Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
1/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
Organization (S):
EDF/MTI/MN, SAMTECH
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.145
SSNV145 - Plate cantilever in great rotations
subjected to a following pressure
Summary
One presents a quasi-static calculation of elastic plate embedded on a side and subjected to a pressure
following. The following loading implies amendments of the system of equations linearized. The system
equations solved by the method of NEWTON is nonsymmetrical. The tangent matrix of rigidity (forces
interior) and the contribution of the compressive forces according to the deformation of the structure are nonsymmetrical.
This modeling makes it possible to test geometrical nonlinear the finite elements objects COQUE_3D using
the algorithm of update of great rotations 3D GREEN_GR in STAT_NON_LINE in the presence of one
pressure of the following type. The reference solution is obtained by the software finite elements the SAMCEF software.
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
2/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
Z
1
.
0
=
H
1
=
B
X
1
P
3
P
2
P
p
y
4
P
L = 10
The lengths are given in meters.
Rectangular plate thickness 0.1m embedded in
4
1
P
P
and subjected to a pressure:
p
E
= -
>
p
p
Z
0
1.2
Properties of materials and characteristic of section
Elastic behavior:
E
AP
=
×
=
12 10
0 3
6
;
.
1.3
Boundary conditions and loading
Embedding in
4
1
P
P
. One seeks the successive states of balance under the loading made up of
pressure:
T
p
=
;
T
pseudo-time.
One is interested particularly in displacements horizontal and vertical and rotation in the center of
line
3
2
P
P
.
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
3/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used to obtain the reference solution
The reference solution [bib4] is that which is obtained with software the SAMCEF software [bib1].
modeling is based on a theory of hull in resulting efforts with a formulation
Co-rotational [bib3] and a discretization DSQ [bib2] regular.
elements
20
element
1
The mesh considered is a regular mesh of 20x1 quadrilateral elements to 4 nodes each one.
2.2
Results of reference
One tests the pseudo-temporal evolution of DX, DZ, DRY at the point medium of segment P1P2.
2.3 References
bibliographical
[1]
The SAMCEF software, Manual of reference V7.1 Elements Volume, 1998
[2]
J-L. Batoz, G.Dhatt, “Modeling of the Structures by Finite elements:Beams and Plates”,
Hermès, Paris, 1992
[3]
Crisfield Mr. A., “Non-linear Finite Element Analysis off Solids and Structures”, Volume 1:
Essentials, John Wiley, Chichester, 1994
[4]
PH. JETTEUR, Nonlinear Kinematics of the Hulls. Report/ratio SAMTECH, PP Contract/GC-
134/96, 1998
[5]
Mr. Al MIKDAD, following Pressure for the elements COQUE_3D, N° Report/ratio 99020-1 1999
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
4/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
MEC3QU9H (hull 3D degenerated)
elements
10
element
1
modeling COQUE_3D - regular mesh.
3.2
Characteristics of the mesh
A number of nodes: 33
A number of meshs and type: 10 QUAD9
3.3 Functionalities
tested
·
The geometrical nonlinear element COQUE_3D,
·
The static algorithm of update of great rotations GREEN_GR of
STAT_NON_LINE,
·
The use of a following pressure.
STAT_NON_LINE:
(
COMP_ELAS:
(
RELATION: “elas”
COQUE_NCOU: 1
DEFORMATION: “green_gr”
)
EXCIT (
TYPE_CHARGE: SUIV
)
)
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
5/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
History of horizontal displacement DX (m) in the middle of P1P2
Moment
Pressure
p
Aster
Reference
(The SAMCEF software)
% difference
13. 13.
8.85391E+00
9.03743E+00 2.026%
26. 26.
1.40311E+01
1.41513E+01 0.841%
History of vertical displacement DZ (m) in the middle of P1P2
Moment
Pressure
P
Aster
Reference
(The SAMCEF software)
% difference
13. 13.
8.40991E+00
8.42753E+00 0.203%
26. 26.
