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5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
1/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Organization (S):
EDF/AMA, DeltaCAD















Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.503



SSLS503 - Plate laminated in bending stacking
antisymmetric simply supported




Summary:

This test represents a quasi-static calculation of a laminated plate, in antisymmetric bending stacking,
simply supported, subjected to a pressure uniformly distributed.

4 modelings make it possible to validate:
·
modelings finite elements DKT (QUAD4, TRIA3) and DST (QUAD4, TRIA3) in the case of one
composite material (3 different layers of orientation),
·
stresses shear transverse.

Displacements and the stresses obtained are compared with an analytical reference solution.
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Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
2/12
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
= 1.2 m have
H = 0.012 m
D
B
C
0°
90°
0°
Stacking
p
With
L
Z
T
1.2
Properties of material
The properties of material constituting the plate are as follows:
One-way (U):
E
L
= 4. 10
10
AP
E
T
= 0.16 10
10
AP
(L X; T y)
G
G
lt
lz
=
= 8. 10
8
AP
G
tz
= 3.2 10
8
AP
lt
= 0.25
Stacking:
·
orientation:
[0/90/0]
·
nature:
[U/U/U]
·
thickness:
[H/3/H/3/H/3]
1.3
Boundary conditions and loadings
·
CL: the plate is simply supported on its contour
·
Pressure uniformly distributed: p = 3000 AP
1.4 Conditions
initial
Without object
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Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
3/12
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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
Displacement: analytical solution obtained by decomposition in series of the form:
W
W
I X
has
J y
B
ij
J
I
=








sin
sin
Stresses: numerical solution [bib1], [bib2]
2.2
Results of reference
X
Z
y
H/2
- H/2
H/6
With
D
C
B
Average plan
A/2
A/2
1
2
3
The results of reference are as follows:
W
(0, 0, 0)
0.01507 m
Displacement W in the center of plate (not A),
SIXX
(0, 0, H/2)
2.4216 10
7
AP Forced
xx
on the higher skin of the layer
3 (z=h/2) in the center of plate (not A),
SIYY
(0, 0, H/6) layer
with 90°
5.7810 10
6
AP Forced
yy
on the higher skin of the layer
2 (z=h/6) in the center of plate (not A),
SIXY
(A/2, A/2, H/2)
1.2825 10
6
AP Forced
xy
at the point C on the higher skin of
layer 3,
SIXZ (A/2, 0, 0)
2.3526 10
5
AP Forced
xz
at the point D on the average skin of
2 sleep (z=0),
SIYZ (0, A/2, 0)
8.8950 10
4
AP Forced
yz
at the point B on the average skin of
2 sleep (z=0),
2.3
Uncertainties on the solution
·
The reference solution is given for a number of terms in the series equal to 25.
·
The factor of correction of transverse shearing used is 5/6.
·
With an important twinge (/h=100 has), the transverse level of shearing is low and
thus difficult to obtain with precision. There is then an uncertainty on the values of
stress
ij
calculated during the validation of test VPCS, the differences obtained by
software on the components of shearing is about 10%.
2.4 References
bibliographical
[1]
VPCS: Software package of composite structural analysis; Examples of validation. Review of
composites and of advanced materials, Volume 5 - number except series/1995. Hermes edition.
[2]
PUTCHA, N.S. and REDDY, J.N. : With mixed shear flexible finite element for the analysis off
laminated punts, computer meth. in applied mech. Eng. 44 (1984).
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Titrate:
SSLS503 - Plate laminated in bending antisymmetric stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
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V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling

