The shell sections are actually quite stiff, as they're two layers of fabric, a layer of felt, heavy machine stitching and a lot of beads, but still not stiff enough - they need to be mounted on something.
The finished sections need to curve, so card is no use as it'll just bend, so hunting through cupboards (I'm trying to do this project from stash, remember), turned up some heavy weight Vilene. I don't think it's quite pelmet weight, but it should do.
I cut out Vilene shapes to match each of the nine shell sections, each one the same size as the stitched area:
They were each placed on the underside of the matching shell section:
The fabric hem was folded over and stretched over the Vilene shape, using herringbone stitch in a linen thread:
I tried to pull the fabric sections taught but not too tight, as I didn't want them to be pulled out of shape.
Here's the same section from the front:
And all nine sections, mounted onto the Vilene:
Next, the backs of the sections need to be covered.