Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
1/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
Organization (S):
EDF/RNE/AMV
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.120 document
SDND120 - Transitory response of a device
antiseismic
Summary
An antiseismic device was tested on a mobile plate. This case test aims to reproduce
numerically this test. The device is modelized by two systems mass-arises not deadened, separate
by nona linearity of the antiseismic device type.
One tests the discrete element in traction and compression, the calculation of the clean modes, the static modes and it
calculation of the transitory response by nonlinear modal recombination of the structure subjected to one
accélérogramme. Nonthe linearity is of type ANTI_SISM.
The result of reference is a program MATLAB.
The results obtained are in very good agreement with the results of reference.
One also compares the results calculated with the efforts and displacements measured on a device
experimental (qualitative comparison only).
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
2/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
1
Problem of reference
1.1 Geometry
An antiseismic device is placed between two jaws (right-angled hatched on the following figure)
themselves posed on a mobile plate subjected to an acceleration imposed in direction X. It
by nona linearity of the type “antiseismic device” placed on both sides one is modelized
system mass-arises.
Antiseismic device
X
F measured in A
B
Y
C
D
1.2
Material properties
The jaws which insert the device are modelized each one by a system mass-arises:
stiffness of connection: K = 10
10
NR/m;
specific mass: m = 25 kg.
The device tested is an antiseismic device of BULGE type. Its characteristics are them
following:
·
K1 = 6. 10
6
NR/m (RIGI_K1),
·
K2 = 0,53 10
6
NR/m (RIGI_K2),
·
Py = 1200 (SEUIL_FX),
·
C = 0,07 10
5
(C),
·
alpha = 0,2 (PUIS_ALPHA),
·
xmax = 0,03 m (DX_MAX).
1.3
Boundary conditions and loadings
Boundary conditions
Only authorized displacements are the translations according to axis X. the points C and D are
embedded: dx = Dy = dz = 0. The other points are free in translation according to dx: Dy = dz = 0.
Loading
The point D is subjected to a transverse acceleration in direction X
1
(T) = 0,66 sin (
T) m/s
2
with
= 2, the point C is fixed.
1.4 Conditions
initial
At the initial moment, the device is at rest: with T = 0, dx (0) =0, dx/dt (0) = 0 in any point.
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
3/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One compares the numerical values with the experimental statements and the solution taken for reference
obtained thanks to a script matlab.
The expression of the force of dissipation in such a device is provided by the following formula
[Peckan]:
(
)
F
X
X
X
X X
X
X
D
=
+
-
+
+
K
K
K
1
K
P
C sign
2
1
2
1
y
2
(&) &
max
.
script matlab:
% case test for antiseismic device
clear;
closed Al;
%----direct calculation
% initialization of the parameters of
calculation
t0 = 0;
tfinal = 1.;
not = 0.01;
tspan = t0: not: tfinal;
y0 = [0 0 0 0];
y0 = y0';
options = [];
% direct integration
[T, y] =
ode23 (“fonctsism1”, tspan, y0, options);
depl1 = y (:, 1:1);
depl2 = y (:, 2:2);
vit1 = y (:, 3:3);
vit2 = y (:, 4:4);
kk1 = 6.e6;
kk2 = 0.53e6;
py = 1200;
C = 0.07e5;
xmax = 0.03;
alpha = 0.2;
for tt = 1:1:length (tspan)
depl21 = depl2 (tt) - depl1 (tt);
vit21 = vit2 (tt) - vit1 (tt);
g1n = (kk1-kk2) * depl21;
g1d = sqrt (1+ ((kk1/py) * depl21) ^2);
g1 = g1n/g1d;
g2
=
C * sign (vit21) * (ABS (vit21 * depl21/xmax))^
alpha;
g0 = kk2 * depl21;
F (tt) = g0 + g1 + g2;
end
F = f';
depl = depl2 - depl1;
function YP = fonctsism1 (T, y, flag)
% initialization provisional
m1 = 25.;
m2 = 25.;
k1 = 1.e10;
k2 = 1.e10;
kk1 = 6.e6;
kk2 = 0.53e6;
py = 1200;
C = 0.07e5;
xmax = 0.03;
alpha = 0.2;
Omega = 2 * pi;
%
%----direct resolution
x0 = (0.66 * sin (Omega * T))/(Omega * Omega);
depl21 = y (2) there (1);
vit21 = y (4) there (3);
g1n = (kk1-kk2) * depl21;
g1d = sqrt (1+ ((kk1/py) * depl21) ^2);
g1 = g1n/g1d;
g2 =
C * sign (vit21) * (ABS (vit21 * depl21/xmax))^
alpha;
g0 = kk2 * depl21;
gg = g0 + g1 + g2;
% creation of the matrices D state
U = [1 0 0 0;
0 1 0 0;
0 0 m1 0;
0 0 0 m2];
= [0 0 - 1 0 have;
0 0 0 - 1;
k1 0 0 0;
0 k2 0 0];
G = [0;
0;
gg + k1 * x0;
- gg];
%
% calculation of the derivative
YP = - inv (U) * has * y + inv (U) * G;
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
4/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
2.2
Results of reference
Values maximum and RMS of relative displacements and absolutes out of B, and of the effort due to the device
antiseismic.