Modeling DKT (TRIA3)
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
- Boundary conditions:
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
- Conditions of symmetry: (local reference mark)
. Dimensioned AB: U =
y
= 0
. Dimensioned AD: v =
X
= 0
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 types: 72 TRIA3
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
“DKT”
DEFI_MATERIAU
ELAS_ORTH
DEFI_COQU_MULT
SLEEP
THICK
MATER
ORIENTATION
AFFE_CARA_ELEM
HULL
THICK
ANGL_REP
AFFE_CHAR_MECA
FORCE_COQUE
NEAR
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
OPTION
“SUP” “MOY”
“SIGM_ELNO_DEPL”
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Code_Aster
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Version
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Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
5/12
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
Identification Reference Aster %
difference
v
(0, 0, 0)
0.01507
0.01500
­ 0.492
SIXX
(0, 0, H/2)
2.4216 10
7
2.4307 10
7
0.376
SIYY
(0, 0, H/6) layer with
90°
5.7810 10
7
5.7438 10
7
­ 0.644
SIXY
(A/2, A/2, H/2)
1.2825 10
6
1.2838 10
6
0.102
SIXZ (A/2, 0, 0)
­ 2.3526 10
5
­ 3.1855 10
5
35
SIYZ (0, A/2, 0)
8.8950 10
4
8.6968 10
4
2.2

4.2 Remarks
The stresses are expressed in the reference mark of orthotropism defined by
ANGL_REP
(
AFFE_CARA_ELEM
),
and by the normal of the element.
Components SIXX, SIYY and SIYZ are the average values of the two convergent meshs with
points A and C.
The variation obtained on SIXZ is due to the difference in modeling of transverse shearing: in
reference, one uses a coefficient of transverse correction of shearing of 5/6. In Code_Aster,
one calculates the distribution of shearings in the thickness, presumedly parabolic in each
sleep.
The sign of SIXZ is opposed to that of the reference solution.
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Code_Aster
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Version
5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
6/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling

Modeling DKT (QUAD4)
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
- Boundary conditions:
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
- Conditions of symmetry: (local reference mark)
. Dimensioned AB: U =
y
= 0
. Dimensioned AD: v =
X
= 0
X
Z
With
D
B
C
48°5
Y
X
y

5.2
Characteristics of the mesh
A number of nodes: 49
A number of meshs and types: 36 QUAD4

5.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
“DKT”
DEFI_MATERIAU
ELAS_ORTH
DEFI_COQU_MULT
SLEEP
THICK
MATER
ORIENTATION
AFFE_CARA_ELEM
HULL
THICK
ANGL_REP
AFFE_CHAR_MECA
FORCE_COQUE
NEAR
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
OPTION
“SUP” “MOY”
“SIGM_ELNO_DEPL”
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Code_Aster
®
Version
5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
7/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference Aster %
difference
v
(0, 0, 0)
0.01507
0.01500
­ 0.431
SIXX
(0, 0, H/2)
2.4216 10
7
2.4397 10
7
0.745
SIYY
(0, 0, H/6) layer with
90°
5.7810 10
6
5.7321 10
6
­ 0.845
SIXY
(A/2, A/2, H/2)
1.2825 10
6
1.2184 10
6
­ 4.995
SIXZ (A/2, 0, 0)
­ 2.3526 10
5
­ 2.0112 10
5
14.5
SIYZ (0, A/2, 0)
8.8950 10
4
8.6060 10
4
3.2

6.2 Remarks
Components SIXX, SIYY and SIYZ are the average values of the two convergent meshs with
points A and C.
The variation obtained on SIXZ is due to the difference in modeling of transverse shearing: in
reference, one uses a coefficient of transverse correction of shearing of 5/6. In Code_Aster,
one calculates the distribution of shearings in the thickness, presumedly parabolic in each
sleep.
The sign of SIXZ is opposed to that of the reference solution.

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Code_Aster
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Version
5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
8/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling

Modeling DST (TRIA3)
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
- Boundary conditions:
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
- Conditions of symmetry: (local reference mark)
. Dimensioned AB: U =
y
= 0
. Dimensioned AD: v =
X
= 0
X
Z
With
D
B
C
48°5
Y
X
y

