Plate stress evaluation in the middle

[dcascap]

Hi,

I'm doing a project about an aircraft skin modification, and my client has some guidelines about the FE model that I would like to discuss with you.

Do you know why for a thin metallic structure as the skin, that are mostly modelled as shell elements (linear static) it is allowed to take the von Mises stress of the middle of the plate to calculate reserve factors?
For me this is counterintuitive as shell elements have bending capabilities, and therefore, top/bottom face tend to have higher stresses.
I can imagine that for ultimate load it is permitted to take the middle layer as the top/bottom will probably yield, and then the stresses will redistribute (I'm not sure if this is the correct reasoning).

Anyone has a similar experience, or can guide me to a more complete explanation?

Thanks!

 

[rb1957]

thin shells (like fuselage skins) are not "plates" but "membranes". They react pressure with hoop stress, in-plane tension loads. Sure there is some small amount of bending, but the typical assumption is that stress is uniform over the thickness ... except in those places where secondary bending is significant, like at the unsupported edge of a doubler.

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

 

[SWComposites]

agree with rb, bending is reacted by the stringers and frames, not the skin; except for local effects at doublers, thickness changes, etc.

 

[dcascap]

Thanks for the answer! That makes sense, but as you said except when secondary bending plays a bigger role. In my case I'm installing a blade antenna with an inner profile attached to the stringers. I was evaluating aero load using the dive speed, and the resultant side force is considerable. This produce local bending on the skin and hat doubler.
But as this is the "approach" that the company has, I'm basically ignoring the higher stresses on top/bottom. In my opinion this doesn't seem such a correct assumption of a membrane type of behavior, I could be wrong...

 

[SWComposites]

if there is that much side load and bending, you probably need to make the doubler plate larger to connect to more stringers. or attach it into a frame with a fitting. can you show a sketch of the installation and fuselage config in the area?

 

[rb1957]

with a large side load the internal provisions should be a channel, something like the depth of the frame. This puts the couple into the frames, where it wants to be, and the direct shear is reacted in-plane in the skin. Pressurised fuselage ? I'd have the dblr tied into the stringers, so secondary bending is relieved by the stringers. There are two schools on this ...
1) support the edge of the dblr on the stringers, to reduce secondary bending in the skin, or
2) have the dblr edges away from the stringer so you can separate the day-time job of the stringers from the added loads of your antenna.

Many ways to skin cats, we each have our preference.

If you are supporting a large side load on skin only (or skin and dblr) I think you'll be in for a world of hurt, or at least a torturous analysis.

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

 

[dcascap]

Thanks for rhe answer, I cannot really show a sketch of the configuration due to IP but with your input I have enough to work with, thanks!

 

[WKTaylor]

Related... As a back-up... would a hand analysis using Peterson's Stress Concentration Factors [3Ed] be of any value?

Regards, Wil Taylor
o Trust - But Verify!
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", HBA forum]
o Only fools and charlatans know everything and understand everything." -Anton Chekhov

 

[rb1957]

Petersen is a good reference for esoteric geometries. Here I think you need a fastener model, a compliance model along the lines of Niu (and others), to get the fastener load, then Niu has a neat formula for combining pinload and by-pass load.

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

 

[Stress_Eng]

When it comes to secondary bending at the 1st and last fasteners, you can derive a strain matching model to determine the load distribution in a doubler plate (fastener shear displacement stiffnesses and plate element stiffnesses between fasteners) and incorporate the load transfer distribution into a beam bending model incorporating axial tension load. It takes some work but it can be done by hand. Some may say do it by FEA, but where's the fun in that!

 

[rb1957]

yes, this is what I call a compliance model. it isn't that hard to set up in excel, I have it as part of my DTA s/sheet (book), since my typical DTA is for fuselage skin under doublers.

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

 

[Stress_Eng]

The fun begins when you create the beam bending equations, taking into account the tension force in the skin and the step moments created by each individual fastener due to their transfer load. Such a model would give you an idea how much secondary bending you’re dealing with, especially for fatigue. There’s always the FEA root! Admittedly, I wouldn’t think a doubler joint would create secondary bending as high as a lap joint.

 

[LiftDivergence]

Admittedly, I wouldn’t think a doubler joint would create secondary bending as high as a lap joint

Not as much, but it does create some.

There is some guidance in the FAA course on repairs and modifications.

We would generally use our own FEM studies to generate similar data. The way this would typically work is to boil it down into tabulated bending/tension (B/T) ratios for different geometries. These general B/T can be used to factor and add equivalent tension from bending for stress purposes.

Given that this is typically done at joints, it would usually be done in conjunction with a joint load transfer analysis. So we would be developing R/P values as well. Bearing and bypass stresses developed using R/P results would be done after development of equivalent tension from secondary bending.

For stress life or strain life, the peak stress should be used. For LEFM, typically you can factor down the bending stress component because the Beta factor for bending is usually on the order of 1/2 what it is for tension.

Keep em' Flying
//Fight Corrosion!

 

[Stress_Eng]

I remember seeing documentation such as you’re describing many years back, when I did F&DT work. There are many aspects to this type of task the OP is going to have to consider. Creating a useful model (or models) is just one small part!

 

[rb1957]

the difference between a lap splice joint and a dblr is the degree of load transfer. If the skin is continuous under the dblr, then only a portion of load is transferred. In a lap splice joint all the load is tranferred, maybe over three rows (where a dblr typically uses 2 rows).

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