Plate bending deflection in 3D 1

[corus]

Does anyone know of a formula (or a reference) for the bending of a plate under a uniformly applied load simply supported at the two extreme edges? I'm not only interested in simple beam type bending of the plate but also the lateral deflection caused by poisson's effect. The only solution I can find is to solve the fourth order PDE by Levy's method. I've also tried

http://www.xcalcs.com

but this gives inconsistent answers, although it does try to offer a numerical solution of sorts.

corus

 

[corus]

jdspear,
For analytical solutions other than rectangular then you'd be better using finite elements. I'm not sure how a trapezoidal section would help (presuming that is the section about which you'd be bending the plate) but perhaps starting with a curved plate that would then bend back into a flat shape might be better. If you were starting with a flat plate then you'd have to bend it about two axis in order to eventually get a curved plate that was flat in the other direction, if you know what I mean.

corus

 

[chicopee]

Reference: Kent"design and Production" 12 th Edition Pg. 8-31 thru 8-35 will give you all the formulae on deflections and max. stresses (radial and tangential) that you may need for flat plates. All formulae can be used by hand.