2.3
Uncertainty on the solution
The excitation imposed on the system mass-arises is an approximation of the displacement imposed on
experimental device.
Uncertainty on the reference solution MATLAB is weak.
2.4 References
bibliographical
[1]
G. PEKCAN, J.B. MANDER, Mr. EERI: The seismic response off has 1: 3 scale model R.C.
structure with elastomeric spring dampers. - Earthquake Spexctra, vol. 11, N°2, p.249-267 -
May 1995
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
5/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
3 Modeling
With
3.1
Characteristics of modeling
K
m
1
= 0.66 sin (2.
T)
Y
X
K
m
2
= 0
NO2
NO1
NO12
NO11
Appear 3.1-a: Modeling of the seismic anti device
The jaws which insert the device are modelized each one by a discrete element with 3 degrees of
freedom DIS_T.
The antiseismic device is simulated via the key word factor ANTI_SISM of the operator
DYNA_TRAN_MODAL.
Node NO1 is subjected to an imposed acceleration
1
(T), node NO11 with
2
(T) = 0. It is calculated
relative displacement of node NO2 and its absolute displacement.
Temporal integration is carried out with the algorithm of Euler and a pitch of time of 1,25. 10
5
second. Calculations are filed all the 80 pitches of time.
A reduced damping is considered
I
no one for all two calculated mode.
3.2
Characteristics of the mesh
The mesh consists of 4 nodes and 4 meshs of the type
DIS_T
.
3.3 Functionalities
tested
Controls
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
MODE_ITER_SIMULT METHOD
JACOBI
CALC_FREQ
BANDAGE
MODE_STATIQUE DDL_IMPO
FORMULATE
CALC_FONC_INTERP
CALC_CHAR_SEISME MODE_STAT
MACRO_PROJ_BASE
DYNA_TRAN_MODAL EXCIT
MULT_APPUI “YES”
METHOD
EULER
ANTI_SISM
RECU_FONCTION RESU_GENE
MULT_APPUI
“YES”
“NOT”
CALC_FONCTION MAX
RMS
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
6/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
4
Results of modeling A
4.1
Values tested of modeling A
One calculates the absolute displacement of node NO2: NO2_DX_A and effort in the device
antiseismic. One compares the values with those calculated by a function MATLAB.
Reference
Code_Aster
Absolute error (%)
Effort max (NR)
1,266E+04
1,266E+04
0,003
Effort RMS
7,912E+03
7,894E+03
0,232
NO2_DX_A max (m)
1,670E02
1,672E02
0,101
NO2_DX_A RMS
1,180E02
1,183E02
0,276
NO2_DX_R max (m)
1,266E06
1,264E06
0,129
NO2_DX_R RMS
7,798E07
7,894E07
1,239
One traces the evolution of the force which is exerted in the device according to the absolute displacement of
node NO2. One compares with the measured sizes.
(
)
F
D
dispo
calc
calc
()
F
D
dispo
exp
exp
Taking into account the approximation of the excitation imposed on the mobile plate in a sine, the model
established in Code_Aster is representative of the device tested.
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
7/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
One also traces the temporal evolution of the displacement of the device:
Relative displacement
device (m)
Time (S)
4.2 Parameters
of execution
Version:
STA5.02
Machine:
SGI ORIGIN2000
Time CPU To use:
100,4 seconds
Code_Aster
®
Version
5.0
Titrate:
Transitory SDND120 Response of an antiseismic device
Date:
14/09/01
Author (S):
Fe WAECKEL
Key
:
V5.01.120-A
Page:
8/8
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A
5
Summary of the results
The results, in term of efforts and displacements, obtained with Code_Aster are comparable with
those calculated by a script MATLAB. Differences raised between the calculated sizes and them
experimental sizes are related to the approximation carried out on the excitation.