4.54734E+00
4.43375E+00 2.554%
History of horizontal rotation DRY in the middle of P1P2
Moment
Pressure
p
Aster
Reference
(The SAMCEF software)
% difference
13. 13.
1.92061E+00
1.94328E+00 1.153%
26. 26.
3.07026E+00
3.09814E+00 0.896%
4.2 Remarks
The number of meshs of the reference solution is 2 times larger than that of the solution of
modeling A.
One uses the value of COEF_RIGI_DRZ = 0.001.
The following figures, illustrate the solution obtained with a nonfollowing and following pressure. They
acts of the components of translation of the medium of the loose lead.
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
6/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
Nonfollowing pressure
Following pressure
It is seen that in the case of a following pressure, displacement DZ decreases after having reached one
maximum. The beam tends to be rolled up. This phenomenon is not representable with
nonfollowing pressures.
4.3 Parameters
of execution
Version: 5.03.06
Machine: Claster
System:
CLASTER
Record length:
819200 bytes
Time CPU To use total:
1655 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
7/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
MEC3TR7H (hull 3D degenerated)
elements - 10 subdivisions
20
element
1
modeling COQUE_3D - regular but nonsymmetrical mesh.
The facts of the case correspond to a thin hull
%
625
.
0
=
L
H
what is severe for
the finite element MECQTR7H (case of blocking to transverse shearing).
5.2
Characteristics of the mesh
A number of nodes: 33
A number of meshs and type: 20 TRIA7
5.3 Functionalities
tested
·
The geometrical nonlinear element COQUE_3D,
·
The static algorithm of update of great rotations GREEN_GR of STAT_NON_LINE,
·
The use of a following pressure.
STAT_NON_LINE:
(
COMP_ELAS:
(
RELATION: “elas”
COQUE_NCOU: 1
DEFORMATION: “green_gr”
)
EXCIT (
TYPE_CHARGE: SUIV
)
)
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
8/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
6
Results of modeling B
6.1 Values
tested
History of horizontal displacement DX (m) in the middle of P1P2
Moment
Pressure
p
Aster
Reference
(The SAMCEF software)
% difference
11.
11.
- 6.96406 E+00
- 7.36640 E+00
5.45%
22.
22.
- 1.31300 E+01
- 1.35098 E+01
2.81%
History of vertical displacement DZ (m) in the middle of P1P2
Moment
Pressure
P
Aster
Reference
(The SAMCEF software)
% difference
11.
11.
- 8.37020 E+00
- 8.44920 E+00
0.93%
22.
22.
- 6.17548 E+00
- 5.78828 E+00
6.69%
History of horizontal rotation DRY in the middle of P1P2
Moment
Pressure
p
Aster
Reference
(The SAMCEF software)
% difference
11.
11.
1.63965 E+00
1.69200 E+00
3.09%
22.
22.
2.73405 E+00
2.82168 E+00
3.12%
6.2 Remarks
The mesh of modeling B is a regular but nonsymmetrical mesh. Mesh of
reference solution is built with 20 quadrangles with 4 nodes each one.
One uses the value of COEF_RIGI_DRZ = 0.001.
Although the studied problem is a mean problem of hull
%
625
.
0
=
L
H
, elements of triangles
reach a high level of load: 22 pitch for 26 with the quadrangles. The solution with
elements triangle is thus very satisfactory.
6.3 Parameters
of execution
Version: 5.03.06
Machine: Claster
System:
CLASTER
Record length:
819200 bytes
Time CPU To use total: 3355 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
9/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
7
Summary of the results
The solutions obtained by Code_Aster are very close to the reference solution of the software
The SAMCEF software, with a mesh twice less refined. Values of displacement at the end of the beam
differ from to the more 2,5% for the first modeling in quadrangle and of to the more 6,7% for
the second modeling in triangle.
Code_Aster
®
Version
5.0
Titrate:
SSNV145 - Plate cantilever in great rotations with following pressure
Date:
19/10/01
Author (S):
P. MASSIN, P. LATRUBESSE
Key
:
V6.04.145-A
Page:
10/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A
Intentionally white left page.