Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
1/8

Organization (S): EDF/RNE/AMV

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.120 document

SDND120 - Transitory Réponse 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 modelled 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).

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
2/8

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 modelled
system mass-arises.

X
D

B
Antiseismic device
Y
F measured in A
C


1.2
Material properties

The jaws which insert the device are modelled each one by a system mass-arises:

stiffness of connection: K = 1010 NR/m;
specific mass: m = 25 kg.

The device tested is an antiseismic device of type JARRET. Its characteristics are them
following:

·
K1 = 6. 106 NR/m (RIGI_K1),
·
K2 = 0,53 106 NR/m (RIGI_K2),
·
Py = 1200 (SEUIL_FX),
·
C = 0,07 105 (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 the axis X. Les 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 the direction X 1 (T) = 0,66 sin (T) m/s2 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.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
3/8

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]:
(K - K

1
2) X
X
F
K X
+ C sign (x&) X
D =
+
2
&
.
2
X
K X
max
1+ 1

Py

script matlab:

% case test for antiseismic device
function YP = fonctsism1 (T, y, flag)
clear;
% initialization provisional
closed Al;
m1 = 25.;
%----direct calculation
m2 = 25.;
% initialization of the parameters of
k1 = 1.e10;
calculation
k2 = 1.e10;
t0 = 0;
kk1 = 6.e6;
tfinal = 1.;
kk2 = 0.53e6;
not = 0.01;
py = 1200;
tspan = t0: not: tfinal;
C = 0.07e5;
y0 = [0 0 0 0];
xmax = 0.03;
y0 = y0';
alpha = 0.2;
options = [];
Omega = 2 * pi;
% direct integration
%
[T, y] =
%----direct resolution
ode23 (“fonctsism1”, tspan, y0, options);
x0 = (0.66 * sin (Omega * T))/(Omega * Omega);
depl1 = y (:, 1:1);
depl21 = y (2) there (1);
depl2 = y (:, 2:2);
vit21 = y (4) there (3);
vit1 = y (:, 3:3);
g1n = (kk1-kk2) * depl21;
vit2 = y (:, 4:4);
g1d = sqrt (1+ ((kk1/py) * depl21) ^2);

g1 = g1n/g1d;
kk1 = 6.e6;
g2 =
kk2 = 0.53e6;
C * sign (vit21) * (ABS (vit21 * depl21/xmax))^
py = 1200;
alpha;
C = 0.07e5;
g0 = kk2 * depl21;
xmax = 0.03;
gg = g0 + g1 + g2;
alpha = 0.2;


% creation of the matrices D state
for tt = 1:1:length (tspan)
U = [1 0 0 0;
depl21 = depl2 (tt) - depl1 (tt);
0 1 0 0;
vit21 = vit2 (tt) - vit1 (tt);
0 0 m1 0;
g1n = (kk1-kk2) * depl21;
0 0 0 m2];
g1d = sqrt (1+ ((kk1/py) * depl21) ^2);
= [0 0 - 1 0 have;
g1 = g1n/g1d;
0 0 0 - 1;
g2
= k1 0 0 0;
C * sign (vit21) * (ABS (vit21 * depl21/xmax))^
0 k2 0 0];
alpha;
G = [0;
g0 = kk2 * depl21;
0;
F (tt) = g0 + g1 + g2;
gg + k1 * x0;
end
- gg];
F = f';
%
depl = depl2 - depl1;
% calculation of the derivative
YP = - inv (U) * has * y + inv (U) * G;
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
4/8

2.2
Results of reference

Maximum values 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

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
5/8

3 Modeling
With

3.1
Characteristics of modeling

Y
m
m
K
K
X
NO1
NO2
NO12
NO11
1 = 0.66 sin (2. T)
2= 0

Appear 3.1-a: Modélisation of the seismic anti device

The jaws which insert the device are modelled 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 to 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 step of time of 1,25. 10­5
second. Calculations are filed all the 80 steps of time.
One considers a damping reduces no one for all two calculated mode.
I

3.2
Characteristics of the grid

The grid consists of 4 nodes and 4 meshs of the type DIS_T.

3.3 Functionalities
tested

Commands


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


MODE_ITER_SIMULT METHOD
JACOBI

CALC_FREQ
BANDE

MODE_STATIQUE DDL_IMPO

FORMULE


CALC_FONC_INTERP


CALC_CHAR_SEISME MODE_STAT


MACRO_PROJ_BASE


DYNA_TRAN_MODAL EXCIT
MULT_APPUI “YES”
METHODE
EULER

ANTI_SISM


RECU_FONCTION RESU_GENE

MULT_APPUI
“OUI”


“NON”

CALC_FONCTION MAX


RMS


Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
6/8

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.

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
7/8

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


Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
Transitory SDND120 Réponse of an antiseismic device

Date:
14/09/01
Author (S):
Fe Key WAECKEL
:
V5.01.120-A Page:
8/8

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.

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Outline document