How Thin is a Thin Plate? 4

[glenn11897]

In shell analysis (i.e. buckling, etc...), I've always wondered how thin is a thin plate. What is considered a thin plate? What is the definition of a thin plate? This is something I missed asking my profesors back in college. Thanks.

 

[jhardy1]

feadude,

My previous comments referred to a test run with the plate being held, but not clamped against rotation, at both ends. Specifically, I found that the non-linear result was within 6.4% of the linear result for deflections up to 3 mm (or 0.3 times plate thickness), and 11.5% at 4 mm deflection.

I have just re-run using the same plate clamped against rotation at both ends as well. In this case, I found that the non-linear result was within 5.7% of the linear result for deflections up to 3 mm, and 10.9% at 4 mm deflection.

That is, the main factor on how non-linear the behaviour is whether membrane stresses can be developed at all, rather than whether the plates edges are clamped against rotation.

 

[feadude]

Julian:
Thank You

 

[feadude]

The ratio of the thickness to the smaller span length should be less than 1/20.

 

[joekm]

From the parent post:

"What is the definition of a thin plate?"

Generally, it's about using either Mindlin plate theory or the Kirchoff boundary condition to deal with end shear. I suspect that's going to be transparant to the user for modern software but, if you're looking for a more technical definition, that's basically it.

Any good text on plate, membrane, and shell theory will go into more detail.

As to the 1/20 rule - that is the generally accepted guideline. I wasn't going to post at all, but, when I saw you has also asked about the definition of a thin plate, I thought I could point you in the right direction to find the answer.

--
Joseph K. Mooney
Director, Airframe Structures - FAA DER
Delta Engineering Corporation

 

[guydo]

I was wondering reading the responses, how 'thin' is the automotive structure. Furthermore is there realy no influence on element size? Can i mesh a 2 mm thick plate with 2 mm lenght shell elements?

Thanks for any reply,

Guydo

 

[brad]

guydo--
You can mesh a 2mm thick plate with 2mm length shell elements and get good results, provided that the "global" dimension lengths are still high (using the 1/20 rule, this would imply a minimum global dimension of 40 mm for your problem).

As others have suggested, the ratio is not "thickness-to-element-size", but rather "thickness-to-global dimension". By "global dimension" I mean the distance between supports, or other constructs which give rise to discontinuities. Although others have suggested 1/20 above, I've also seen 1/10 frequently employed as a rule of thumb.

Brad

 

[stellad]

Hi everyone,
I was reading the thread intently as I am trying to model, on Ansys, a thin elastomer that will act as plate. Ansys does not seem to have any thin plates, only shell formulations, the closest to a thin plate would be a 2D plane element, but this does not permit pressure to be applied on the plane, just the sides. Would it be alright to model the elastomer in 3D solid elements? The thickness of my specimen is 20 microns, for small deflections one can assume the stress across the z direction will be linear. Any suggestions?
Thanks

Stella