# Composite design

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#### ragflyer

##### Well-Known Member
I am reasonably well versed in analyzing wood and Aluminum aircraft structures. I have decided to try my hand at composite analysis now. The math is fine as I have advanced degrees in (non aero) engineering. However I would like to validate my approach with folks that have actually analyzed composite structures.

As a start I am analyzing a fuselage structure. I realize that minimum gauge rules but I would like to calculate and get a feel for the margins involved.

I am considering a 0.5inch core (styrofoam 2lbs) with 2 and 3 layers of rutan uni and bid. I am using flat plate theory to calculate maximum loads. Then I am checking buckling of the sandwich panels- for this I assume the sides top and bottom are simply supported on the corners. Finally I check for wrinkling. in general I have found buckling to be critical. I am assuming the width of the panels to be 36inches and no intermediate bulkheads between tail and wing attach (is this typical?), i.e. long panels.

Assuming a layup of (0uni;45bid;0.5"foam;-45bid;0Uni) of rutan fabric and 2lbs/ft^3 styrofoam

 D11 8,427.15 Ec 1,500.00 D22 3,606.83 Es 1,000.00 D12 1,651.11 t 0.54 D66 1,990.12 tf 0.04

I get the following results:
N max -1100 lbs per inch (ultimate compression)
N wrk 359.1226411 lbs per inch (Wrinkling)
N bkl 169.741159 lbs per inch (Buckling)

Hence buckling is critical and I can take at most 359lbs/inch in compression before the top buckles. Is this in line with expectation? In my old case I have a 1000lbs load on the stabilizer and a 10 ft tail lever arm. This results in about ~100lbs per inch of compression load on the top panel so I have significant (~70%)margin. Reasonable? I know this is a little technical but any comments are appreciated.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Ragflyer,

I am willing to check your work, what are your reference texts? I like Tsai and Hahn. What methods (reference and pages) are you using to estimate wrinkling and buckling stress thresholds?

You show [D] and I can check against my estimators on that. Share [A] and I can check that too. I am not recognizing Ec and Es... please explain.

Vacuum bagged, 1 UNI + 1 BID is about 0.016" thick. One laminate on each side makes the laminate 0.032" thick. If you combine that with "book" E's for the vacuum bagged fiberglass, you will have a pretty good estimate of [ABBD]. Or if you use 0.040" because that is how thick these laminates check out at in open wet layups, you had better have an adjusted (lower) set of E's for those laminates. Thicker fiberglass with no more cloth in it is just heavier, but not materially stronger or stiffer.

How are you doing these calculations? I hope you are using Excel or MatLab etc.

Feel free to communicate with me on private messages, we can share emails and data from there.

Billski

#### plncraze

##### Well-Known Member
HBA Supporter
If you are willing please keep sharing this conversation. It offers some great practical advice

#### ragflyer

##### Well-Known Member
Thanks Billski, appreciate your help and offer to PM! PlaneCraze your comments makes sense. I will try and keep here as long as it works, though PM is no doubt more efficient.

Calculations in Excel. Ec is the Young's modulus of core. Es is bad terminology on my part, it would read better if I said Gc, i.e. shear modulus of core. I am using 1500PSI (Ec) and 1000PSI (Gc) respectively for styrofoam.

I am using for hand lay up 0.009" and 0.013" for UNI and BID respectively.

Buckling load per inch: I am assuming simply supported long plate with width b =36.

Nbkl= 2*pi^2/b^2 * (sqrt(D11*D22)+D12+2*D66)

This is a little conservative as the sides would carry some load when the top or bottom buckles postponing complete collapse.

Wrinkling stress, i have a used a variant of Hoff's formula adjusted for orthotropic facings.

F wrinkle = 0.5*(12(D11)f/tf^3 * Ec * Gc)^0.33

D11f is D11 of just the compression facings without the core, as wrinkling models facing on elastic foundation and pulling/pushing into core. D11f captures the bending stiffness of the facings. I am using 0.5 in the formula as it conservative but various authors use within a range from 0.44 to 0.63.

The above two formulas are from Practical Analysis of Aircraft Composites by Brian Esp. I am familiar with Tsai. As such great textbook for introduction to laminate theory and concepts. However it does not cover semi-empirical formulas that are so valuable to actual design practice, for example when dealing with stability failure modes such as wrinkling and buckling etc.

Here is the A matrix

 A11 121,794 A22 54,436 A12 25,025 A16 0 A26 0 A66 29,907

I would really appreciate any comments, particularly validation with your numbers for strength and buckling.

#### DeepStall

##### Well-Known Member
To clarify, are you analyzing fuselage sides loaded in shear, or a top/bottom skin loaded in compression (Fx) reacting the moment My created by the stabilizer load (Fz)?

