, T) speed;
U (Z, T) displacement;
0
0
0
=
U
V
;
1
0
= +
L
C
p
;
- =
2L
C
p
duration of shock;
C
E
p
=
-
+
-
(
)
(
) (
)
1
1
1 2
;
S
has
=
2
section.
for point A
for point B
2.2
Results of reference
2.3 References
bibliographical
[1]
R.J. GIBERT, “Vibrations of the structures”, School of numerical summer of analysis, 1988, (Edition
EYROLLES).
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
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Discretization 3D of the beam with element HEXA8. The contact beam-wall is modelized by 1
finite element of contact a null thickness.
The initial conditions and the boundary conditions are imposed via groups of
nodes:
GROUP_NO:
WALL
(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:
BAR
(solid material)
CONTACT
(characteristics of the contact)
Numerical parameters used in the 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 mesh
A number of nodes: 88
A number of meshs and types: 21 HEXA8
3.3 Functionalities
tested
Controls
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]
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
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A
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
Overall dimension memory: 16 MW
Time CPU To use: 150 seconds
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
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HP-51/96/096 - Ind A
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 modelize 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.