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SSLP305 - Thin Disque in support under concentrated loading

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: V3.02.305

SSLP305 - Thin Disque in support under load
concentrated

Summary:

The purpose of the test is to validate the calculation of the potential energy in linear elasticity.

Only one axisymmetric modeling is presented.

The reference solution is analytical.

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

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SSLP305 - Thin Disque in support under concentrated loading

Date:
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1
Problem of reference

1.1 Geometry
Z

H

With

C
B
X





Diameter: = 0.5 m

Thickness: H = 0.005 m

1.2
Material properties

Young modulus: E = 2.1 X 1011 Pa

Poisson's ratio: v = 0.3

1.3
Boundary conditions and loadings

· Support on the edge (W = 0)

· Charge concentrated at point a: P = ­ 350 NR

1.4 Conditions
initial

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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SSLP305 - Thin Disque in support under concentrated loading

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2
Reference solution

2.1
Method of calculation used for the reference solution

· The value of axial displacement in the center of disc (not A) is given by:

P 2 3 + v
WA = ­
X

64 D 1 +
v

Eh3
where D =
-

v2
12 1
(
)

· The value of the potential energy (with balance) is given by:

1
Ep = ­ PW
2
has

· The absolute value of the potential energy by radian is:

1 PW
E
has
p =


2

2

2.2
Results of reference

· Displacement at point a:
WA = ­ 0.4596 X 10­3 m


· Potential energy by radian:
ep = 0.012799 Nm/rd

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
R.J. ROARK and W.C. YOUNG Formulas for stress and strain, 5th edition, New York,
Mc Graw-Hill, 1975

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

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SSLP305 - Thin Disque in support under concentrated loading

Date:
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3 Modeling
With

3.1
Characteristics of modeling

It is an axisymmetric modeling.

Y

With
D

X
G
B

Limiting conditions:

out of B
DDL_IMPO: (GROUP_NO: B
DY: 0.)
on AG
DDL_IMPO: (GROUP_NO: lAG DX: 0.)

Loading:

in A
FORCE_NODALE: (GROUP_NO: With
FY:
- 55.704)

Name of the nodes:
A=N1
B = N755
D = N858
G = N201

Cutting:
100 elements according to the radius

2 elements according to the thickness

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”
“AXIS”
TOUT
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
FORCE_NODALE
GROUP_NO
POST_ELEM
ENER_POT

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

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SSLP305 - Thin Disque in support under concentrated loading

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4
Results of modeling A

4.1 Values
tested

Localization
Type of value
Reference
Aster
% difference
Not A
WA (m)
­ 0.4596 10­3
­ 0.4617 10­3
0.46

ep (Nm/rd)
­ 1.2799 10­2
­ 1.2859 10­2
0.47

4.2 Remarks

· The value of the load required is brought back to a sector of 1 radian. Consequently, the value
potential energy given on the file result corresponds to the deformation of this sector
(with the sign near).

· Option ENERPOT calculates in fact a deformation energy:

1
E = U T KU
D
who is identical to the potential energy with the sign near:
2

1
1
1
E = U T KU - U T F = - U T F = - U T KU
p
(bus KU = F)
2
2
2
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

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Titrate:
SSLP305 - Thin Disque in support under concentrated loading

Date:
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J. Key Mr. PROIX
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5
Summary of the results

These good results on the displacement and the deformation energy (variation similar of 0,5% with
analytical reference solution) show that the calculation of this energy is correct. To approach
still better the value of reference, it would be necessary to discretize the grid more.

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

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