Max Deflection Hand Calculations: Find 1.734in Plate Bending

[Stephen Miller]

TL;DR

Max Deflection Hand Calculations

Summary: Max Deflection Hand Calculations

I have to do a project that involves FEA on a thin plate in NX NASTRAN 11, finding the max deflection, and then proving that answer with hand calculations. The max deflection is 1.734 in. I have absolutely no idea how to do the hand calculations. Everything that I've seen is very cryptic or includes infinite series. I just need to be guided in the right direction.

Given values:
thickness = t = 0.125 in
Young's Modulus = E = 10E6 psi
Mass Density ρ = 0.101 lb * m/in^3
Rectangular Plate with dimensions 12 x 8 in
Poisson's Ratio = v = 0.33
And there's a applied pressure of 100 psi.

Attached files are the results from using the FEA, and the tutorial that was provided in case I missed some information.

 

[jrmichler]

Get a copy of Formulas for Stress and Strain, by Roark. You don't need the latest edition, my 5th Edition has almost 20 pages of formulas for small deflections of rectangular flat plates.

Your case is one of large deflection, where those formulas do not apply. There is also a discussion, with some formulas, in Roark of large deflections.

If the plate yields, none of the above formulas apply. In that case, verifying the FEA analysis requires an experiment.