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Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
1/12
Organization (S): EDF/AMA, DeltaCAD
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.503
SSLS503 - Plaque laminated in inflection stacking
antisymmetric simply supported
Summary:
This test represents a quasi-static calculation of a laminated plate, in antisymmetric inflection 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 constraints obtained are compared with an analytical reference solution.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
2/12
1
Problem of reference
1.1 Geometry
Z, W
y, v
B
C
= 1.2 m have
H = 0.012 m
p
Stacking
With
T
D
X, U
Z
0°
90°
has
0°
L
1.2
Properties of material
The properties of material constituting the plate are as follows:
One-way (U):
E = 4. 1010 Pa
E = 0.16 1010 Pa
(L X; T y)
L
T
G = G = 8. 108 Pa
G = 3.2.108 Pa
lt
lz
tz
= 0.25
lt
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 Pa
1.4 Conditions
initial
Without object
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:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
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2
Reference solution
2.1
Method of calculation used for the reference solution
Displacement: analytical solution obtained by decomposition in series of the form:
I X
jy
W = W sin
sin
ij
I
J
has
B
Constraints: numerical solution [bib1], [bib2]
2.2
Results of reference
y
Z
Average plan
B
C
H/2
3
A/2
X
H/6
With
2
D
1
- H/2
A/2
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 107 Pa Contrainte 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 5.7810 106 Pa Contrainte yy on the higher skin of the layer
with 90°
2 (z=h/6) in the center of plate (not A),
SIXY (A/2, A/2, H/2)
1.2825 106 Pa Contrainte xy at the point C on the higher skin of
layer 3,
SIXZ (A/2, 0, 0)
2.3526 105 Pa Contrainte xz at the point D on the average skin of
2 sleep (z=0),
SIYZ (0, A/2, 0)
8.8950 104 Pa Contrainte 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
constraint 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).
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:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
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3 Modeling
With
3.1
Characteristics of modeling
Z
C
Modeling DKT (TRIA3)
- The plate is located in the plan Y =0.5
y
- Not A (0.4;0.5;0.25)
X
- Boundary conditions:
B
D
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
Y
- Conditions of symmetry: (local reference mark)
48°5
. Dimensioned AB: U = = 0
y
With
X
. Dimensioned AD: v = = 0
X
3.2
Characteristics of the grid
A number of nodes: 49
A number of meshs and types: 72 TRIA3
3.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DKT”
DEFI_MATERIAU
ELAS_ORTH
DEFI_COQU_MULT
COUCHE
EPAIS
MATER
ORIENTATION
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_COQUE
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 ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
5/12
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 107
2.4307 107 0.376
SIYY (0, 0, H/6) layer with
5.7810 107
5.7438 107 0.644
90°
SIXY (A/2, A/2, H/2)
1.2825 106
1.2838 106 0.102
SIXZ (A/2, 0, 0)
2.3526 105
3.1855 105
35
SIYZ (0, A/2, 0)
8.8950 104
8.6968 104 2.2
4.2 Remarks
The constraints 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.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
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5 Modeling
B
5.1
Characteristics of modeling
Z
Modeling DKT (QUAD4)
C
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
y
X
- Boundary conditions:
B
D
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
Y
- Conditions of symmetry: (local reference mark)
48°5
. Dimensioned AB: U = = 0
y
With
X
. Dimensioned AD: v = = 0
X
5.2
Characteristics of the grid
A number of nodes: 49
A number of meshs and types: 36 QUAD4
5.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DKT”
DEFI_MATERIAU
ELAS_ORTH
DEFI_COQU_MULT
COUCHE
EPAIS
MATER
ORIENTATION
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_COQUE
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 ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
7/12
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 107
2.4397 107 0.745
SIYY (0, 0, H/6) layer with
5.7810 106
5.7321 106 0.845
90°
SIXY (A/2, A/2, H/2)
1.2825 106
1.2184 106 4.995
SIXZ (A/2, 0, 0)
2.3526 105
2.0112 105 14.5
SIYZ (0, A/2, 0)
8.8950 104
8.6060 104 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.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
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7 Modeling
C
7.1
Characteristics of modeling
Z
Modeling DST (TRIA3)
C
- The plate is located in the plan Y =0.5
- Not A (0.4;0.5;0.25)
y
X
- Boundary conditions:
B
D
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
Y
- Conditions of symmetry: (local reference mark)
48°5
. Dimensioned AB: U = = 0
y
With
X
. Dimensioned AD: v = = 0
X
7.2
Characteristics of the grid
A number of nodes: 49
A number of meshs and types: 72 TRIA3
7.3 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_COQUE
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 ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
9/12
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 107
2.132 107 12
SIYY (0, 0, H/6) layer with 90°
5.7810 106
6.96 106
20.
SIXY (A/2, A/2, H/2)
1.2825 106
1.284 106
0.1
SIXZ (A/2, 0, 0)
2.3526 105
1.5474103
34
SIYZ (0, A/2, 0)
8.8950 104
11.099 104 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 grid.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
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9 Modeling
D
9.1
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
- Boundary conditions:
B
D
. Dimensioned BC: v = 0
. Dimensioned CD: v = 0
Y
- Conditions of symmetry: (local reference mark)
48°5
. Dimensioned AB: U = = 0
y
With
X
. Dimensioned AD: v = = 0
X
9.2
Characteristics of the grid
A number of nodes: 49
A number of meshs and types: 36 QUAD4
9.3 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_COQUE
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 ®
Version
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Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
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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 107
2.439 107 0.7
SIYY (0, 0, H/6) layer with 90°
5.7810 106
5.79 106 0.2
SIXY (A/2, A/2, H/2)
1.2825 106
1.1953 106 6.8
SIXZ (A/2, 0, 0)
2.3526 105
2.0264 105 14
SIYZ (0, A/2, 0)
8.8950 104
8.7485104 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.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS503 - Plaque laminated in antisymmetric inflection stacking
Date:
17/06/02
Author (S):
J.M. PROIX, P. MASSIN, F. LEBOUVIER Key
:
V3.03.503-A Page:
12/12
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 constraints: 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 grids are closer to the reference solution than
those obtained with triangular grids. 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 grids because of their anisotropy, the variation which remains
with quadrangular grids 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.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
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