A friend asked me to build some corner wall shelves for his son's room for him to store/display his small toys. He wanted a simple, clean look with no brackets, just the shelves floating on the walls. That made a stress panel seem like the best approach. I've built stress panels with wooden grids in the past but they take substantial time to construct so to keep the cost down I decide to use foam panels instead. That also allowed me to use 1/4" plywood which is actually less than 3/16" these days and so flimsy it would never look flat only supported on a grid system. I would have had to have used 1/2" plywood with a wooden grid, driving up the cost and weight.
After cutting the 1-1/2" thick pink foam to size I calibrated the thickness by running them through my drum sander, which works really well with it. The edges of the shelves are made from pieces of poplar with a rabbet cut on both edges to cover the edges of the plywood, and mitered at the corners. I attached the poplar edging to one piece of plywood first using glue and pin nails. when that was dry I assembled the panel like this.
Gorilla Glue sticks great to insulating foam. I used yellow glue to hold the plywood to the poplar edging. The space at the back of the shelf is where it will fit over a wooden ledger first screwed to the walls. I was going to do the glue up in a vacuum bag but decided it would be easier with some cauls and clamps since I didn't need much force as I'm dealing with foam.
After painting and installation the shelves look like this:
I also made a hanging wall desk, but used a more conventional approach for that. The walls were so curved and out of plumb that it took a lot of scribing and work with a belt sander to get the desk to fit well to the walls.
I got this photo a few hours later. I guess his boy likes them.
John