flat plate buckling

[bnrg]

Has anyone seen information on the buckling of a flat plate with uniform pressure load applied across it? Stress and deflection are easy but I was surprised to not find a buckling case in Roark (5th ed). My plate is essentially an acrylic window with 1 ATM across and while the stresses are really low I am concerned that excessive deflection could cause it to collapse.

 

[Bbird]

Buckling is a term associates with compression failure on a slender member. Is your flat window subjected to in plane compression or just a load normal to the plane?

For large deformation at nearly failure condition the analysis may have to be nonlinear and inlastic.

Roark formulas are essentially for linear-elastc applications.

 

[bnrg]

Hi Bluebird, the load is normal to the plane

 

[fsi]

if you have large deflections, you have a situation called bending with stress stiffening. what happens the plate starts carrying membrane stresses even though load is normal to it. outer perimeter will be in tangential compression due to strss stiffening. your actual deflection will be less than just with bending. you should perform a geometric nonlinear FEA.
If you do not have FEA access, you might be able to do a combination bending/stress stiffening analysis using formulas in theory of plates books.
fsi

 

[flamby]

In plane load is essential to make buckling an issue. If the load is normal to the plane and stresses are in allowable range, the plate will not buckle.

However, if the plate is VERY large (.ie. heigh), it can buckle under its own weight. To take care of this, the edges should be fixed and fastened to the frame effectively so that its weight to taken by the frame, not the plate itself.

HTH

 

[prex]

Timoshenko's Theory of Elastic Stability has an extensive (90 pages) treatment of the buckling of thin plates, however it is only related to in plane loading.
If the phenomenon that concerns you is as suggested by Bbird (buckling due to compression at the border under transverse loading), then I think it shouldn't really be dangerous. As you mention a plastic flat plate, I must assume the thickness is quite large with respect to width or diameter (as 1 atm is a relatively high pressure for a flat plate). Also buckling would produce waves at the outer tip, and this should be quite well contrasted by the containing frame.

prex

http://www.xcalcs.com

Online tools for structural design

 

[tincan]

Roark's 3rd edition of Formulas for Stess and Strain has deflection equations for square & rectangular plates with uniform normal loading. Also,Advanced Mechanics of Materials by Seely & Smith.

Best, Tincan