Ideal Material for a model rigid airship

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I am building a model rigid airship, and in order to maintain it's structure I used a balsa frame. Unfortunately this weighs a fair bit and can take up to half of the lift generated from the light gas, and it is not particularly strong.

Since I use polyurethane for the outer skin, I am wondering whether it would be possible to inflate the airship to the size I would like it to be, and then treat this material with some kind of chemical to make it hold it's rigidity? I would be open to any kind of method that is similar to this and ends up giving me a lightweight rigid structure. I also know that this may be not possible, but any ideas I would love to hear about.
 
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How about making a foam mandrel, and then wrapping carbon fiber into some sort of
crude isotruss shape, then dissolving the mandrel with acetone? The fiber would need to be impregnated with resin, and later covered with any type of nonporous covering, such as used in R/C aircraft. If super light weight is not a concern, perhaps fiberglass or other fibers would work and be cheaper.
 
Carbon composite from me as well.

My own variation: you can find tubes and rods, ready to use, from kite or model aeroplane suppliers. Industrial suppliers exist as well. Far better than first learning to use carbon composites.

Full-scale airships also tested internal structures made of inflated plastic hoses. Advantage: they resist a shock, and don't punch the envelope.