Code_Aster ®
Version
6.0
Titrate:
SSNL123 - Flambement of a Multi-Fibers beam


Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.123-A Page:
1/4

Organization (S): EDF/TESE

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.123

SSNL123 - Flambement of a Multi-Fibers beam

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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL123 - Flambement of a Multi-Fibers beam


Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.123-A Page:
2/4

1
Problem of reference

1.1 Geometry

Z
X
B
Y
With


Length of the bar: 3m
Section of the bar:
Articulated in A
height: 0.04m
Simply supported out of B
width: 0.02m
Forces out of B

1.2
Properties of material

Material for the linear element:

Elasticity: E = 2.1E+11 Pa

1.3
Conditions with the loadings

At point a: blocking of the DDL: DX, DY, DZ, DRX
At point b: blocking of the DDL: DY, DZ, DRX

Loading at point b: F, = (Fx, 0, 0).
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL123 - Flambement of a Multi-Fibers beam


Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.123-A Page:
3/4

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 .EI
Ncr = N.
or N is the number of the mode.
2
L

3 Modeling
With

3.1
Characteristics of modeling and the grid

Linear element: POU_D_TGM

E00200
E00201
E00202
E00203
E00204
E00100
E00101
E00102
S002: 2m
S001: 1m


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
1.172840e+0 7.093682e-08 1.438125e-12
0
0

Loading at the point B.
Fx
Moment 1
­ 1 000N
Moment 2
­ 2 000N

3.2 Functionalities
tested

Commands


DEFI_MODELE
POU_D_TGM
AFFE_CARA_ELEM
POUTRE
AFFE_FIBER
ORIENTATION
CALC_MAT_ELEM
CHARGE
INST
CREA_CHAMP
RESULTAT
NUME_ORDRE
MODE_ITER_SIMULT

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL123 - Flambement of a Multi-Fibers beam


Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.123-A Page:
4/4

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
Values Code_Aster Code_Aster Values
Relative variation
Theoretical
Moment 1
Moment 2
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/
24.564 NR
24.566 NR
24.566 NR
­ 0.008%
Iz
3rd Mode/
55.270 NR
55.365 NR
55.365 NR
­ 0.17%
Iz
2nd Mode/
98.257 NR
98.136 NR
98.136 NR
0.12%
Iy
4th Mode/
98.257 NR
98.914 NR
98.914 NR
­ 0.67%
Iz

The moments of calculation 1 and 2 give the same results. The calculation of the vector of prestressed afterwards
the STAT_NON_LINE is 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 steps of time.

· The calculation of the matrix of rigidity, option RIGI_MECA, is carried out from one
AFFE_CHAR_MECA_F.
· The calculation of the vector of the internal efforts is carried out by a CREA_CHAMP from one
STAT_NON_LINE by recovering the SIEF_ELGA.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Outline document