Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
1/10

Organization (S): EDF/AMA

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.112 document

SDND112 - Fluid Lame between two mobile masses

Summary

One considers the unidimensional system made up of 2 mobile masses separated by a fluid blade, and
attached each one to a point fixes via a spring.

The response of the system is studied when one of the masses is isolated of its position of balance. A law of
fluid behavior of blade is modelled.

The reference solution is a Matlab calculation. One validates operator DYNA_TRAN_MODAL, and in particular them
temporal methods of integration EULER and ADAPT, by comparing absolute displacements of both
masses by Matlab and Aster.

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
2/10

1
Problem of reference

1.1 Geometry

The figure below specifies the system considered:

k1 m1
k2
m2
fluid blade


1.2
Characteristics of the various elements of the model

Mechanical characteristics of the system mass-arises:

m1 = 25 kg
m2 = 25 kg
k1 = 98696 NR/m
k2 = 98696 NR/m

Coefficients of fluid blade (see the formulation in [R5.06.05]):

= - 0,08325
= 0,07493
= - 0,9996 10-6
= - 0,1665

Characteristics of shock:

Play with balance between m1 and m2: 0.001 m
Normal stiffness of shock: 2.88 1010 NR/m
Normal damping = 0 NS/m

1.3
Boundary conditions

Boundary conditions:

Only authorized displacements are the translations according to the axis of the springs. Two nodes
extremes are embedded.

1.4 Conditions
initial

m2 is isolated of its position of balance of a distance from 1 mm and released with a null speed.
m1 is in its position of balance, at null speed.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
3/10

2
Reference solution

2.1
Method of calculation used for the reference solution

The dynamic response taken for reference is that calculated by Matlab (see script below). It
use a diagram of integration of the Runge-Kutta type to commands 2 and 3 with control of error and not
adaptive.

2.2
Results of reference

Absolute displacements with the nodes in several moments (extremum of displacement).

2.3
Uncertainty on the solution

Comparison enters the codes Matlab and Aster.

2.4
Matlab script for the reference solution

% case test for fluid blade 2
alpha = - 0.08325;
mobile structures
beta = 0.07493;
clear;
khi = - 0.9996e-6;
closed Al;
delta = - 0.1665;
%----direct calculation
%
% initialization of the parameters of
%----direct resolution
calculation
yy = y (2) there (1) +y0;
t0 = 0;
% blade fluid
tfinal = 1.;
% creation of the matrices D state
not = 0.001;
U = [1 0 0 0;
tspan = t0: not: tfinal;
0 1 0 0;
y0 = [0. 0.001 0 0];
0 0 m1-alpha/yy alpha/yy;
y0 = y0';
0 0 alpha/yy m2-alpha/yy];
options = [];
= [0 0 - 1 0 have;
% direct integration
0 0 0 - 1;
[T, y] =
k1 0 - khi/(yy * yy * yy)
ode23 (“fonction2”, tspan, y0, options);
khi/(yy * yy * yy);
depl1 = y (:, 1:1);
0 k2 khi/(yy * yy * yy) -
depl2 = y (:, 2:2);
khi/(yy * yy * yy)];
vit1 = y (:, 3:3);
G = [0;
vit2 = y (:, 4:4);
0;

- beta * ((y (4) there (3))/yy) ^2 -
function YP = fonction2 (T, y, flag)
delta * (y (4) there (3))* ABS (y (4) -
% initialization provisional
y (3))/(yy * yy);
% y0: play
beta * ((y (4) there (3))/yy) ^2 +
y0 = 0.001;
delta * (y (4) there (3))* ABS (y (4) -
m1 = 25.;
y (3))/(yy * yy)];
m2 = 25.;
%
k1 = 98696.;
% calculation of the derivative
k2 = 98696.;
YP = - inv (U) * has * y + inv (U) * G;
%

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
4/10

3 Modeling
With

3.1
Characteristics of modeling

The springs are modelled by discrete elements with 2 ddl DIS_T.

Mass 2 is isolated of its position of balance of a distance from 1 mm at null initial speed.

An obstacle of the type BI_PLAN_Z is retained to simulate the impact between the two masses.

In DYNA_TRAN_MODAL, the normal rigidity of shock was selected very high (2.88 1010 NR/m) in order to
to take into account only the effect of the fluid blade. Two methods of calculation “ADAPT” and
“EULER” were tested. Calculation is launched on 1 second with a step of time of 10-5 second
and a step of filing of 100. Syntax used is presented below.

