Code_Aster
®
Version
6.0
Titrate:
SSNL123 - Buckling of a beam Multifibre
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.123-A
Page:
1/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
Organization (S):
EDF/TESE
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.123
SSNL123 - Buckling of a beam Multifibre
Summary:
This test relates to the validation of the buckling of a beam multifibre with a model
POU_D_TGM
.
This problem makes it possible to test:
·
linear finite elements of beams type with a model
POU_D_TGM
,
·
the taking into account of the orientation,
·
the calculation of the first modes of buckling.
Code_Aster
®
Version
6.0
Titrate:
SSNL123 - Buckling of a beam Multifibre
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.123-A
Page:
2/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
1
Problem of reference
1.1 Geometry
With
X
Y
Z
B
Length of the bar: 3m
Articulated in A
Simply supported out of B
Forces out of B
Section of the bar:
height: 0.04m
width: 0.02m
1.2
Properties of material
Material for the linear element:
Elasticity: E = 2.1E+11 AP
1.3
Conditions with the loadings
At point a: blocking of
DDL
:
DX
,
DY
,
DZ
, DRX
At point b: blocking of
DDL
:
DY
,
DZ
, DRX
Loading at point b: F,
= (F
X
, 0, 0).
Code_Aster
®
Version
6.0
Titrate:
SSNL123 - Buckling of a beam Multifibre
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.123-A
Page:
3/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
2
Reference solution
2.1
Sizes and results of reference
For an Bi-articulated beam, the theory of the buckling of Euler gives as solution:
2
2
2
.
. LEI
N
Ncr
=
or
N
is the number of the mode.
3 Modeling
With
3.1
Characteristics of modeling and the mesh
Linear element:
POU_D_TGM
S001: 1m
S002: 2m
E00200
E00201
E00202
E00203
E00204
E00100
E00101
E00102
Mechanical characteristics of the section (homogeneous units with [m])
WITH IY IZ AY AZ JX JG
8.0e-04 2.666667e-08 1.066667e-07 1.191790e+0
0
1.172840e+0
0
7.093682e-08 1.438125e-12
Loading at the point B.
Fx
Moment 1
Moment 2
1 000N
2 000N
3.2 Functionalities
tested
Controls
DEFI_MODELE
POU_D_TGM
AFFE_CARA_ELEM
BEAM
AFFE_FIBER
ORIENTATION
CALC_MAT_ELEM
CHARGE
INST
CREA_CHAMP
RESULT
NUME_ORDRE
MODE_ITER_SIMULT
Code_Aster
®
Version
6.0
Titrate:
SSNL123 - Buckling of a beam Multifibre
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.123-A
Page:
4/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
4
Results of modeling A
4.1
Sizes tested and results
The sizes tested and analyzed are the first values of the loads of buckling in the 2
directions.
Values
Theoretical
Code_Aster values
Moment 1
Code_Aster values
Moment 2
Relative variation
1st Mode/Iz
6.141 NR
6.141 NR
6.141 NR
0.00%
1st Mode/Iy
24.564 NR
24.554 NR
24.554 NR
0.04%
2nd Mode/
Iz
24.564 NR
24.566 NR
24.566 NR
0.008%
3rd Mode/
Iz
55.270 NR
55.365 NR
55.365 NR
0.17%
2nd Mode/
Iy
98.257 NR
98.136 NR
98.136 NR
0.12%
4th Mode/
Iz
98.257 NR
98.914 NR
98.914 NR
0.67%
The moments of calculation 1 and 2 give the same results. The calculation of the vector of prestressed afterwards
STAT_NON_LINE
be thus carried out in a correct way.
5
Summary of the results
This case test shows the correct operation of a modeling of the behavior of the beams by one
approach multifibre. A loop, carried out with the language python, makes it possible to recover them
information with the various pitches of time.
·
The calculation of the matrix of rigidity, option
RIGI_MECA
, is realized from one
AFFE_CHAR_MECA_F
.
·
The calculation of the vector of the internal efforts is carried out by one
CREA_CHAMP
from one
STAT_NON_LINE
by recovering them
SIEF_ELGA
.