Plate four points bending equation for a plate

pierebean

Hello,

I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory.

I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam.

However I cannot apply the beam theory to a plate.

Does someone know a tutorial or an article giving specifically the four-points bending of a plate and its solution?

Thank you

PhanthomJay

That's a tough one that i don't think even Roarke's Stress and Strain covers. This old timer took graduate courses in Theory of Plates and Theory of Elasticity eons ago. All I remember is a bunch of unsolvable partial differential equations.
Stay away from square or rectangular plates supported on 4 corners. Consider a statically determinate circular plate instead, supported at 3 equidistant simple supports, then get a copy of Roark's book. Beyond that, i cannot help, sorry.

Dr Bwts

Well Roark's is definitly the go to book but like PhantomJay I dont remember seeing that in there but you never know.

My solution would be use FEA. I know you wont get an analytical solution but you may be able to validate it via a simple experiment.

Studiot

"Theory of Plates and Shells", Timoshenko & Krieger

Article 49, p 218 in my copy

"Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free"

Dr Bwts

Nice reference thanks.

Studiot

Roark is oft quoted at PF, (as here) however a much more modern book ( and at least twice as thick) is

Formulas for Stress Strain and Structural Matrices

Pilkey

go well