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Analysis of Simply Supported Composite Plates with Uniform Pressure using ANSYS and Maple

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.

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Analysis of Simply Supported Composite Plates with Uniform Pressure using ANSYS and Maple

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  1. Analysis of Simply Supported Composite Plates with Uniform Pressure using ANSYS and Maple Second Progress Report 11/28/2013

  2. 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

  3. Material Properties and Governing Equations • wmax = α*q*a4/D • D = E*h3/12*(1-ν2)

  4. ANSYS Model with Mesh • 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 1 Side 1 Side 4 Side 4 Side 2 Side 2 Origin Origin Side 3 Side 3

  5. Results of Aluminum Plate • From governing equations:wmax = 0.941399” • From ANSYSwmax = 0.941085” • % Error = 0.033%

  6. Material Properties of Composite Laminate

  7. Governing Equations ABD Matrix: Analysis and Performance of Fiber Composites: Agarwal & Nroutman

  8. Governing Equations (cont.) For Cross-ply Laminates the [D] matrix simplifies and the governing equation reduces to: Mechanics of Composite: Jones

  9. Governing Equations (cont.) • For symmetric angle laminates, the ABD matrix is fully defined. • The boundary conditions for a symmetric angle laminate are:

  10. 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

  11. ANSYS Model with Mesh • 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 1 Side 1 Side 4 Side 4 Side 2 Side 2 Origin Origin Side 3 Side 3

  12. Results of Composite Plate • Composite Plate Results • [0 90 0 90]s Laminate • From governing equations:wmax = 0.7146” • From ANSYSwmax = 0.7182” • % Error = -0.5%

  13. Results of Composite Plate (ANSYS)

  14. Failure Criterion

  15. Failure Criterion (cont.) • The Tsai-Wu Failure Criterion is based on the following equations:

  16. Failure Criterion (cont.) Maximum Stress Criterion for bi-axial loading of composite plate:

  17. Failure Criterion (cont.) Tsai-Wu Criterion for bi-axial loading of composite plate:

  18. 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.

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