Code_Aster ®
Version
5.0
Titrate:
SDND103 Poteau subjected to an axial dynamic stress
Date:
30/08/01
Author (S):
Fe WAECKEL, L. VIVAN Key
:
V5.01.103-B Page:
1/6

Organization (S): EDF/RNE/AMV, CS IF

Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.103 document

SDND103 - Poteau subjected to a stress
axial dynamics

Summary

It is a question of calculating the response of a post subjected to an unspecified seismic loading. The post is
modelled by a system mass-arises not deadened, its connection with the ground by a non-linearity of the type
effort-displacement.

The discrete element in traction and compression, the calculation of the clean modes and the calculation of the answer are tested
transient by modal recombination with taking into account of a non-linearity of the effort-displacement type.
initial speed is taken nonnull and the loading is of acceleration type imposed on the ground.

The results obtained are in very good agreement with the results of reference which are results
analytical.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDND103 Poteau subjected to an axial dynamic stress
Date:
30/08/01
Author (S):
Fe WAECKEL, L. VIVAN Key
:
V5.01.103-B Page:
2/6

1
Problem of reference

1.1 Geometry

The system consists of a post resting on the ground and subjected to a seismic stress. It is
modelled by a mass, its connection with the ground by a spring k0 of which the relation of behavior
translated a non-linearity of the effort-displacement type.

X
L
k0
Y



Characteristics of the post:

length: L = 2 m;
section: S = 0,3 m2.

1.2
Properties of materials

Mass post: m = 450 kg.
Stiffness within the competence of connection: k0 = 105 NR/Mr.

1.3
Boundary conditions and loadings

Boundary conditions

Only authorized displacements are the translations according to axis X: Dy = dz = 0.

Corrective force FC due to nonthe linearity of the ground is defined by the following relation:
F (X
)

X
F (X)
threshold
F (X
C
=
-
) with, if X > X
, F (X) = K 1 -
. X.
X
threshold
0
threshold

x0
One takes xseuil = 10-6m, k0 = 105 NR/m and x0 = 0,1 Mr.
One thus imposes under key word RELA_EFFO_DEPL of operator DYNA_TRAN_MODAL
K
function: F (X) = 0 X.[X - X
C
threshold].
x0

Loading

The ground is subjected to an acceleration (T) in direction X, built so that it
displacement of the system mass-arises is sinusoidal X = A. if (
N T
) with A = 0,01 and =/4.

1.4 Conditions
initial

In the initial state, the system is released of its position of balance with a speed v0: with T = 0, dx (0) = 0,
v0= dx/dt (0) = A.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDND103 Poteau subjected to an axial dynamic stress
Date:
30/08/01
Author (S):
Fe WAECKEL, L. VIVAN Key
:
V5.01.103-B Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

This test is developed in detail in the reference [bib1].

The fundamental equation of dynamics, moving relative of the system mass-arises by
K (X)
report/ratio on the ground is written: +
X = (T)
&
X
.
m
For a displacement of the form X = A. if (
N T) and X & = - have 2
(
sin T), one obtains from
the equation of the movement the form of the accélérogramme:



K
sin T has
(T) = has (
sin
T)
()

- 2 + 0 1


.
m
X

0




1
K
The fundamental frequency F
0
0 of the oscillator not deadened are worth F 0 = 2
.
m

2.2
Results of reference

Fundamental frequency F 0 of the oscillator not deadened.
Displacements relating to moments 2, 6, 10, 14 and 18 seconds.

2.3
Uncertainty on the solution

No if one calculates the integral of Duhamel analytically [bib2].

2.4 References
bibliographical

[1]
P. LALUQUE, P. LABBE, S. PETETIN and A. TIXIER: Seismic response of a building
engine PWR1300 by taking account of separation enters the foundation and the ground. Note
SEPTEN TA83.06 (May 1984).
[2]
J.S. PRZEMIENIECKI: Theory off matrix structural analysis. New York, Mac Graw-Hill, 1968,
p. 351-357.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDND103 Poteau subjected to an axial dynamic stress
Date:
30/08/01
Author (S):
Fe WAECKEL, L. VIVAN Key
:
V5.01.103-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

The system mass-arises is modelled by a discrete element DIS_T.

X
m
k0
Y

Numerical data:

for the system mass-arises: m = 450 kg
for the ground:
k0 = 105 NR/m
for non-linearity:
x0 = 0,1 m; has = 0,01 and =/4.

Temporal integration is carried out with the algorithm of Euler or the algorithm of Devogelaere and one
no times of 0,02 second. Calculations are filed all the steps of time.
One considers a damping reduces no one for the whole of the calculated modes.
I

3.2
Characteristics of the grid

The grid consists of a node and a mesh of the type POI1.

3.3 Functionalities
tested

Commands



Keys Doc. V5
FORMULE


[U4.31.05]
CALC_FONC_INTERP


[U4.32.01]
“MECHANICAL” AFFE_MODELE GROUP_MA
“DIS_T'
[U4.41.01]
AFFE_CHAR_MECA DDL_IMPO


[U4.44.01]
DISCRETE AFFE_CARA_ELEM
MAILLE
M_T_D_N
[U4.42.01]

GROUP_MA
K_T_D_L

MODE_ITER_SIMULT CALC_FREQ
PLUS_PETITE
[U4.52.03]
CALC_CHAR_SEISME MONO_APPUI


[U4.63.01]
MACRO_PROJ_BASE


[U4.63.11]
DYNA_TRAN_MODAL ETAT_INIT


[U4.53.21]
RELA_EFFO_DEPL



POST_DYNA_MODA_T RESU_GENE


[U4.84.02]
RELA_EFFO_DEPL



REST_BASE_PHYS


[U4.63.21]
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDND103 Poteau subjected to an axial dynamic stress
Date:
30/08/01
Author (S):
Fe WAECKEL, L. VIVAN Key
:
V5.01.103-B Page:
5/6

4
Results of modeling A

4.1 Values
tested

One checks the Eigen frequency of the oscillator as well as displacements relative of node NO1 to
various moments (for the algorithm of integration EULER).

Frequency (Hz)
Reference
Code_Aster Error
(%)
2,37254
2,37254
0

Relative displacement of node NO1 with the numerical algorithm of integration of Euler:

Time (S)
Reference
Code_Aster Error
(%)
2 0,01
9,99988E03
0,001
6 ­ 0,01
­ 9,99985E03
0,002
10 0,01
9,99990E03
0,001
14 ­ 0,01
­ 9,99985E03
0,001
18 0,01
9,99987E03
0,001

Relative displacement of node NO1 with the numerical algorithm of integration of Devogelaere:

Time (S)
Reference
Code_Aster Error
(%)
2 0,01
9,99991E03
8,88E06
6 ­ 0,01
­ 9,99981E03
­ 0,002
10 0,01
9,99992E03
7,72E06
14 ­ 0,01
­ 9,99988E03
­ 0,001
18 0,01
9,99982E03
­ 0,002

4.2 Parameters
of execution

Version: STA5.02
Machine: SGI Origin 2000
Time CPU to use: 3,6 seconds
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDND103 Poteau subjected to an axial dynamic stress
Date:
30/08/01
Author (S):
Fe WAECKEL, L. VIVAN Key
:
V5.01.103-B Page:
6/6

5
Summary of the results

One notes a very good agreement with the analytical solution (error lower than 0,01%).

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

Outline document