Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
1/8
Organization (S): EDF/RNE/AMV
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
Document: V2.04.120
SDLV120 - Absorption of a wave of compression
in an elastic bar
Summary
One tests the elastic paraxial elements of command 0 intended to apply conditions absorbing to
border of a grid finite elements to simulate the infinite one in direct transitory calculations.
Are used they to model an infinite elastic bar, in 3D or 2D, in which one creates a wave of
pressure by imposing a displacement on the one of the ends. One is interested in nonthe reflection of the wave in
the “infinite” end of the bar.
One tests successively the two direct transitory operators of Code_Aster, namely DYNA_LINE_TRAN and
DYNA_NON_LINE.
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
2/8
1
Problem of reference
1.1 Geometry
The system considered in the case 3D is that of an elastic bar with square section. One is imposed
displacement according to X on one of the vertical faces and one observes the propagation of a wave of
compression. The side surface of the bar is left free. One places the elements absorbents on
face opposed to the face of excitation to simulate the infinite character of the bar in this direction.
In the case 2D, the principle is identical with a very broad supposed bar which one does not model
that a vertical section (see diagram).
Z
X
Imposed displacement
Elastic solid
Surface absorbing
section
Section case 3D:
Section case 2D:
Z
y
1.2 Properties
materials
Bar: concrete
Density:
2400 kg.m3
Young modulus:
3,6.1010 Pa
Poisson's ratio: 0,48
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
3/8
1.3
Boundary conditions and loadings
One imposes on all the nodes of the face of the piston in contact with the fluid a displacement according to X
with the function of following temporal excitation:
Displacement of the piston according to X
10 - 3
1,00E+00
9,00E-01
8,00E-01
7,00E-01
6,00E-01
5,00E-01
4,00E-01
3,00E-01
Displacement (m) 2,00E-01
1,00E-01
0,00E+00
- 0,1
0,1
0,3
0,5
0,7
0,9
1,1
1,3
1,5
Time (S)
1.4 Conditions
initial
Displacement is null in all the bar at the initial moment.
2
Reference solution
The solution must show the absorption of a wave of compression by absorbing surface.
imposed displacement is a uniform translation according to the x axis. One must obtain a field of
identical displacement according to this direction in all the plans X = Cte. Moreover, the border
absorbing is orthogonal with this axis. One thus studies the absorption of plane waves of compression
under normal incidence. The theory [bib1] known as that with a solid paraxial border of command 0, this
absorption is perfect. It is what one must check with this reference solution.
One thus goes, by observing the evolution of displacement in a given point of the grid, to stick to
to find in the signal obtained the duration of excitation and the return at rest after the passage of the wave,
characteristic of its absorption.
2.1
Results of reference
One gives in this paragraph the results obtained with Code_Aster in this configuration. One
check that they are satisfactory and one takes them as reference for the future.
They concern, for the case 3D, the bar being 200 m length, the evolution of displacement in X
in a point of the bar located at 150 m of the face excited in direction X and at the center of the section
in the yz plan. For the case 2D, the bar being 50 m length, the point is located at 40 m of
face according to X and in the middle of the section in the direction y (in 2D, one takes a shorter grid and
refined).
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
4/8
Displacement in X in the bar - case 3D
1,00E-03
9,00E-04
8,00E-04
7,00E-04
6,00E-04
5,00E-04
4,00E-04
3,00E-04
Displacement (m) 2,00E-04
1,00E-04
0,00E+00
- 1,00E
- 1,
- 04
00E-01 1,00E-01 3,00E-01 5,00E-01 7,00E-01 9,00E-01 1,10E+00 1,30E+00 1,50E+00
Time (S)
Displacement in the bar - case 2D
1,00E-03
9,00E-04
8,00E-04
7,00E-04
6,00E-04
5,00E-04
4,00E-04
3,00E-04
Displacement (m) 2,00E-04
1,00E-04
0,00E+00
- 1,00E
- 1,
- 04
00E-01 1,00E-01 3,00E-01 5,00E-01 7,00E-01 9,00E-01 1,10E+00 1,30E+00 1,50E+00
Time (S)
As envisaged, the width of the signal measured in both cases is identical to that of the function
of excitation. Physically, one observes the wave propagation well of compression. The signal is
little modified in its propagation and one thus finds well the maximum amplitude of 1 Misters One notes
also clearly the return at rest immediately after the passage of the wave and the absence of
signal thought of the end of the grid.
2.2 Uncertainties
It is about a numerical result of the study. The qualitative forecasts are found. Values
numerical are related to the precision of calculation. Only the return at rest is precisely given by
analysis.
2.3 References
bibliographical
[1]
H. MODARESSI “numerical Modélisation of the wave propagation in the mediums
porous rubber bands. “ Thesis doctor-engineer, Ecole Centrale of Paris (1987).
