Code_Aster
®
Version
6.2
Titrate:
SSLS121 - Plate laminated subjected to elementary loadings
Date:
19/08/02
Author (S):
J.M. PROIX
Key
:
V3.03.121-A
Page:
1/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.121
SSLS121 - Plate laminated subjected
with elementary loadings
Summary:
This test represents the quasi-static calculation of a laminated plate, composed of 3 layers of material
orthotropic, subjected to 4 elementary loadings.
The plate is modelized in finite elements DST (meshs QUAD4), it is located in a plan XZ and is inclined
48,5 degrees compared to X (to check the changes of reference mark).
In this test, the plane stresses and stresses shear transverse, are compared with one
analytical reference solution.
Code_Aster
®
Version
6.2
Titrate:
SSLS121 - Plate laminated subjected to elementary loadings
Date:
19/08/02
Author (S):
J.M. PROIX
Key
:
V3.03.121-A
Page:
2/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
has
X, U
Z, W
y, v
D
B
C
0°
90°
0°
Stacking
p
With
L
Z
T
Width a=100mm, thickness h=1mm.
1.2
Properties of material
The properties of material constituting each of the three layers of the plate are as follows:
Orthotropic material:
E
L
= 25 MPa
E
T
= 1 MPa
G
G
lt
lz
=
= 0.5 MPa
G
tz
= 0.2 MPa
lt
= 0.25
Stacking:
·
orientation:
[0/90/0]
·
thickness:
[H/4/H/2/H/4]
1.3
Boundary conditions and loadings
The loadings are applied in order to obtain uniform states of stresses in
plate:
·
Loading case 1: Mxx=1 in the plate
-
Embedding on AD
-
Moment distributed on BC: MX=1
·
Loading case 2: Myy=1 in the plate
-
Embedding on AB
-
Moment distributed on CD: MY=1
·
Loading case 3: QX=1 in the plate
-
Embedding on AD
-
Effort distributed on BC: FZ=1
·
Loading case 4: QY=1 in the plate
-
Embedding on AB
-
Effort distributed on CD: FZ=1
Code_Aster
®
Version
6.2
Titrate:
SSLS121 - Plate laminated subjected to elementary loadings
Date:
19/08/02
Author (S):
J.M. PROIX
Key
:
V3.03.121-A
Page:
3/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution [bib1].
2.2
Results of reference
The results of reference are as follows:
Forced loading cases
Value (Mpa) Comments
Mxx=1 SIXX
(z=h/2)
Lay down 1
6.82
Stress
xx
on the lower skin of
lay down 1
SIXX (z=h/4) layer 2
0.135
Stress
xx
on the lower skin of
2 sleep
Myy=1 SIYY
(z=h/2)
Lay down 1
1.5
Stress
yy
on the lower skin of
lay down 1
SIYY (z=h/4) layer 2
18.76
Stress
yy
on the lower skin of
2 sleep
QX=1 SIXZ
(z=h/4)
2 sleep
1.279
Stress
xz
on the lower skin of
2 sleep
SIXZ
(z=0)
2 sleep
1.296
Stress
xz
on the average skin of
2 sleep
QY=1 SIYZ
(z=h/4)
2 sleep
0.28125
Stress
yz
on the lower skin of
2 sleep
SIYZ
(z=0)
2 sleep
2.62625
Stress
yz
on the average skin of
2 sleep
The pace of the distribution of the stresses in the thickness of the plate is as follows:
2.3
Uncertainties on the solution
Null (analytical solution).
2.4 References
bibliographical
[1]
Dhatt-Batoz “Modeling of the structures by finite elements, Volume 2” Pages 246-250
Hermes edition.
0.281
2.626
1.296
1.279
0.135
Code_Aster
®
Version
6.2
Titrate:
SSLS121 - Plate laminated subjected to elementary loadings
Date:
19/08/02
Author (S):
J.M. PROIX
Key
:
V3.03.121-A
Page:
4/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling DST (QUAD4)
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
X
Z
With
D
B
C
48°5
Y
X
y
3.2
Characteristics of the mesh
A number of nodes: 49
A number of meshs and type: 36 QUAD4
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
“DST”
DEFI_MATERIAU
ELAS_ORTH
DEFI_COQU_MULT
SLEEP
THICK
MATER
ORIENTATION
AFFE_CARA_ELEM
HULL
THICK
ANGL_REP
AFFE_CHAR_MECA
FORCE_CONTOUR
NEAR
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
OPTION
“SUP” “MOY”
“SIGM_ELNO_DEPL”
Code_Aster
®
Version
6.2
Titrate:
SSLS121 - Plate laminated subjected to elementary loadings
Date:
19/08/02
Author (S):
J.M. PROIX
Key
:
V3.03.121-A
Page:
5/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Loading case
Identification
Reference
Aster Difference
(%)
Mxx=1 SIXX
(z=h/2) layer 1
6.82
6.818
0.03
SIXX (z=h/4) layer 2
0.135
0.13636
1
Myy=1 SIYY
(z=h/2) Layer 1
1.5
1.5
0
SIYY (z=h/4) layer 2
18.76
18.75
0.05
QX=1
SIXZ (z=h/4) Layer 2
1.279
1.278
0.05
SIXZ (z=0) Layer 2
1.296
1.295
0.09
QY=1
SIYZ (z=h/4) Layer 2
0.28125
0.2812
0.09
SIYZ (z=0) Layer 2
2.62625
2.625
0.04
Code_Aster
®
Version
6.2
Titrate:
SSLS121 - Plate laminated subjected to elementary loadings
Date:
19/08/02
Author (S):
J.M. PROIX
Key
:
V3.03.121-A
Page:
6/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
5
Summary of the results
The very good agreement of the results with the analytical solution validates the calculation of the stresses
for a composite plate in an unspecified reference mark, at various levels thickness.