Analysis of Simply Supported Aluminum and Composite Plates with Uniform Loading to Determine Equivalent Plate Ply Stack-Up

Second Progress Report10/28/2013

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-the-

middle plane of the plate remain on the normal-to-the-middle surface of the plate after bending

• The normal stress in the direction transverse to the plate can be disregarded

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

Analysis and Performance of Fiber Composites: Agarwal & Nroutman

Governing Equations (cont.)

Mechanics of Composite: Jones

ANSYS Model with Mesh

Side 2

Side 1

Side 4

Side 3

Origin

• 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

Side 2

Origin

Side 4

Side 1

Side 3

Results of Composite PlateComposite Plate Results

[0 90 0 90]s Laminate

•From governing equations:wmax = 0.7146”

• From ANSYSwmax = 0.7182”

• % Error = -0.5%

Aluminum Plate Results (ref. First Progress Report)

Aluminum Plate Results

•From governing equations:wmax = 0.941399”

• From ANSYSwmax = 0.941085”

• % Error = 0.033%

Results of Composite Plate (ANSYS)Laminate Stack-up Deflection (in)

[0 90]s 5.653

[0 90 0 90]s 0.7182

[0 90 0 90 0 90]s 0.2141

[0 90 0 90 0 90 0 90]s 0.091

[+/-30 0]s 1.404

[+/-45 0]s 1.271

[+/-60 0]s 1.405

[+/-30 0 +/-30 0]s 0.1592

[+/-45 0 +/-45 0]s 0.1452

[+/-60 0 +/-60 0]s 0.1600

[90 60 45 30 0]s 0.0014

[90 30 0]s 0.0014

[90 45 0]s 0.0036

[90 60 0]s 0.0044

Findings

• From Slide 8, most of the ply arrangements that were created will perform better than the 0.25” thick aluminum plate.

• I will now continue the analysis of these plates to determine if any of the laminates will fail under this loading.

Upcoming Deadlines

• Work on Thin Plate Analysis for Composite Plate for Laminate that aren’t cross-ply

• Failure Criterion Methods for Composite Stack-up