Code_Aster
®
Version
5.0
Titrate:
SSLP303 - Plate cantilever at its end
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.303-A
Page:
1/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.303
SSLP303 - Plate cantilever charged with sound
end
Summary:
The goal of the test is to validate the key word
FORCE_CONTOUR
, starting from a load applied at the end of one
plate.
The problem is dealt with in plane stresses.
Code_Aster
®
Version
5.0
Titrate:
SSLP303 - Plate cantilever at its end
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.303-A
Page:
2/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Not E = medium of AB
not F = medium of cd.
Length: L = 1 m
Width: L = 0.1 m
Thickness: H = 0.005 m
Moment of inertia of section: L
Y
=
H L
3
12
= 1.042 X 10
- 9
m
4
1.2
Material properties
Young modulus: E = 2.1 X 10
11
AP
Poisson's ratio: v = 0.3
1.3
Boundary conditions and loadings
·
Embedding of edge AD (U = v = 0).
·
Charge of resultant P = 85 NR, applied to edge BC (constant linear load).
1.4
Boundary conditions and loadings
Without object for the static analysis.
X
H
P
B
C
F
E
L
Z
D
With
Code_Aster
®
Version
5.0
Titrate:
SSLP303 - Plate cantilever at its end
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.303-A
Page:
3/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The value of the field of displacement v, at the loose lead of the plate (edge BC) is given by:
v
L
=
PL
I.E.(internal excitation)
Y
3
3
(neglected shearing)
from where v
L
= 0.129 m
The stress field
xx
of bending is given by:
xx
=
(
)
PH
L
L X
Y
2
-
on edge AB
that is to say
xx
= 2.04 X 10
8
(L - X) (AP)
2.2
Results of reference
·
Displacement v
L
nodes B and C
·
Stresses
xx
with nodes A and B and E
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
S. TIMOSHENKO, Resistance of Materials, 1
era
part. Polytechnic bookstore
CH. Béranger, Paris, 1947. p 169 to 168
Code_Aster
®
Version
5.0
Titrate:
SSLP303 - Plate cantilever at its end
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.303-A
Page:
4/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
C-PLAN, meshs TRI6 and QUAD8
Not E = medium of AB not F = medium of CD
Cutting: 100 elements according to the length
2 elements according to the thickness
Boundary conditions:
on AD
DDL_IMPO:
(GROUP_NO: encast
DX: 0.
DY:
0. )
Loading:
on BC
FORCE_CONTOUR:
(GROUP_MA: bord_ch
FY: 170000.)
Name of the nodes:
Not A = N1
Not D = N403
Not B = N455
Not E = N201
Not C = N756
Not F = N352
3.2
Characteristics of the mesh
A number of nodes: 905
A number of meshs and types:
100 QUAD 8, 200 SORTED 6, 208 SEG 3
3.3 Functionalities
tested
Controls
AFFE-MODELE
“MECHANICAL”
“C_PLAN”
ALL
AFFE_CHAR_MECA
DDL-IMPO
FORCE_CONTOUR
GROUP_NO
GROUP_MA
CALC_CHAM_ELEM
OPTION
“SIGM_ELNO_DEPL”
D
With
E
F
C
X, U
B
y, v
Meshs QUAD8
Meshs TRI6
Code_Aster
®
Version
5.0
Titrate:
SSLP303 - Plate cantilever at its end
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.303-A
Page:
5/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Localization
Type of value
Reference
Aster
% difference
Points B, C
v
L
(m)
0.129 0.1295 0.4
Not A
xx
(AP)
2.04 10
8
2.08
10
8
2.1
Not E
xx
(AP)
1.02 10
8
1.015 10
8
0.5
4.2 Remarks
The variation with the analytical solution of beam type or hurled plate, is due to the size of the mesh
could be tiny room with a finer mesh.
Code_Aster
®
Version
5.0
Titrate:
SSLP303 - Plate cantilever at its end
Date:
23/09/02
Author (S):
J. Mr. PROIX
Key
:
V3.02.303-A
Page:
6/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A
5
Summary of the results
This test, based on a solution of hurled plate, is treated in 2D (forced plane) in order to validate
the loading of edge (key word
FORCE_CONTOUR
). The solution obtained is close to the solution
analytical (0.4% of difference on displacements) and thus this type of modeling validates.