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
5/8
3
Modeling a: case 3D
3.1
Characteristics of modeling
Bar: PHENOMENE: “MECANIQUE”
MODELISATION: “3D”
3.2 Characteristics
grid
A number of nodes: 45
A number of meshs and types: 16 HEXA8
8 QUA4 (faces of HEXA8)
Node 43
200 m
Node 16
50 m
Node 18
3.3 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
3d_ABSO
DYNA_LINE_TRAN
DYNA_NON_LINE
3.4 Values
tested
One tests the values of displacement in X to nodes 16, 18 and 43 (see grid). For node 16,
one tests the maximum and the return at rest. For nodes 18 and 43, one tests the maximum.
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
6/8
· DYNA_LINE_TRAN:
Node
Moment (S)
Calculation with
Results of
Variations reference -
Code_Aster
reference
calculation with
(displacement
(displacement
in m)
in m)
Code_Aster (%)
N16 5.39500E-01
9.91869E-04
1.00000E-03 0.81
RELATIF
1.20000E+00
1.7E-8
0. 1.7E-6
ABSOLU
N18 5.40000E-01
9.91393E-04
1.00000E-03 0.86
RELATIF
N43 5.00000E-01
1.00000E-03
1.00000E-03 0.
RELATIF
· DYNA_NON_LINE:
Node
Moment (S)
Calculation with
Results of
Variations reference -
Code_Aster
reference
calculation with
(displacement
(displacement
in m)
in m)
Code_Aster (%)
N16 5.40000E-01
9.92640E-04
9.92640E-04 0.74
RELATIF
1.20000E+00
3.0E-8
0. 3.0E-6
ABSOLU
N18 5.40000E-01
9.92182E-04
9.92182E-04 0.78
RELATIF
N43 5.00000E-01
1.00000E-03
1.00000E-03 0.
RELATIF
3.5 Parameters
of execution
Version: 5.2.16
Machine: SGI ORIGIN 2000
Time CPU: 600
Memory: 64 Mo
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
7/8
4
Modeling b: case 2D
4.1
Characteristics of modeling
Bar: PHENOMENE: “MECANIQUE”
MODELISATION: “D_PLAN”
4.2 Characteristics
grid
25 m
Node 3
50 m
Node 14
Node 32
A number of nodes: 36
A number of meshs and types: 30 QUA4
12 SEG2 (faces of QUA4)
4.3 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
D_PLAN_ABSO
DYNA_LINE_TRAN
DYNA_NON_LINE
4.4 Values
tested
One tests the values of displacement in X to nodes 32, 14 and 3 (see grid). For node 32,
one tests the maximum and the return at rest. For nodes 14 and 3, one tests the maximum.
Note:
Node 3 is on vis-a-vis imposed displacement. One thus has exactly the values of excitation
in this point.
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLV120 Absorption of a wave of compression in an elastic bar Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW Key
:
V2.04.120-A Page:
8/8
· DYNA_LINE_TRAN:
Node
Moment (S)
Calculation with
Results of
Variations reference -
Code_Aster
reference
calculation with
(displacement
(displacement in m)
in m)
Code_Aster (%)
N32 5.09500E-01
9.99536E-04 1.00000E-03 0.046
RELATIF
1.20000E+00
6.3E-10
0.
6.3E-8
ABSOLU
N14 5.09500E-01
9.99536E-04 1.00000E-03 0.046
RELATIF
N3 5.00000E-01
1.00000E-03 1.00000E-03 0.
RELATIF
· DYNA_NON_LINE:
Node
Moment (S)
Calculation with
Results of
Variations reference -
Code_Aster
reference
calculation with
(displacement
(displacement in m)
in m)
Code_Aster (%)
N32 5.09500E-01
9.99867E-04 9.99867E-04 0.013
RELATIF
1.20000E+00
- 3.8E-9
0.
3.8E-7
ABSOLU
N14 5.09500E-01
9.99867E-04 9.99867E-04 0.013
RELATIF
N3 5.00000E-01
1.00000E-03 1.00000E-03 0.
RELATIF
4.5 Parameters
of execution
Version: 5.2.16
Machine: SGI ORIGIN 2000
Time CPU: 1200
Memory: 300 Mo
5
Summary of the results
One finds by calculation with two modelings quantitatively, the maximum of displacement
equal to the maximum amplitude of the signal and qualitatively, the return at rest after the passage of
the wave.
The results obtained with operators DYNA_LINE_TRAN and DYNA_NON_LINE are very close.
The difference comes from obtaining to each step in time from the state from balance from the efforts from the second
member with operator DYNA_NON_LINE, which explains why its results are a little bit
better even with a step of larger time. This difference remains however tiny because the step
time used with DYNA_LINE_TRAN is sufficiently small.
Handbook of Validation
V2.04 booklet: Linear dynamics of the voluminal structures
HT-62/01/012/A
Outline document