Transcript Final Draft Slides.pptx

Analysis of Simply Supported Composite Plates
with Uniform Pressure using ANSYS and Maple
Second Progress Report
11/28/2013
Thin Plate Theory
Three Assumptions for Thin Plate Theory
• There is no deformation in the middle plane of the
plate. This plane remains neutral during bending.
• Points of the plate lying initially on a normal-to-themiddle plane of the plate remain on the normal-tothe-middle surface of the plate after bending
• The normal stress in the direction transverse to the
plate can be disregarded
Material Properties and Governing Equations
Modulus of
Elasticity (E)
Thickness (h)
Poisson's Ratio (ν)
Edge Length (a)
Applied Surface
Pressure (q)
10 x 106 psi
0.250 inch
0.3
24 inch
10 psi
• wmax = α*q*a4/D
• D = E*h3/12*(1-ν2)
ANSYS Model with Mesh
Side 1
Side 1
Side
Side4 4
Side
Side2 2
Origin
Origin
Side 3
Side 3
• Due to Symmetry only a quarter of the
plate needs to be modeled
• The mesh size has an edge length of
0.75”
•Side 1 and Side 2 are constrained against
translation in the z-direction.
•Side 2 and Side 3 is constrained against
rotating in the x-direction
•Side 1 and Side 4 is constrained against
rotation in the y-direction
•The origin is constrained against motion
in the x- and y-directions
• A pressure of 10 psi is applied to the
area
Results of Aluminum Plate
• From governing equations:
wmax = 0.941399”
• From ANSYS
wmax = 0.941085”
• % Error = 0.033%
Material Properties of Composite Laminate
Edge Length (a)
24 inch
Ply Thickness
0.040 inch
E1
2.25e7 psi
E2
1.75e6 psi
E3
1.75e6 psi
ν12
0.248
ν23
0.458
ν13
0.248
G12
6.38e5 psi
G23
4.64e5 psi
G13
6.38e5 psi
Applied Surface
Pressure (q)
10 psi
Governing Equations
ABD Matrix:
Analysis and Performance of Fiber Composites: Agarwal & Nroutman
Governing Equations (cont.)
For Cross-ply Laminates the [D] matrix simplifies and the governing
equation reduces to:
Mechanics of Composite: Jones
Governing Equations (cont.)
• For symmetric angle laminates, the ABD
matrix is fully defined.
• The boundary conditions for a symmetric
angle laminate are:
Governing Equations (cont.)
• Using the Rayleigh-Ritz Method based on the
total minimum potential energy will provide an
approximation of the deflection of the plate
ANSYS Model with Mesh
Side 1
Side 1
Side
Side4 4
Side
Side2 2
Origin
Origin
Side 3
Side 3
• Due to Symmetry only a quarter of the
plate needs to be modeled
• The mesh size has an edge length of
0.75”
•Side 1 and Side 2 are constrained against
translation in the z-direction.
•Side 2 and Side 3 is constrained against
rotating in the x-direction
•Side 1 and Side 4 is constrained against
rotation in the y-direction
•The origin is constrained against motion
in the x- and y-directions
• A pressure of 10 psi is applied to the
area
Results of Composite Plate
Composite Plate Results
[0 90 0 90]s Laminate
•From governing equations:
wmax = 0.7146”
• From ANSYS
wmax = 0.7182”
• % Error = -0.5%
Results of Composite Plate (ANSYS)
Laminate Stack-up
Deflection - ANSYS (in)
Deflection - Maple (in)
Percent Error
[0 90]s
5.682
5.666
-0.282
[0 90 0 90]s
0.7182
0.7146
-0.50
[0 90 0 90 0 90]s
0.2141
0.21196
-1.0
[0 90 0 90 0 90 0 90]s
0.091
0.0895
-1.7
[+/-30 0]s
1.404
1.4585
3.74
[+/-45 0]s
1.271
1.3822
8.04
[+/-60 0]s
1.405
1.4628
3.95
[+/-30 0 +/-30 0]s
0.1592
0.1777
10.4
[+/-45 0 +/-45 0]s
0.1452
0.1685
13.81
[+/-60 0 +/-60 0]s
0.1600
0.1796
10.9
[+/-30]s
6.299
5.7712
-9.15
[+/45]s
5.796
5.680
-2.04
[+/-60]s
6.299
5.7712
-9.15
[+/-30 +/-30]s
0.5966
0.5546
-7.57
[+/-45 +/-45]s
0.4989
0.5614
11.13
[+/-60 +/-60]s
0.5966
0.5546
-7.57
[+/-30 +/-30 +/-30]s
0.1528
0.1719
11.11
[+/-45 +/-45 +/-45]s
0.1371
0.1611
14.9
[+/-60 +/-60 +/-60]s
0.1528
0.1719
11.29
Failure Criterion
Failure Criterion (cont.)
• The Tsai-Wu Failure Criterion is based on the
following equations:
Failure Criterion (cont.)
Maximum Stress Criterion for bi-axial loading of composite plate:
Failure Criterion (cont.)
Tsai-Wu Criterion for bi-axial loading of composite plate:
Conclusions
•
•
•
•
•
The composite plate that had the smallest deflection was the 12 ply
[+/-45 +/-45 +/-45]s laminate.
The thinnest plate that had the smallest deflection was the 8 ply
[+/-30 +/-30]s and [+/-60 +/-60]s laminates
The larger percent error for the results occurred for the symmetric angle ply trials. This is because
of the nature of the Rayleigh-Ritz Method. When the composite has symmetric angle plies there is
a full [D] matrix. The full [D] matrix does not allow for a separation of variables method to be used
to calculate the deflection because not all of the boundary conditions can be satisfied. The
Rayleigh-Ritz Method approximates the deflection by using a Fourier expansion for the total
potential energy.
The calculated percent error seems to be within reason for the analysis that was done for this
project. The Rayleigh-Ritz Method does not provide an exact solution when compared to the
method for a specially orthotropic plate.
The most reasonable plate arrangement that would be suitable for replacing the aluminum plate is
the 8 ply orientations of [+/-30 +/-30]s, [+/-45 +/-45]s, [+/-60 +/-60]s. These three ply
combinations can withstand a significant stress in the 1-direction, 2-direction, and 12-direction
(shear) in comparison to other composite plates. These 8 ply plates will also be marginally thicker
than the 0.25" aluminum plate, but provide a significant decrease in overall weight.