Stiffness of shell vs plate

[sushi75]

Hello!

I try to understand why a shell is stiffer than a plate. I've read a note on the internet explaining that moving a point out of the surface of a thin shell like an egg takes more energy as the adjacent fibers have to be stretched, unlike a plate.

But it does not make much sense, and I cannot really see why with physical sense why it is stiffer. does that mean that a shell is less likely to buckle than a plate?

Does someone has an clearer explanation for that?

Thanks a lot for your help!

 

[MacGruber22]

I am not an expert on standards for FEM element terms, but I would think you need to understand the analytical formulation of the elements. Very sophisticated FEM programs tend to have many variations of planer elements, some of which account for shear deformation & membrane action, among many other properties. It seems you are implying out-of-plane stiffness. The manual for your software should tell you which formulation (Kirchhoff, et al) is used for each element. Small deformation consideration is very important too. Once you see the formulation/derivation, you can decide whether it sufficiently accounts for the expected behavior in reality.

"It is imperative Cunth doesn't get his hands on those codes."

 

[sushi75]

Hi,

thanks for your quick reply. Actually the question is not necessarily related to FE, it's more a matter of structural mechanics and try to understand and be able to explain with word, why physically a shell surface will be stiffer than the same flat structure.

I can sort of picture it from gut feel but can't understand why!

 

[SAIL3]

a shell has an out-of-plane component of the reaction to an applied load because of it's curvature.....study Timoshenko's book on Plates and Shells

 

[BAretired]

Not all shells are stiffer than plates. Take a sheet of paper, roll it into the shape of a cylinder and tape the edges together. This is a cylindrical shell and is subject to substantial deflections when applying very feeble lateral forces.

Plates and cylindrical shells resist applied loads primarily by developing moment resistance. If the plate is thin, its moment resistance is small. Shells such as light bulbs or egg shells resist applied loads primarily by membrane stresses, a totally different mechanism and this is the main reason why shells are usually stiffer than plates.

BA

 

[MacGruber22]

Ohhhh....I was wayyy off

"It is imperative Cunth doesn't get his hands on those codes."

 

[sushi75]

Thanks all!!

So BAretired, when you mention that shell resist applied load primarily by membrane stresses, can you elaborate the mechanism occuring? this is probably the point I did not manage to understand

Cheers

 

[ShellsPlatesMeshes]

As an example, consider so-called "shallow shell", which is geometrically close to plate, but has some curvature; the corresponding images can be found on the following webpage:

http://members.ozemail.com.au/~comecau/quad_shell_shallow_shell.htm

Suppose, a vertical, distributed load is applied to that shell (which corresponds to the force of gravity).
If that object is just planar, the plate bending theory applies, i.e. the plate load-bearing capacity depends on the stresses arising in the top and/or bottom fibers of the plate. If, however, the object has some curvature (ie. it is a shallow shell), compression forces arise through the thickness of the shell. In other words, not only top and/or bottom fibers are now responsible for the load-bearing capacity of the shell, but all fibers, from top surface to bottom surface, are involved. As a result, compression stresses are evenly distributed through the thickness, and their values are much lower than they would be in case if the object can resist bending only. That example is analysed in detail in the book: "Computational Geometry of Surfaces and Its Application to the Finite Element Analysis of Shells" (O.Axenenko and A.Tsvelikh, 2014) on pages 286-295 (the book also contains source codes on a separate CD, so you can run the program and see all the stresses in digits, change the parameters, etc.)

Hope this helps.

 

[rb1957]

plates react out-of-plane force by bending, with zero force on the neutral axis. deflection should be limited to something like 1/2 the thickness.

membranes (shells) react out-of-plane force by axial loads, with constant stress across the section. Typically you see very large displacements. A balloon is an example

another day in paradise, or is paradise one day closer ?

 

[BAretired]

I don't think balloons are the kind of thin shells the OP was talking about.

A concrete dome of 4" thickness can span a diameter of 200' with no trouble. Try doing that with a 4" slab. It is clear that the shell is much stiffer than the flat plate.

BA

 

[KootK]

I can sort of picture it from gut feel but can't understand why!

For a fundamental understanding, you might be best served by going back to a simple, analogous stick model as shown below. If you run this in conventional FEM software, or just in your head, you will find that the analogous "shell" on the right will deflect much less than the analogous "plate" on the left. That's because forces are generally resisted more efficiently with via pure axial strain than they are via flexural strain. That is just as true for shell elements as it is for stick elements.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.