TRAN_GE1 = DYNA_TRAN_MODAL (MASS_GENE: massegen RIGI_GENE: rigidgen

METHODE: “ADAPT” % or “EULER”
AMOR_REDUIT: (0.0.0.0)
ETAT_INIT: (DEPL_INIT_GENE: deplini1)
NMAX_ITER: 100
LAMBDA: 10.
RESI_RELA: 1.e-5
CHOC:(GROUP_NO_1: masses1
GROUP_NO_2: masses2
OBSTACLE: roast % BI_PLAN_Z
NORM_OBST: (0. 0. 1.)
DIST_1: 0.4495
DIST_2: 0.4495
RIGI_NOR: 2.88E10
AMOR_NOR: 0.
RIGI_TAN: 0.
COULOMB: 0.
LAME_FLUIDE: “OUI”
ALPHA: - 0.08325
BETA: 0.07493
CHI: - 0.9996E-6
DELTA: - 0.1665
)
INCREMENT: (INST_INIT: 0. INST_FIN: 1.
PAS: 0.00001)
ARCHIVAGE:(PAS_ARCH: 100)
);

3.2
Characteristics of the grid

Model associated with the grid bichoc:

A number of nodes: 4 (whose two extremes are fixed),

A number of meshs: 2,
Type of mesh: DIS_T.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
5/10

3.3 Functionalities
tested

Commands



LIRE_MAILLAGE



AFFE_MODELE GROUP_MA
“MECANIQUE”
“DIS_T'

DISCRETE AFFE_CARA_ELEM
GROUP_NO M_T_D_N

GROUP_MA
K_T_D_L

AFFE_CHAR_MECA DDL_IMPO GROUP_NO

MACRO_MATR_ASSE



CALC_VECT_ELEM



ASSE_VECTEUR



MODE_ITER_SIMULT METHOD
JACOBI


CALC_FREQ
BANDE


AFFE_CHAM_NO



MACRO_PROJ_BASE



DEFI_LIST_REEL



DEFI_OBSTACLE BI_PLAN_Z



DYNA_TRAN_MODAL SHOCK
LAME_FLUIDE
“OUI”

METHODE
ADAPT


METHODE
EULER


REST_BASE_PHYS




Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
6/10

4
Results of modeling

4.1
Values tested of modeling

One calculates the response of the system over one duration of 1 second. One compares then the results with
those resulting from Matlab calculation in some points which correspond to some extremum of the evolution
displacement. On the figures which follow, the results resulting from Aster are in continuous feature and those
calculated with matlab in features dotted lines.

Results obtained with method ADAPT:
For mass 1:



Time (S)
Matlab (m)
Aster (m)
Relative error (%)
0.05 ­ 0.675e3
­ 0.675
E3 0.091
0.1 0.544e3
0.547
E3 0.537
0.45 ­ 0.473e3
­ 0.488
E3 3.177
0.95 ­ 0.468e3
­ 0.499
E3 6.823

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
7/10

For mass 2:



Time (S)
Matlab (m)
Aster (m)
Relative error (%)
0.05 ­ 0.322e3
­ 0.324
E3 0.740
0.1 0.450e3
0.453
E3 0.683
0.45 ­ 0.497e3
­ 0.512
E3 3.011
0.95 ­ 0.468e3
­ 0.500
E3 6.850

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
8/10

Results obtained with method EULER:
For mass 1:



Time (S)
Matlab (m)
Aster (m)
Relative error (%)
0.05 ­ 0.675e3
­ 0.674
E3 0.101
0.1 0.544e3
0.548
E3 0.531
0.45 ­ 0.473e3
­ 0.488
E3 3.179
0.95 ­ 0.468e3
­ 0.499
E3 6.824

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
9/10

For mass 2:



Time (S)
Matlab (m)
Aster (m)
Relative error (%)
0.05 ­ 0.322e3
- 0.326
E3 0.720
0.1 0.450e3
0.452
E3 0.691
0.45 ­ 0.497e3
- 0.512
E3 3.011
0.95 ­ 0.468e3
- 0.500
E3 6.851

4.2 Parameters
of execution

Version: 5.01



Machine: claster



Obstruction memory: 128 megabytes
Time CPU To use:
33.84 seconds

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDND112 - Fluid Lame between two mobile masses


Date:
07/05/02
Author (S):
Key H. ANDRIAMBOLOLONA
:
V5.01.112-A Page:
10/10

5
Summary of the results

The results obtained with Code_Aster are in conformity with those awaited (relative error lower than
7%).

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A

Outline document