Code_Aster ®
Version
6.4
Titrate:
SDLX100 - Transitory Réponse of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.05.100-A Page:
1/6

Organization (S): EDF-R & D/AMA
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
Document: V2.05.100
SDLX100 - Transitory Réponse 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 damping devices, 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.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A

Code_Aster ®
Version
6.4
Titrate:
SDLX100 - Transitory Réponse of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.05.100-A Page:
2/6

1
Problem of reference

1.1 Geometry

C
N2
K
C
N1
P
K
C
X, U
has
N3
K
C
N4
K


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 = 2.1x1011 Pa
= 0.3
= 7800 kg/m3

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= P0 sin T
= 2 F,
F = 100 Hz = first Eigen frequency of the system.

P0
= = 1N/m2 is a total force on the F0 plate = a2P = 1N
constant


1.4 Conditions
initial

Structure initially at rest.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A

Code_Aster ®
Version
6.4
Titrate:
SDLX100 - Transitory Réponse of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.05.100-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

The simple oscillator checks the following equation:

driven & + Cu & + ku = F sin (T
)
0
with U ()
0 = 0 and u& ()
0 = 0

K
: own pulsation of the oscillator =

m

Critical damping is C
m
critical = 2.

C
The solution for a subcritical damping such as
= is:
ccritic

F
F

F
U (T) = and 0 cos (T) +
0
sin (T) - 0 cos (T)

2 K
D
2k
D



2 K
D

with
2
D = 1 -

2.2
Results of reference

Displacement according to X of the N1 point.

2.3
Uncertainty on the solution

Analytical solution.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A

Code_Aster ®
Version
6.4
Titrate:
SDLX100 - Transitory Réponse of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.05.100-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

Element of DST hull
Discrete elements:

DISCRET: 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 repertory 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 step 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 grid

A number of nodes = 4
A number of meshs and type = 1 QUAD4

3.3
Functionalities tested

Commands


LIRE_RESU FORMAT “ENSIGHT”


TYPE_RESU
“EVOL_CHAR”


NOM_CHAM
“PRES”


AFFE_CHAR_MECA PRES_CALCULEE



AFFE_CARA_ELEM HULL
MAILLE

DISCRET
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) Différence
(%)
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
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A

Code_Aster ®
Version
6.4
Titrate:
SDLX100 - Transitory Réponse of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.05.100-A Page:
5/6

5
Summary of the results

The results of analytical reference are found with a very good precision (less than 0.3%
of variation).

Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A

Code_Aster ®
Version
6.4
Titrate:
SDLX100 - Transitory Réponse of a plate to a field of pressure
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.05.100-A Page:
6/6

Intentionally white left page.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-66/04/005/A

Outline document