When is a panel classed as a 'thin' panel? 2

[Lisa_247]

Hi,

Im looking to do a thin panel buckling analysis - but what actually classifies a panel as being 'thin'? I remember hearing somewhere that it was to do with the relationship between the width and the thickness, but cant find anything written down. Can anyone help? Thanks.

 

[rb1957]

my suggestion is to work it through for yourself (not meant to be as snitty as it sounds).

I'd work through curved panel analysis with different curvatures and see the curved panel behaves like a flat panel.

For me a 6" wide panel with a radius of 60" is near enough flat.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SWComposites]

width and thickness have nothing to do with "flat". The amount of curvature determines how conservative a flat panel analysis will be relative to a curved panel analysis.

Thickness relative to width and length determines whether transverse shear displacement effects are significant or not. As does the transverse shear modulus if the panel is not homogeneous.

 

[Lisa_247]

Apologies, i asked completely the wrong question! What i meant to ask was what classifies a panel as 'thin' - not 'flat'! Apologies again for the confusion!

 

[WKTaylor]

Lisa247... there is a inter-relationship between panel thickness and curvature [out-of-plane'ness]... RE the buckling resistance/analysis.

I assume that Your analysis presumes theoretical panel has 'exact constant thickness' and is 'dead-flat' for waviness.

NOTE1. 'Real-world' sheet and plate materials have tolerances for thickness and waviness per material fabrication specifications. Average sheet metal from purchased from metal-OEMs often displays waviness and thickness variations within ANSI/AA H35.2 limits. However, the company I work for has a 'special' tolerances it CAN [but not usually] demand from the OEMs for 'extraordinary' controls on sheet thickness and waviness... at a premium cost.

NOTE2. Pure stress/strain is rare... real loads/strains induce deflections/waviness. For very thin sheet buckling to elastic tension wrinkles is acceptable and desirable.

AND HERE is where structure design philosophy can diverge radically.

For instance Boeing tends toward thin skins/webs [claimed weight savings] that are allowed to elastically buckle below limit-loads to ultimate... which can be very noticeable from the outside of fuselages and the stabilizers [also]. I've sorta thought-of Boeing thin-skin structure as 'wet floppy noodles'. Ughhhh.

On-the-other-hand Lockheed [cargo birds] tend toward thick skins/webs which resists any visible [noticeable] buckling deflections until ~at/well-above limit load. I've thought of most Lockheed structure as 'stiff-dry-pasta noodles'. Buckling is less of an issue relative to fatigue cracking.

OK, Time for me to stop wandering around this subject and 'shut-up' and get back-to-work.

Regards, Wil Taylor
o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

 

[Lisa_247]

Hi, thanks for your replies. Ive been a stress engineer for 20 years and have used the equations for 'buckling of thin sheets' given in chapter 11 of 'Airframe Stress Analysis and Sizing' by Michael Niu many times for the analysis of panels, webs etc. but i was just wondering if there was a general rule of thumb to determine whether a panel can be classed as 'thin' - i seem to remember reading somewhere that the thickness should be at least 20 x smaller than the width, or something along those lines. Im just writing some guidance notes for junior members of staff.

 

[rb1957]

I'm surprised that buckling is a matter of thickness. Of course thickness changes the buckling strength, but "thin" verses "thick" (like in plates in bending) ? Are we talking shear buckling ? i would have thought the "thin" limitation would be defined by the equations, maybe in Niu's references (NACA 2661 ?)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SWComposites]

No, thin vs thick has to do with whether the classical buckling equations, that only account for bending deformations, are valid. For "thick" plates or for sandwich panels with thick and/or low stiffness core, the thru-thickness shear deformation can become significant and need to be accounted for. There are also boundary condition effects for "thick" plates. For a homogeneous isotropic material plate, anything less than ~ 20:1 L or W to t ratio is probably not "thin". I don't recall the limit in the Boeing design manual. You could check Timoshenko and Gere, Theory of Elastic Stability text to see if it has some guidance. Kind of surprised there is no guidance in Niu, but I'm too lazy right now to go look.

 

[LiftDivergence]

Hi Lisa_247

From an applied theory standpoint this is actually pretty well defined. We should be cognizant that most engineering methods are semi-empirical and are intended to save us from the labor associated with solving equations of the theory of elasticity directly. Unlike the theory of elasticity, where equilibrium is imposed on an infinitesimal element's stresses and body forces, engineering plate & membrane theory imposes equilibrium on the stresses and applied forces.

In engineering theory of thin plates and membranes, stresses in the thickness (transverse) direction are generally ignored. The equilibrium equations for the stress resultants and applied forces are for 2 dimensions only. That is, thin plate equations are set up under the assumption of plane stress. Any transverse shearing deformations are neglected.

You can think if this the same way you might think of Euler-Bernoulli beam theory. This is an engineering method which assumed the neutral plane of the beam remains plane, and that sections normal to this plane remain normal during deflection. Obviously transverse shear Tau = VQ/Ib can be predicted in this method, but shear deformations of the cross section are neglected.

Situations where you might need to apply Timoshenko beam theory are: deep beams, beams of non-uniform cross section or built-up beams, etc.

This is analogous to plates in that there are also situations where a plate's geometry will inherently necessitate a treatment as a "thick" plate. Thin plate theory makes similar assumptions (normals to the surface remain normal during deflection).

Like Timoshenko theory, there is a more detailed method for plates that accounts for these issues and can be applied to thick plates. This is called Mindlin-Reissner plate theory. The plate equivalent of Euler-Bernoulli is called Kirchoff-Love theory

There are a few ways in which you could determine when treatment as a "thick" plate is appropriate.

For example, if you are using an approximate method for thin plates such as Rayleigh-Ritz and you are approximating loads as concentrated forces, the "real" dimensions of the area on which the force is applied should be less than the thickness of the plate. Or, maybe if you are predicting large deformations using thin plate theory.

Another good litmus test would be to check the plane strain transition thickness for the material in question. If the plate is thick enough to act in plane strain, you should probably use a thick plate method. I have seen a couple articles which generally state Kirchoff-Love is best for plates whose thickness < about 10% of the average side length. This would generally be more restrictive than simply checking the plane strain transition thickness.

So there is no hard and fast rule of thumb, but the basis of the answer is whether or not it is acceptable to ignore shear deformations through the thickness of the plate.

A caveat: the above is specific to bending and extension of plates. "Thick" vs "thin" with reference to instability would be different



Keep em' Flying
//Fight Corrosion!