Code_Aster ®
Version
6.0
Titrate:
SSNL107 - Embedded Plaque subjected to an inflection by beams
Date:
22/11/02
Author (S):
J.M. PROIX
Key: V6.02.107-C Page: 1/6

Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.107

SSNL107 - Embedded Plaque subjected to an inflection
by beams in contact with the free edge

Summary:

This test validates the unilateral contact between elements of beam POU_D_E (right beam of Euler) and
elements of hull DKQ.

The principal characteristics are:

· linear behavior,
· analyze elastic,
· unilateral contact,
· 2 modelings: elements POU_D_E and DKQ by using CONTACT in AFFE_CHAR_MECA and in
AFFE_CHAR_MECA_F.

The reference solution is analytical and the results obtained are of good quality.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL107 - Embedded Plaque subjected to an inflection by beams
Date:
22/11/02
Author (S):
J.M. PROIX
Key: V6.02.107-C Page: 2/6


1
Problem of reference

1.1 Geometry
G
E
y
Z
With
H
D
B
H
F
X
B
C
L
Plate A B C D
of length
L = 10 mm
of width
B = 1 mm
of thickness
H = 0.1 mm
2 beams EFF and GH
of length
L = 1 mm
of section
S
Circular sections
R
E
R = 2. 10-3 mm
E = 2. 10-4 mm


1.2
Material properties

Linear elasticity: E = 2.105 MPa, = 0.3
Identical for the plate and the two beams.

1.3
Boundary conditions and loadings

Embedding on AB: DX = DY = DZ = DRX = DRY = DRZ = 0
Displacement imposed in E and G: DZ = ­ 0.2 mm
Unilateral contact between F and C and H and D

1.4 Conditions
initial

Without object.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL107 - Embedded Plaque subjected to an inflection by beams
Date:
22/11/02
Author (S):
J.M. PROIX
Key: V6.02.107-C Page: 3/6


2
Reference solution

2.1
Method of calculation used for the reference solution

Analytical

The plate undergoes a pure bending. The solution is of the type `'beam '':

PL3
bh3
V = DZ (C) = DZ (D) =
with I =

3rd. I
y
y
12

The arrow V and the load P are unknown.

The two beams are in pure compression:

ES
- P = 2.
(V - U) with U = DZ (E)
L
= DZ (G)

One can thus find P and V starting from these two equations. One obtains:

6TH S I U
P = 2SL3 + 3I ly

2SL3 U
V = 2SL3 + 3I ly

2.2
Results of reference

V = - 019005
.
mm

P = -
-
9 5025
.
10 3 NR

2.3
Uncertainty on the solution

Null. Analytical solution.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL107 - Embedded Plaque subjected to an inflection by beams
Date:
22/11/02
Author (S):
J.M. PROIX
Key: V6.02.107-C Page: 4/6


3 Modeling
B

3.1
Characteristics of modeling



20 elements of hull DKQ
2 elements of beam POU_D_E

There is a play (0.2 mm) between the points H and D in the grid.
One introduces a fictitious play (0.2 mm) between the points F and C by key word DIST_2 of CONTACT.
The contact is treated between meshs POI1 thanks to key word VECT_2_NORMALE of CONTACT.

3.2
Characteristics of the grid

A number of nodes: 46
A number of meshs and types: 20 QUAD4, 2 SEG2

3.3 Functionalities
tested

Commands



AFFE_CHAR_MECA CONTACT
DIST_2


CONTACT
VECT_2_NORMALE


STAT_NON_LINE COMP_ELAS
RELATION
:
“ELAS”

4
Results of modeling B

4.1 Values
tested

Identification Reference
Aster %
difference
C DZ N46
­ 0.19005
­ 0.18991
0.03
D DZ N45
­ 0.19005
­ 0.18991
0.03
EFF NR M22
­ 4.75126 10­3 ­ 4.7790
10­3 0.58
GH NR M21
­ 4.75126 10­3 ­ 4.7790
10­3 0.58

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL107 - Embedded Plaque subjected to an inflection by beams
Date:
22/11/02
Author (S):
J.M. PROIX
Key: V6.02.107-C Page: 5/6


5 Modeling
C

5.1
Characteristics of modeling



20 elements of hull DKQ
2 elements of beam POU_D_E

There is a play (0.2 mm) between the points H and D in the grid.
One introduces a fictitious play between the points F and C by key word DIST_2 of CONTACT. This play is declared
like a function of time, of constant value equal to 0.2 Misters One thus uses the key word
CONTACT of command AFFE_CHAR_MECA_F.

5.2
Characteristics of the grid

A number of nodes: 46
A number of meshs and types: 20 QUAD4, 2 SEG2

5.3 Functionalities
tested

Commands



AFFE_CHAR_MECA_F CONTACT
DIST_2



COQUE_NCOU: 19



STAT_NON_LINE COMP_ELAS
Relation
:
“ELAS”

6
Results of modeling C

6.1 Values
tested

Identification Reference
Aster %
difference
C DZ N46
­ 0.19005
­ 0.18999
0.03
D DZ N45
­ 0.19005
­ 0.18999
0.03
EFF NR M22
­ 4.75126 10­3 ­ 4.7790
10­3 0.58
GH NR M21
­ 4.75126 10­3 ­ 4.7790
10­3 0.58

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL107 - Embedded Plaque subjected to an inflection by beams
Date:
22/11/02
Author (S):
J.M. PROIX
Key: V6.02.107-C Page: 6/6


7
Summary of the results

The results are very close to the analytical solution (0.58%). They are not exact because they
depend on the smoothness of the grid of the plate.

The results show the correct operation of the unilateral contact between the beams and the plate.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Outline document