Did you ever notice when your IKEA Arstid lamp stands close to the wall, and someone touches, it, the lamp screen will tilt and fall down?
Now no more. Print 3 of these and just clip them at the top ring of the lamp. It will keep the cloth tight enough to the lamp, so it won't tear off and fall down anymore.

I designed this, using Autodesk REvit, becuase of the complex geometry. I found, that TinkerCAD has a revolve-SVG shape, so this one would have worked as well.