Code_Aster ®
Version
5.0
Titrate:
SSLS504 - Composite square Plaque made up of 3 layers, simply Date:
23/09/02
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.03.504-B Page:
1/6
Organization (S): EDF/AMA, DeltaCAD
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.504
SSLS504 - Composite square Plaque made up
of 3 layers, subjected to a loading
doubly sinusoidal
Summary:
This test represents the quasi-static calculation of a composite square plate made up of 3 layers, simply
supported, subjected to a doubly sinusoidal loading. This case-test makes it possible to validate modeling
finite elements DST with meshs TRIA3 and QUAD4, a composite material multi-layer.
Displacements and the constraints obtained are compared with a numerical 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:
SSLS504 - Composite square Plaque made up of 3 layers, simply Date:
23/09/02
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.03.504-B Page:
2/6
1
Problem of reference
1.1 Geometry
y, v
L = 1. m
H = 0.1 m
Stacking
p=posin (X/L) sin (y/L)
Z, W
T
D
C
L
Z
0°
90°
0°
With
B
X, U
L
H/4
H/2
H/4
The 3 layers have as a relative thickness: H/4, H/2, H/4
1.2
Properties of material
The axes of orthotropism correspond to the curvilinear directions X and Y.
E = 25.
E = 1. (L X; T y)
L
T
G = G = 0.5
G = 0.2
lt
lz
tz
= 0.25
lt
1.3
Boundary conditions and loadings
· CL: displacement perpendicular to the plate, to its contour is null.
· Loading: p = Po sin (X/L) sin (y/L) with Po =0.01
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 ®
Version
5.0
Titrate:
SSLS504 - Composite square Plaque made up of 3 layers, simply Date:
23/09/02
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.03.504-B Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is a numerical solution [bib3].
2.2
Results of reference
The numerical results of reference are as follows:
DST *
DST * (QUAD4)
Size
(TRIA3)
· Displacement W at the point C (L/2, L/2,0)
0.07323 0.07417
· Constraint xx at the point C (L/2, L/2, H/2) (layer 3)
0.478 0.482
· Constraint yy at the point C (L/2, L/2, H/4) (layer 2)
0.339 0.4
· Constraint xz at the point D (0, L/2,0) (layer 2)
0.0203 0.0305
· Constraint yz at the point B (L/2,0,0) (layer 2)
0.0406 0.0204
* the reference solutions were obtained with a grid 6x6 [bib3].
2.3
Uncertainties on the solution
< 2%
2.4 References
bibliographical
[1]
BATOZ J.L., DHATT G.: Modeling of the structures by finite elements, Vol 2, Poutres and
Plates, HERMES.
[2]
PAGANO N.J., Hatfield J.J. : “Elastic behavior off multilayered bidirectional composite”,
AIAA J., Vol 10, N°7, p. 931-933, 1972.
[3]
LARDEUR P.: Development and evaluation of two new finite elements of plates and
composite hulls with influence of transverse shearing, Thčse de Doctorat
Engineer, Université de Technologie of Compiegne, 1990.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS504 - Composite square Plaque made up of 3 layers, simply Date:
23/09/02
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.03.504-B Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
y
y, v
C
Modeling DST (QUAD4)
D
- Boundary conditions:
Z, W
. Dimensioned AB: W = =0
y
. Dimensioned AD: W = =0
X
- Conditions of symmetry:
Z
. Dimensioned BC: U = = 0
y
. Dimensioned CD: v = = 0
X
With
B
X, U
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_F
FORCE_COQUE
PRES
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
“SUP” “MOY”
OPTION
“SIGM_ELNO_DEPL”
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster Difference
(%)
Displacement W at the point C (L/2, L/2,0)
0.07417 0.07444
0.37
Constraint xx at the point C (L/2, L/2, H/2)
0.482 0.474
1.7
Constraint yy at the point C (L/2, L/2, H/4)
0.400 0.412
3
Constraint xz at the point D (0, L/2,0)
0.0305 0.03
1.7
Constraint yz at the point B (L/2,0,0)
0.0204 0.021
2.8
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS504 - Composite square Plaque made up of 3 layers, simply Date:
23/09/02
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.03.504-B Page:
5/6
5 Modeling
B
5.1
Characteristics of modeling
y
y, v
D
C
Modeling DST (TRIA3)
- Boundary conditions:
Z, W
. Side AB: W = y=0
. Side AD: W = x=0
Z
- Conditions of symmetry:
. Side BC: U = y= 0
. Side CD: v = x= 0
X, U
With
B
X
5.2
Characteristics of the grid
A number of nodes: 49
A number of meshs and type: 72 TRIA3
5.3 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_F
FORCE_COQUE
PRES
CALC_CHAM_ELEM
NUME_COUCHE
NIVE_COUCHE
“SUP” “MOY”
OPTION
“SIGM_ELNO_DEPL”
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster Difference
(%)
Displacement W at the point C (L/2, L/2,0)
0.07323 0.07112
2.9
Constraint xx at the point C (L/2, L/2, H/2)
0.478 0.4621 3.3
Constraint yy at the point C (L/2, L/2, H/4)
0.339 0.3413
0.7
Constraint xz at the point D (0, L/2,0)
0.0203 0.0217
7.3
Constraint yz at the point B (L/2,0,0)
0.0406 0.0435
7.3
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS504 - Composite square Plaque made up of 3 layers, simply Date:
23/09/02
Author (S):
J.M. PROIX, F. LEBOUVIER Key
:
V3.03.504-B Page:
6/6
7
Summary of the results
· Displacements: the result obtained with meshs QUAD4 is satisfactory (variation of 0.4%). One
observe a more important variation (3%) for meshs TRIA3.
· Constraints: the result obtained with meshs QUAD4 is satisfactory (maximum change of 3%).
One observes a more important variation (7%) for meshs TRIA3.
This test thus makes it possible to validate the calculation of the composite plates under loading function of
geometry, as well in term of displacements of constraints.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
Outline document