Cutout with rounded edges (should be easy)

I am trying to model a scene built out of pastry-cutter style shapes and I want them to have rounded (bevelled) edges.
I have tried various methods but have found it surprisingly difficult. If my 2D starting mesh is complicated then I can’t get the bevel modifier to produce more than a tiny bevel.

So I have been trying a different approach, starting with a boundary mesh which I extrude and then apply a solidify modfier. I then choose the inner perimeter and fill it with a face. After setting to render it smooth I found that the inner face is rendered concave (see image).

Surely there’s a simple reliable way of doing what I want. I’d appreciate some advice.

Thanks (in advance)

did you try to Ctrl-A you object !

happy bl

From top to bottom:

  • Bezier curve in 2D mode, extruded and beveled. Settings on the right
  • Mesh, cleaned, face loop around the perimeter. Solidify, subsurf and bevel modifier used. Settings on the right
  • Same mesh as previous but extruded and beveled manually