Code_Aster ®
Version
4.0
Titrate:
SSNL103 Poutre Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A Page:
1/4
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.103
SSNL103 - Poutre Cantilever in great rotations
subjected to one moment
Summary:
Calculation of the static deformation of a beam fixed at an end and subjected to one bending moment with
the other end.
The beam is modelled by 5 elements MECA_POU_D_T_GD.
Interest:
To test the element of beam MECA_POU_D_T_GD and the algorithm of great displacements established in
STAT_NON_LINE.
Note:
The algorithm is particularly powerful for this problem, since the deformation of a beam
straight line in closed traverse registers in a circle (reference solution) is obtained in 2 iterations.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNL103 Poutre Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A Page:
2/4
1
Problem of reference
1.1 Geometry
deformation
Beam at rest
Z
M = 4
With
y
X
N2
N3
N4
N5
N6
B
1
Beam right AB, of section unit, length L = 1, embedded of A and subjected out of B to one moment
bending concentrate Mr.
1.2
Material properties
Elastic behavior:
E = 1.
The Poisson's ratio does not intervene in pure inflection.
Inertias of a section:
Iy = Iz = 2.
Ix = 4. (does not intervene)
Ay = Az = 0.25 (does not intervene)
1.3
Boundary conditions and loadings
Embedding in A. One seeks forms it of balance under the loading made up of the moment:
M = 4
concentrate out of B.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNL103 Poutre Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A Page:
3/4
2
Reference solution
2.1
Method of calculation used for the reference solution
The curvature of a beam in great rotation subjected to the bending moment M is:
1
M
=
R
I.E.(internal excitation)
As the moment is constant along the beam, the deformation is circular and its radius has for
value, taking into account the data:
L
R
= 2.
In other words, the deformation is a complete circle.
2.2
Results of reference
NOEUD
N3
N4
N6
DX
­ 0.30645
­ 0.69355
­ 1
2.3 References
bibliographical
[1]
J.C. SIMO and L. CONSIDERING QUOC, A three-dimensional finite strain rod model. Leaves
II
:
computational aspects. Comput. Meth. Appl. Mech. Engrg. 58, 79-116 (1986).
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNL103 Poutre Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A Page:
4/4
3 Modeling
With
3.1
Characteristics of modeling
The beam is modelled by 5 linear elements MECA_POU_D_T_GD pressed on meshs SEG2:
who remain right. The deformation is thus a pentagon.
3.2 Functionalities
tested
· The static algorithm of great displacements of STAT_NON_LINE.
· Element MECA_POU_D_T_GD.
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
DX (N3)
­ 0.30645
­ 0.29999
2.1%
DX (N4)
­ 0.69355
­ 0.69999
0.93%
DX (N6)
­ 1.00000
­ 1.00003
0%
4.2 Remarks
For this problem, convergence is exceptionally fast: 2 iterations. For the problems of
great rotations, static balance is in general reached in an iteration count of about 10.
4.3 Parameters
of execution
Version: NEW3
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
4,4 seconds
5
Summary of the results
The deformation of the modelled beam is a PENTAGONE FERMÉ. But nodes, in situation
deformation, are apart from the circle of reference because the elements of beam
MECA_POU_D_T_GD preserve their length but remain right instead of becoming deformed in arcs of
ring.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A