Is there a simple closed form solution for the deflection and maximum moments, of a flat constant thickness isotropic plate loaded either with uniform distributed load or point load in center, supported at the four corners?
Can this problem be solved by superposition of common load cases in a reference text such as Roark's?
Our custoimers commonly come up with designs having load cases such as this.
I played with a beam program, placing a uniform load of 20 lb/ft on a
10 foot beam of cross section 1 X 1 inch, and found a max deflection of 2.2 inch and 21 ksi bending stress. I could not generate a defensible basis to generalize this beam to a plate of 10 X 10 ft and 1 inch thick, supported at four corners, and uniformly loaded in order to estimate the maximum deflection and the bending stress.So I think it would be much more sensible for me to get hold of a plate program (I think Archon has one) if I had this load case to work repeatedly.
Brian Whatcott Altus OK
I have a hunch that the pure-plate-bending solution with concentrated corner support loads may not converge. It seems that Roark would need a good reason like that to leave it out.
Hth, Fred Klingener
The problem with simple solutions is at the corners, where stress trends to infinite.
-- Jonathan
Barnes's theorem; for every foolproof device there is a fool greater than the proof.
To reply remove AT
The simple answer is "no" -- plate problems rarely have a simple closed form solution.
As usual, Timoshenko is the best handy source for this. Pages 218-221 >Is there a simple closed form solution for the deflection and maximum
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