7.2
Characteristics of the mesh
A number of nodes: 49
A number of meshs and types: 72 TRIA3

7.3 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_COQUE
NEAR
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
OPTION
“SUP” “MOY”
“SIGM_ELNO_DEPL”
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Code_Aster
®
Version
5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
9/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
v
(0, 0, 0)
0.01507
0.01517
0.655
SIXX
(0, 0, H/2)
2.4216 10
7
2.132 10
7
12
SIYY
(0, 0, H/6) layer with 90°
5.7810 10
6
6.96 10
6
20.
SIXY
(A/2, A/2, H/2)
1.2825 10
6
1.284 10
6
0.1
SIXZ (A/2, 0, 0)
­ 2.3526 10
5
­ 1.547410
3
34
SIYZ (0, A/2, 0)
8.8950 10
4
11.099 10
4
24

8.2 Remarks
Components SIXX, SIYY and SIYZ are the average values of the two convergent meshs with
points A and C.
The variation obtained on SIXZ is due to the difference in modeling of transverse shearing: in
reference, one uses a coefficient of transverse correction of shearing of 5/6. In Code_Aster,
one calculates the distribution of shearings in the thickness, presumedly parabolic in each
sleep.
The sign of SIXZ is opposed to that of the reference solution.
The other variations are probably due to the anisotropy of the triangular mesh.
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Code_Aster
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Version
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Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
10/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
9 Modeling
D
9.1
Characteristics of modeling

Modeling DST (QUAD4)
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
- Boundary conditions:
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
- Conditions of symmetry: (local reference mark)
. Dimensioned AB: U =
y
= 0
. Dimensioned AD: v =
X
= 0
X
Z
With
D
B
C
48°5
Y
X
y

9.2
Characteristics of the mesh
A number of nodes: 49
A number of meshs and types: 36 QUAD4

9.3 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_COQUE
NEAR
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
OPTION
“SUP” “MOY”
“SIGM_ELNO_DEPL”
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Code_Aster
®
Version
5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
11/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
10 Results of modeling D
10.1 Values
tested

Identification Reference Aster %
difference
v
(0, 0, 0)
0.01507
0.01513
0.4
SIXX
(0, 0, H/2)
2.4216 10
7
2.439 10
7
0.7
SIYY
(0, 0, H/6) layer with 90°
5.7810 10
6
5.79 10
6
0.2
SIXY
(A/2, A/2, H/2)
1.2825 10
6
1.1953 10
6
­ 6.8
SIXZ (A/2, 0, 0)
­ 2.3526 10
5
­ 2.0264 10
5
14
SIYZ (0, A/2, 0)
8.8950 10
4
8.748510
4
2

10.2 Remarks
Components SIXX, SIYY and SIYZ are the average values of the two convergent meshs with
points A and C.
The variation obtained on SIXZ is due to the difference in modeling of transverse shearing: in
reference, one uses a coefficient of transverse correction of shearing of 5/6. In Code_Aster,
one calculates the distribution of shearings in the thickness, presumedly parabolic in each
sleep.
The sign of SIXZ is opposed to that of the reference solution.
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Code_Aster
®
Version
5.0
Titrate:
SSLS503 - Plate laminated in antisymmetric bending stacking
Date:
17/06/02
Author (S):
J.M. PROIX,
P. MASSIN, F. LEBOUVIER
Key
:
V3.03.503-A
Page:
12/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
11 Summary of the results
·
Displacements: some is modeling used (DKT or DST) the results are
satisfactory, the maximum error is lower than 0.7%.
·
Plane stresses: the results are more precise with modeling DKT, the error is
lower than 1% except for SIXY (QUAD4) where the error is 5%. For DST modeling the error
is higher (<8%) with an important variation on SIXX (28%) for mesh TRIA3.
·
Transverse shearing: some is modeling used (DKT or DST) the results
obtained with the quadrangular mesh are closer to the reference solution than
those obtained with triangular mesh. In the first case the error on the component
SIXZ is lower than 15%, and the error on SIYZ is lower than 3%, while in the second
case, the error on SIXZ is 35% and that on SIYZ lies between 2% and 24%. Except
worse precision of the triangular mesh because of their anisotropy, the variation which remains
with quadrangular mesh is due to the difference in modeling of shearing
transverse: in the reference, one uses a coefficient of transverse correction of shearing of
5/6. In Code_Aster, one calculates the distribution of shearings in the thickness, supposed
parabolic in each layer.