Blender has a cloth modeling system that can realistically animate planes as though they were different kinds of cloth. A fun trick I've found is putting different things between a cloth object and the floor and then printing the result of it falling for a few dozen frames.
Provided you can either get your slicer to infer that the "inside" is what's under the dome or just extrude plastic along the perimeter, these will print readily.
I've included the .blend file, but be sure to check out the excellent BlenderCookie tutorial for more details on using the cloth simulator:
Note: I think if you used Blender's "solidify" modifier you could get them in shape enough to take 'em to Shapeways...