This will give you a basic idea:
Omni Frame Specifically designed for the Zippy and Urban Zippy, the Omni Frame will add rigidity to the bag and allow for better carrying capability when need. The Omni Frame will also fit in the water bladder pocket of any Omni pack. Weight: 14.8oz Dimensions: 16.5" x 7.5" Color: Black...
kifaru.net
They add carbon fiber arrow stays (supports) to increase rigidity.
You can also add aluminum stays to stiffen it further:
DIY internal frame for your backpack. This article will go over how to make a plastic frame sheet with an aluminum stay. Make your own backpacking gear.
www.stitchbackgear.com
Quarter Panel Frame Specifically designed for the Bane pack, the Quarter Panel Frame will add rigidity to the bag and allow for better carrying capability when needed. Weight: 5.6oz without stay Weight: 10.4oz w/ aluminum stay Dimensions: 18.75" x 9.25" Color: Black Material: HDPE Frame sheet...
kifaru.net
Real use gear for backcountry travelers
hillpeoplegear.com
Sewing a stave sleeve is probably best, but gluing a sleeve on with epoxy or something might be a viable hack, or even bolting it on.
I have one pack that uses a plain HPDE sheet in a sleeve (the size of the front of the pack, that sits against my back). It isn't very structural but it is light and it helps the bag maintain it's shape.