Membrane stress- in thin bended plate 1

[potenza03]

Dear all,
I am working on the coaxial ring-on-ring test. It is a thin circular plate supported on the bottom side with one ring, and loaded with the ring on the upper side. The loading ring has a smaller diameter than the supporting ring.
After applying the load, plate bends.
The problem occurs when the deflection becomes higher than the 0.5 thickness of the plate, due to the non-linearity.

I was wondering does anyone know the equation for the membrane (diaphragm) stress for the mentioned or similar task?
Because the total stress which FEA shows is a sum of the bending stress and the membrane stress. But I would like to know how much is the membrane stress.
I know the equation for the bending stress, but I don't know it for the membrane stress.
Also, some explanation of the membrane stress would be very useful for me, if anyone knows...

Thanks in advance

Peter

 

[prex]

Look in the first site below, under Plates -> Large defo -> Supp.&held -> Annular load.
If I correctly understand your setup, you could be in a support condition intermediate between 'Supported' and 'Supp.&held', depending on the section area of the outer ring.
The solution is obtained with a numerical procedure. Can you share the equation for bending? I'm not aware of any closed form solution for these problems.

prex

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[rb1957]

having the equation for membrane reaction is only 1/2 the battle ... the structure reacts the loads with a combination of membrane and plate bending ... i guess the right combination could be found with castigliano

 

[EdR]

The stress distribution across the plate thickness is a linear combination of bending and axial (membrane) stresses so if you have the distribution across the thickness of the plate the axial component is simply the average of stresses on the top and bottom and the bending stresses is the total minus the axial stresses.....

Ed.R.

 

[rb1957]

yes, but how much of the load is reacted by plate bending, and how much by membrane ?

 

[EdR]

rb:

If its linear the load (stress) ratio (axial/total) should be the same (or very close) as the membrane/total stress ratio....If it is not linear (material) then would need to give it more thought....and get an estimate of how much the linear range is exceeded by......

Ed.R.

 

[rb1957]

ed,
i agree that if you had the stress distribution thru the thickness, then you'd be able to figure out how much membrane, and how much bending ... but i don't think the OP has the stress profile, i think all he has is the applied load. using the plate equation (assuming the pressure is reacted by bending) gives a large displacement. membrane loads depend on the out-of-plane deflection (creating an arc) ... for any deflection, membrane can react the applied pressure.

the real world, and particularly this case, is a combination of plate bending and membrane reactions. maybe prex's large displacement handles both, i assumed it was either a thick plate or a thin membrane (and yes, i know what happens when i assume ...)

 

[BPVFEA]

"Because the total stress which FEA shows is a sum of the bending stress and the membrane stress. But I would like to know how much is the membrane stress."

From FEA you can get membrane stress by displaying reults at the mid plane of shell elements. In ANSYS you can get it from 'Postprocessor>Options for output>Shell Results from'. Make Powergraphics off before taking plot.

If you have used solid elements, then use the "Stress Linearisation" concept to get the membrane and bending stress component sepreately.

 

[EdR]

rb:

You are correct....I just assumed he would have information about the stresses at the top, bottom, and maybe mid-plane..

By the way the old saw he mentioned about only getting good results for less than 1/2 the thickness depends on the type of element being used as well as what the model looks like...

Ed.R.

 

[potenza03]

I get good results till deflection reaches 0.5 of thickness because by that point membrane stress is negligible and results are compared only to the linear bending theory.

BPVFEA- I prefer working in Workbench so I find similar of what you suggested me.

I have a stress distribution over the thickness. So, membrane stress is the average of the top and the bottom stress? Some explanations, due to what?

Thanks for the replies.

 

[rb1957]

sorry Ed, it sounds like he has stresses (from his FEA) so determining how much membrane is easy (which he seems to be doing).

ok, so it sounds like you're comparing FE output with theory and it match plate bending up to deflections of 1/2 the thickness. have you looked into prex's large displacement theory results ?

have you tried NL FEA, since linear FE assumes small deplacements ? do your plate elements have a "shear deflection" option (unlikely) ??

 

[potenza03]

Exactly. FEA results can be compared only in the small deflection, due to the bending stress only.

I am curious for the large deflection, when membrane stresses occur.

I cannot do it with prex´s web page because now I need to pay for it.

As I work in ANSYS WB, there are not many commands as in the Classic. So, there is no ´shear deflection´.

I am doing it in the NL FEA, and it is working fine, but I want to support it with theory.

 

[rb1957]

download timoshenko "plates and shells" ... more differential equations than you can solve in a fortnight