I imagine that it gains a lot of strength from being bent into compound curves.

Flat thin things are weak. Curved thin things are much stronger. Add compound curves and you're really talking.

You'll see this all over if you look for it: ribbed metal siding and roofing, waffle slab cement, automotive hood strength comes from the thin stamped sheet metal on the inside, floor pans have ribbing, soda bottles that you can stand on when empty, etc.

You'd probably want to use something like tent stakes to keep it in place, but being bent like it is will give it good holding strength.