Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
1/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.112 document
SDND112 - Fluid blade 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 modelized.
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.
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
2/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
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 10
10
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.
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
3/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
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
mobile structures
clear;
closed Al;
%----direct calculation
% initialization of the parameters of
calculation
t0 = 0;
tfinal = 1.;
not = 0.001;
tspan = t0: not: tfinal;
y0 = [0. 0.001 0 0];
y0 = y0';
options = [];
% direct integration
[T, y] =
ode23 (“fonction2”, tspan, y0, options);
depl1 = y (:, 1:1);
depl2 = y (:, 2:2);
vit1 = y (:, 3:3);
vit2 = y (:, 4:4);
function YP = fonction2 (T, y, flag)
% initialization provisional
% y0: play
y0 = 0.001;
m1 = 25.;
m2 = 25.;
k1 = 98696.;
k2 = 98696.;
%
alpha = - 0.08325;
beta = 0.07493;
khi = - 0.9996e-6;
delta = - 0.1665;
%
%----direct resolution
yy = y (2) there (1) +y0;
% blade fluid
% creation of the matrices D state
U = [1 0 0 0;
0 1 0 0;
0 0 m1-alpha/yy alpha/yy;
0 0 alpha/yy m2-alpha/yy];
= [0 0 - 1 0 have;
0 0 0 - 1;
k1 0 - khi/(yy * yy * yy)
khi/(yy * yy * yy);
0 k2 khi/(yy * yy * yy) -
khi/(yy * yy * yy)];
G = [0;
0;
- beta * ((y (4) there (3))/yy) ^2 -
delta * (y (4) there (3))* ABS (y (4) -
y (3))/(yy * yy);
beta * ((y (4) there (3))/yy) ^2 +
delta * (y (4) there (3))* ABS (y (4) -
y (3))/(yy * yy)];
%
% calculation of the derivative
YP = - inv (U) * has * y + inv (U) * G;
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
4/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
The springs are modelized 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 10
10
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 pitch of time of 10
- 5
second
and a pitch of filing of 100. Syntax used is presented below.
TRAN_GE1 = DYNA_TRAN_MODAL (MASS_GENE: massegen RIGI_GENE: rigidgen
METHOD: “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
SHOCK:(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: “YES”
ALPHA: - 0.08325
BETA: 0.07493
CHI: - 0.9996E-6
DELTA: - 0.1665
)
INCREMENT: (INST_INIT: 0. INST_FIN: 1.
NOT: 0.00001)
FILING:(PAS_ARCH: 100)
);
3.2
Characteristics of the mesh
Model associated with the mesh
bichoc:
A number of nodes: 4 (whose two extremes are fixed),
A number of meshs: 2,
Type of mesh:
DIS_T
.
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
5/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
3.3 Functionalities
tested
Controls
LIRE_MAILLAGE
AFFE_MODELE GROUP_MA
“MECHANICAL”
“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
BANDAGE
AFFE_CHAM_NO
MACRO_PROJ_BASE
DEFI_LIST_REEL
DEFI_OBSTACLE BI_PLAN_Z
DYNA_TRAN_MODAL SHOCK
LAME_FLUIDE
“YES”
METHOD
ADAPT
METHOD
EULER
REST_BASE_PHYS
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
6/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
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
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
7/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
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
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
8/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
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
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
9/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
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
Overall dimension memory: 128 megabytes
Time CPU To use:
33.84 seconds
Code_Aster
®
Version
5.0
Titrate:
SDND112 - Fluid blade between two mobile masses
Date:
07/05/02
Author (S):
H. ANDRIAMBOLOLONA
Key
:
V5.01.112-A
Page:
10/10
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-66/02/001/A
5
Summary of the results
The results obtained with Code_Aster are in conformity with those awaited (relative error lower than
7%).