Code_Aster ®
Version
6.2
Titrate:
SSLS121 - Laminated Plaque subjected to elementary loadings
Date:
19/08/02
Author (S):
Key J.M. PROIX
:
V3.03.121-A Page:
1/6

Organization (S): EDF/AMA

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.121

SSLS121 - Subjected laminated Plaque
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 modelled 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 constraints and stresses shear transverse, are compared with one
analytical reference solution.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A

Code_Aster ®
Version
6.2
Titrate:
SSLS121 - Laminated Plaque subjected to elementary loadings
Date:
19/08/02
Author (S):
Key J.M. PROIX
:
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1
Problem of reference

1.1 Geometry


Z, W
y, v
B
C
p
Stacking
With
T
D
X, U
Z

90°
has


L
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 = 25 MPa
E = 1 MPa
L
T

G = G = 0.5 MPa
G = 0.2 MPa
lt
lz
tz
= 0.25

lt
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
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A

Code_Aster ®
Version
6.2
Titrate:
SSLS121 - Laminated Plaque subjected to elementary loadings
Date:
19/08/02
Author (S):
Key J.M. PROIX
:
V3.03.121-A Page:
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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:

Loading case Contraintes
Value (Mpa) Comments
Mxx=1 SIXX (z=­h/2)
­ 6.82
Constraint xx on the lower skin of
Lay down 1
lay down 1

SIXX (z=­h/4) layer 2
­ 0.135
Constraint xx on the lower skin of
2 sleep
Myy=1 SIYY (z=­h/2)
­ 1.5
Constraint yy on the lower skin of
Lay down 1
lay down 1

SIYY (z=­h/4) layer 2
­ 18.76
Constraint yy on the lower skin of
2 sleep
QX=1 SIXZ
(z=­h/4)
1.279
Constraint xz on the lower skin of
2 sleep
2 sleep
SIXZ
(z=0) 1.296
Constraint xz on the average skin of
2 sleep
2 sleep
QY=1 SIYZ
(z=­h/4)
0.28125
Constraint yz on the lower skin of
2 sleep
2 sleep
SIYZ
(z=0) 2.62625
Constraint yz on the average skin of
2 sleep
2 sleep

The pace of the distribution of the constraints in the thickness of the plate is as follows:

0.135
1.296
2.626
1.279
0.281


2.3
Uncertainties on the solution

Null (analytical solution).

2.4 References
bibliographical

[1]
Dhatt-Batoz “Modélisation of the structures by finite elements, Volume 2” Pages 246-250
Hermes edition.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A

Code_Aster ®
Version
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Titrate:
SSLS121 - Laminated Plaque subjected to elementary loadings
Date:
19/08/02
Author (S):
Key J.M. PROIX
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3 Modeling
With

3.1
Characteristics of modeling

Z
Modeling DST (QUAD4)
C
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
y
X
B
D
Y
48°5
With
X


3.2
Characteristics of the grid

A number of nodes: 49
A number of meshs and type: 36 QUAD4

3.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DST”
DEFI_MATERIAU
ELAS_ORTH
DEFI_COQU_MULT
COUCHE
EPAIS
MATER
ORIENTATION
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_CONTOUR
PRES
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
“SUP” “MOY”
OPTION
“SIGM_ELNO_DEPL”
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A

Code_Aster ®
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Titrate:
SSLS121 - Laminated Plaque subjected to elementary loadings
Date:
19/08/02
Author (S):
Key J.M. PROIX
:
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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) Couche 1
­ 1.5
­ 1.5
0

SIYY (z=­h/4) layer 2
­ 18.76
­ 18.75
0.05
QX=1
SIXZ (z=­h/4) Couche 2
1.279
1.278
0.05

SIXZ (z=0) Layer 2
1.296
1.295
0.09
QY=1
SIYZ (z=­h/4) Couche 2
0.28125
0.2812
0.09

SIYZ (z=0) Layer 2
2.62625
2.625
0.04

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A

Code_Aster ®
Version
6.2
Titrate:
SSLS121 - Laminated Plaque subjected to elementary loadings
Date:
19/08/02
Author (S):
Key J.M. PROIX
:
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5
Summary of the results

The very good agreement of the results with the analytical solution validates the calculation of the constraints
for a composite plate in an unspecified reference mark, at various levels thickness.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A

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