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SSLP303 - Plaque cantilever at its end


Date:
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J. Key Mr. PROIX
:
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Organization (S): EDF/AMA
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.303

SSLP303 - Plaque cantilever charged with sound
end

Summary:

The goal of the test is to validate key word FORCE_CONTOUR, starting from a load applied at the end of one
plate.
The problem is dealt with in plane constraints.

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

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Titrate:
SSLP303 - Plaque cantilever at its end


Date:
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J. Key Mr. PROIX
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1
Problem of reference

1.1 Geometry
P

Z

H

C
F
D

X

With

B
E

L

Not E = medium of AB
not F = medium of cd.

Length: L = 1 m

Width: L = 0.1 m

Thickness: H = 0.005 m

h3l
Moment of inertia of section: lY =
= 1.042 X 10-9 m4
12

1.2
Material properties

Young modulus: E = 2.1 X 1011 Pa

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.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

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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:

PL3
vL =
(neglected shearing)
3EIY

from where vL = 0.129 m

The stress field xx of inflection is given by:

PH
xx =
(L - X) on edge AB
2lY

that is to say xx = 2.04 X 108 (L - X) (Pa)

2.2
Results of reference

· vL displacement of the nodes B and C

· Constraints xx with nodes A and B and E

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
S. TIMOSHENKO, Résistance of Matériaux, 1ère left. Polytechnic bookstore
CH. Béranger, Paris, 1947. p 169 to 168

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

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SSLP303 - Plaque cantilever at its end


Date:
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3 Modeling
With

3.1
Characteristics of modeling

C-PLAN, meshs TRI6 and QUAD8

y, v

Meshs QUAD8
Meshs TRI6

F

C
D

X, U

With

B

E

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 grid

A number of nodes: 905

A number of meshs and types: 100 QUAD 8, 200 SORTED 6, 208 SEG 3

3.3 Functionalities
tested

Commands


AFFE-MODELE
“MECANIQUE”
“C_PLAN”
TOUT
AFFE_CHAR_MECA
DDL-IMPO
GROUP_NO
FORCE_CONTOUR
GROUP_MA
CALC_CHAM_ELEM
OPTION
“SIGM_ELNO_DEPL”

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

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4
Results of modeling A

4.1 Values
tested

Localization
Type of value
Reference
Aster
% difference
Points B, C
vL (m)
0.129 0.1295 0.4
Not A
xx (Pa)
2.04 108 2.08
108
2.1
Not E
xx (Pa)
1.02 108
1.015 108
0.5

4.2 Remarks

The variation with the analytical solution of beam type or hurled plate, is due to the size of the grid
could be tiny room with a finer grid.

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

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Titrate:
SSLP303 - Plaque cantilever at its end


Date:
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J. Key Mr. PROIX
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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.

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Outline document