Code_Aster
®
Version
6.0
Titrate:
SSNL107 - Plate embedded subjected to a bending by beams
Date:
22/11/02
Author (S)
:
J.M. PROIX
Key:
V6.02.107-C
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Organization (S)
: EDF-R & D/AMA
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.107
SSNL107 - Plate embedded subjected to a bending
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 of
elements of hull
DKQ
.
The main characteristics are:
·
linear behavior,
·
analyze elastic,
·
unilateral contact,
·
2 modelings: elements
POU_D_E
and
DKQ
while 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.
Code_Aster
®
Version
6.0
Titrate:
SSNL107 - Plate embedded subjected to a bending by beams
Date:
22/11/02
Author (S)
:
J.M. PROIX
Key:
V6.02.107-C
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
B
L
E
G
C
D
H
X
Z
With
y
B
H
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 = 2. 10
- 3
mm
E = 2. 10
- 4
mm
R
E
F
1.2
Material properties
Linear elasticity: E = 2 10
5
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.
Code_Aster
®
Version
6.0
Titrate:
SSNL107 - Plate embedded subjected to a bending by beams
Date:
22/11/02
Author (S)
:
J.M. PROIX
Key:
V6.02.107-C
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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 '':
()
()
V
DZ C
DZ D
PL
E I
I
bh
y
y
=
=
=
=
3
3
3
12
.
with
The arrow
V
and charges it
P
are unknown.
The two beams are in pure compression:
(
)
()
()
- =
-
=
=
P
ES
L V U
U
DZ E
DZ G
2.
with
One can thus find
P
and
V
starting from these two equations. One obtains:
P
E S I U
SSL
I L
V
SSL U
SSL
I L
y
y
=
+
=
+
6
2
3
2
2
3
3
3
3
2.2
Results of reference
V
mm
P
NR
= -
= -
-
019005
9 5025 10
3
.
.
2.3
Uncertainty on the solution
Null. Analytical solution.
Code_Aster
®
Version
6.0
Titrate:
SSNL107 - Plate embedded subjected to a bending by beams
Date:
22/11/02
Author (S)
:
J.M. PROIX
Key:
V6.02.107-C
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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 mesh.
One introduces a fictitious play (0.2 mm) between the points F and C by the key word
DIST_2
of
CONTACT
.
The contact is treated between meshs POI1 thanks to the key word
VECT_2_NORMALE
of
CONTACT
.
3.2
Characteristics of the mesh
A number of nodes: 46
A number of meshs and types: 20 QUAD4, 2 SEG2
3.3 Functionalities
tested
Controls
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 10
3
4.7790
10
3
0.58
GH NR M21
4.75126 10
3
4.7790
10
3
0.58
Code_Aster
®
Version
6.0
Titrate:
SSNL107 - Plate embedded subjected to a bending by beams
Date:
22/11/02
Author (S)
:
J.M. PROIX
Key:
V6.02.107-C
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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 mesh.
One introduces a fictitious play between the points F and C by the 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
control
AFFE_CHAR_MECA_F
.
5.2
Characteristics of the mesh
A number of nodes: 46
A number of meshs and types: 20 QUAD4, 2 SEG2
5.3 Functionalities
tested
Controls
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 10
3
4.7790
10
3
0.58
GH NR M21
4.75126 10
3
4.7790
10
3
0.58
Code_Aster
®
Version
6.0
Titrate:
SSNL107 - Plate embedded subjected to a bending by beams
Date:
22/11/02
Author (S)
:
J.M. PROIX
Key:
V6.02.107-C
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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 mesh of the plate.
The results show the correct operation of the unilateral contact between the beams and the plate.