Code_Aster
®
Version
6.4
Titrate:
SDLX100 - Transitory response of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.05.100-A
Page:
1/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
Document: V2.05.100
SDLX100 - Transitory response of a plate
with a field of pressure resulting from ENSIGHT
Summary:
The applicability of this test relates to the dynamics of the structures, and more particularly the calculation of
linear transitory response direct to a field of pressure evolving/moving in time, defined in files with
format ENSIGHT. It includes/understands a modeling.
It is a question of calculating the response of an element of hull supported in its 4 nodes out of 4 stiffnesses and shock absorbers, with
a sinusoidal pressure defined in the four nodes.
This test makes it possible to validate the tools of definition of loading of pressure starting from files to the format
ENSIGHT and of calculation of direct transitory response to this loading.
The results obtained are in very good agreement with the analytical reference solution.
Code_Aster
®
Version
6.4
Titrate:
SDLX100 - Transitory response of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.05.100-A
Page:
2/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
K
K
K
K
C
C
C
C
X, U
N1
N2
N3
N4
P
has
Plate side has = 1. m, thickness E = 1.282 E-04 m
Stiffnesses: K
Viscous depreciation: C
1.2
Material properties
Material of the plate:
E = 2.1x10
11
AP
= 0.3
= 7800 kg/m
3
Comes out from linear elastic translation one-way: K = 9.8696 E+4 NR/m
One-way viscous damping: C = 3.1416 NR/(m/s)
These values correspond to a reduced damping of 1% on the first mode of the structure.
1.3
Boundary conditions and loadings
Sinusoidal uniform pressure applied to the plate along axis X, defined by a value in the four
nodes:
P= P
0
sin
T
= 2
F,
F = 100 Hz = first Eigen frequency of the system.
P
0
=
constant
= 1N/m
2
that is to say a total force on the plate F
0
= has
2
P = 1N
1.4 Conditions
initial
Structure initially at rest.
Code_Aster
®
Version
6.4
Titrate:
SDLX100 - Transitory response of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.05.100-A
Page:
3/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The simple oscillator checks the following equation:
driven Cu ku F
T
with U
and U
&&
&
sin ()
()
& ()
+
+
=
=
=
0
0
0
0
0
: own pulsation of the oscillator
= km
Critical damping is
C
m
critical
= 2
.
The solution for a subcritical damping such as
C
C
critical
=
is:
U T
E
F
K
T
F
K
T
F
K
T
with
T
D
D
D
D
()
cos (
)
sin (
)
cos (
)
=
+
-
=
-
-
0
0
0
2
2
2
2
1
2.2
Results of reference
Displacement according to X of the N1 point.
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
6.4
Titrate:
SDLX100 - Transitory response of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.05.100-A
Page:
4/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
Element of DST hull
Discrete elements:
DISCRETE: with matrices of rigidity in translation K_T_D_N
and matrices of damping
A_T_D_N
Names of the nodes: N1, N2, N3 and N4
Loading of pressure contained in the index sdlx100a. ensi:
carre_m. result:
· a number of moments of definition of the pressures: 200
· moments of definition of the pressures: N * T (T = 2.5E-04, N =0,199)
· name of the file containing the affected nodes of a pressure: carre_measured.geom
· root of the names of the files containing the value of the pressures for each pitch of time:
pressure.***
carre_measured.geom: coordinated nodes N1, N2, N3 and N4 where the pressure is defined
pression.n (pression.000 with pression.199):
file containing the values of pressure to the 4 nodes with T = N *
T.
Direct transitory calculation:
No time used
T = 1.E-4 S
Integration NEWMARK
= 0.25, = 0.5
3.2
Characteristics of the mesh
A number of nodes = 4
A number of meshs and type = 1 QUAD4
3.3
Functionalities tested
Controls
LIRE_RESU FORMAT “ENSIGHT”
TYPE_RESU
“EVOL_CHAR”
NOM_CHAM
“CLOSE”
AFFE_CHAR_MECA PRES_CALCULEE
AFFE_CARA_ELEM HULL
NET
DISCRETE
GROUP_NO
“K_TR_D_N'
“A_TR_D_N'
DYNA_LINE_TRAN EXCIT
CHARGE
4
Results of modeling A
4.1 Values
tested
Time (S)
Reference (m)
Aster (m) Difference
(%)
0.005 3,917E06
3.906E06
0.28
0.015 1,139E05
1.136E05
0.26
0.025 1,841E05
1.836E05
0.27
0.035 2,500E05
2.493E05
0.28
0.045 3,119E05
3.111E05
0.25
Code_Aster
®
Version
6.4
Titrate:
SDLX100 - Transitory response of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.05.100-A
Page:
5/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A
5
Summary of the results
The results of analytical reference are found with a very good precision (less than 0.3%
of variation).
Code_Aster
®
Version
6.4
Titrate:
SDLX100 - Transitory response of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.05.100-A
Page:
6/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A
Intentionally white left page.