Deflection vs plate thickness

[amorrison]

rb1957 stated in another thread that

"if a plate deflects much more than it's thickness, then it probably isn't working as a plate, and more like a membrane"

Are there any further comments or points to be made about this statement? Discuss please.

 

[corus]

He/she is referring to membrane stiffness, like a drum skin.

corus

 

[jte]

Picture a round disc, like corus' example. But let's say its a flat steel plate clamped on the edges. As I put a pressure load on it the plate initially resists the loading (carries the forces) through bending and a bit of shear. But when it does that, it deforms - now it has some curvature. This curvature allows it to carry some of the load through membrane action by going into tension. Just like the threads on a trampoline: No strength until you deform them.

jt

 

[GBor]

I think we need to go back to the theories that drive the equations that are implemented into the FEA software. If you recall, "thin plate" theory requires "small deflections" (it assumes small angles for the deformation). Once the deflection exceeds the thickness of the plate, the assumption of "small deflection" is no longer valid. The assumptions and theories that do fit are membrane, large deformation, non-linear (geometric, not necessarily material) theories.

 

[40818]

If i remember from Timoshenko, that it isn't really the fact of deflecting greater than its thickness, but what the radius of curvature is.
Linear small deflection theory can be used for large deflection problems in many instances. Imagine bending a plastic ruler it remains elastic and easily calculable for massive thickness/deflection ratios.

 

[johnhors]

40818, linear FEA cannot accurately handle large deflections, since the stiffness matrix assembled by the FE solver is only valid for very small deflections as GBor stated. As a structure deflects its stiffness changes, therefore for FEA to provide meaningful results in a structure undergoing large deformation a non-linear geometry option has to be invoked, regardless of whether the material yields or not.

 

[GregLocock]

Yes, but the correct scaling factor to consider is not the ratio of the deflection to the section thickness, it is more closely connected to the angular mismatch of the 'neutral plane' in adjacent elements. A sufficiently large structure made of thin material could deflect by many thicknesses yet remain linear.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[40818]

Johnors, i didn't think we were talking about FEA.

 

[corus]

In a linear analysis the geometry is always based upon the undeformed structure. Stresses may remain within yield and be 'linear', but the application and position of the load will change with the deformed geometry. You can bend a ruler and it'll spring back but the position of the bending force will move to reduce the moment as the ruler changes shape. The stresses may well be linear but the load application isn't. Basing the non-linearity on deflections greater than the thickness is a reasonable rule of thumb to take.

corus

 

[GregLocock]

Sorry, no.

To take a simple example:

Consider a long beam. If it is very thin, the deflection at the centre of the beam can be many many multiples of the beam's depth, yet linearity, and FEA, will still work perfectly well.





Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rb1957]

the analogy i use is a balloon ... the thin membrane obviously has not bending stiffness and reacts the internal pressure with inplane membrane stresses.

if i do a FE analysis of a thin plate, i'd want a non-linear analysis ... i personally don't like linear elements "fudged" for large displacements.

and corus ... "he" is just fine ... "he/she" whilst being politically correct, possibly expresses a dubious gender ambiguity (which i'm pretty sure i don't suffer from) ... sometimes i'll say "he, in the non-gender specific sense,".