Your buckling-dominant failure mode matches my experience, and failure loads look like right order-of-magnitude. A 10' long x 3' wide panel (a/b=3.33) isn't geometrically unreasonable (in isolation). That said, after satisfying static strength, if it's still failing, there's a weight and manufacturing trade involved. Either extra core thickness is needed to satisfy buckling (but then wrinkling can become controlling and drive extra facesheet plies or denser core), or you start adding intermediate frames and getting a/b down=>improve buckling constant (but with extra joint weight, parts count, and fabrication+assembly effort).

An additional caveat would be that in general stability-driven calculations (both buckling and wrinkling) tend to be sensitive to part details (geometry, fixity, load eccentricity, manufacturing defects / details like ply splices, ...), so high safety factors (FS>=2) would be a good idea until you convince yourself that lower is OK. Assume all your failure loads are ultimate -- with composites there's generally no yielding to get you down safe with a bent bird. If that 1000 lb load is limit (FS not yet applied) then you're not showing enough positive margin for my comfort zone. (ultimately, your call how conservative you want to be)

#### ragflyer

##### Well-Known Member

To clarify, are you analyzing fuselage sides loaded in shear, or a top/bottom skin loaded in compression (Fx) reacting the moment My created by the stabilizer load (Fz)?
Yes Top or bottom in compression.

Your buckling-dominant failure mode matches my experience, and failure loads look like right order-of-magnitude. A 10' long x 3' wide panel (a/b=3.33) isn't geometrically unreasonable (in isolation). That said, after satisfying static strength, if it's still failing, there's a weight and manufacturing trade involved. Either extra core thickness is needed to satisfy buckling (but then wrinkling can become controlling and drive extra facesheet plies or denser core), or you start adding intermediate frames and getting a/b down=>improve buckling constant (but with extra joint weight, parts count, and fabrication+assembly effort).
yes that’s what I am finding. Though Keep in mind I have ample positive margin ~70% in this case. If I did not have positive margin then increasing core thickness prevents buckling but taken a little further, as you say, wrinkling becomes critical. At that point replacing core with higher density (consequently higher Ec and Gc) is needed to tackle wrinkling.

An additional caveat would be that in general stability-driven calculations (both buckling and wrinkling) tend to be sensitive to part details (geometry, fixity, load eccentricity, manufacturing defects / details like ply splices, ...), so high safety factors (FS>=2) would be a good idea until you convince yourself that lower is OK. Assume all your failure loads are ultimate -- with composites there's generally no yielding to get you down safe with a bent bird. If that 1000 lb load is limit (FS not yet applied) then you're not showing enough positive margin for my comfort zone. (ultimately, your call how conservative you want to be)
1000 in my case is ultimate load. On wrinkling, I am assuming the 0.5 factor is meant to compensate for inevitable eccentricities. Is the practice to add a further knock down factor?

#### DeepStall

##### Well-Known Member
I haven't seen anything to indicate that the constant in the Hoff wrinkling equation is a knockdown, any more than the constant in a buckling formula is a knockdown vs. a physical fixity factor. Equations predict ultimate, how close you cut it (and how you report it) is then up to you. In the wrinkling test campaign I was involved in, we plotted a dozen or so configurations vs. the equation terms, and it is usually looked like someone sneezed on the graph rather than collapsing to anything resembling a curve. The math will happily give you a number that's potentially bogus in real life. There be dragons -- I'd recommend steering well clear of that failure mode.

#### pictsidhe

##### Well-Known Member
I believe that composite aircraft are generally designed with a safety factor of 2. Are the units dragons?

#### dsigned

##### Well-Known Member
pictsidhe said:
I believe that composite aircraft are generally designed with a safety factor of 2. Are the units dragons?
I'd imagine the dragons are the unpredictability failure near the theoretical limit. As I've mentioned before, in my (admittedly outclassed) opinion, with carbon there is no reason to skirt anywhere near the edge unless you are building for competition, very concerned about money/time and/or can afford to be wrong. You can get dramatically lighter than any other material being discussed and still overbuild. The quality of the composite produced will itself likely be the bigger variable.

DeepStall said:
In the wrinkling test campaign I was involved in, we plotted a dozen or so configurations vs. the equation terms, and it is usually looked like someone sneezed on the graph rather than collapsing to anything resembling a curve.
Any idea what the variation in failure is due to? Is it inevitable variability in the finished sandwich? Or something else?

#### DeepStall

##### Well-Known Member
Any idea what the variation in failure is due to? Is it inevitable variability in the finished sandwich? Or something else?
No, never figured out what was going on. We had decent agreement among all coupons tested at a given configuration, the coupons were sized to force a wrinkling failure mode, and visually appeared to be failing that way. The problem was the data points we collected did not seem to be behaving according to any of the terms in the wrinkling equation. Lacking the desire to pursue a PhD in this topic (or time/budget from the bosses to do so), we tabled the correlation effort and sized parts against our experimental wrinkling allowable, with an extra 15% uncertainty factor on top of our usual FS. In situations where the as-designed part didn't match one of our test configurations, we interpolated between experimental data points rather than trusting the as-calculated number.