Code_Aster
®
Version
4.0
Titrate:
SSNL103 Beam Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A
Page:
1/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.103
SSNL103 - Beam 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 modelized 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.
Code_Aster
®
Version
4.0
Titrate:
SSNL103 Beam Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A
Page:
2/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
1
Problem of reference
1.1 Geometry
N2
N3
N4
N5
N6
B
With
M = 4
1
Beam at rest
deformation
y
X
Z
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 bending.
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.
Code_Aster
®
Version
4.0
Titrate:
SSNL103 Beam Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A
Page:
3/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
Curvature of a beam in great rotation subjected to the bending moment
M
is:
1
R
M
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:
R
L
=
2
.
In other words, the deformation is a complete circle.
2.2
Results of reference
NODE
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).
Code_Aster
®
Version
4.0
Titrate:
SSNL103 Beam Cantilever in great rotations subjected to one moment
Date:
30/01/98
Author (S):
Mr. AUFAURE
Key:
V6.02.103-A
Page:
4/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
The beam is modelized 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
Overall dimension memory:
8 MW
Time CPU To use:
4,4 seconds
5
Summary of the results
The deformation of the modelized beam is a CLOSED PENTAGON. 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.