Unless you believe Daedelus, lighter-than-air craft were mankind's first successful venture into flight. Dirigibles are perhaps my favorite flying craft, followed closely by blimps. But the shape of the dirigible is dictated by the lifting gases, and itself doesn't contribute much beyond simply containing
Forcing the lifting envelope into a shape could permit some dynamic lift that would make the dirigible capable of much, much more. With dynamic lift, the craft could perhaps be made to fly at a negative-buoyancy loading. This would dictate higher flight speeds and also require a runway, but would also allow a greater degree of control.
To force the envelope to hold a shape requires that there be less pressure within the envelope, and a framework to hold it in the shape desired. A network of cells, filled completely with aerogel like a parcel stuffed with expanding foam, mostly fills the volume of the airship. The rest is a network of long, high-pressure "bones" that force the cells to hold their relation to one another. The relationship of compressive strength in the cells and rigidity in the bones will permit the dirigible to hold its shape even under the static stress of the payload and the dynamic stresses of flight.
The cells themselves, having considerable compressive strength, could even hold their lifting gases at a partial vacuum, to further offset their own weight. The bones can be nothing more complex than long, strong tubes that are inflated at 2-3 psi, again with lifting gases.
I would love to be able to recommend the entire airship lifting volume be one enormous, monolithic block of aerogel, but as I understand it aerogel is a bit tricky to make, and to make such an enormous batch would be just about impossible. Also, aerogels are kind of brittle - when struck too hard, they shatter. I don't want my airship to shatter. That's the other reason for packing the aerogels into individual cells, which are then separated by the bones - the bones provide buffer space to protect the friable cells from shock loads.
Biggest downside: the aerogel adds extra mass. But with the potential to load the cells at a partial vacuum, that may be completely offset. The aerogels, due to their insulative nature, may also permit use of hydrogen for a little bit more lift.