How can I secure stiff fabric to wood without risking ripping and without adhesives? I am planning a project using simple 1" x 2" pieces of wood and attaching a length of textile between the planks.

The wood will be about 12 inches long, and the fabric will go from long-edge to long edge and up to 3-4 feet wide. So, 12 inch by 36-46 inch pieces of fabric.

The ends of the fabric will be flush with the outer edges of the wood, and each end will be sandwiched between two of the pieces of wood. 

Once everything is assembled, the fabric will be taut, but still flexible, and need to support up to 40 pounds without the fabric tearing from screws I use to attach the top and bottom wood strips to one another.

I want to be able to attach the fabric to the wood, without having to use glue. I want to be able to swap out the fabric with different lengths as desired, or attach multiple pieces that branch out in different directions. Some type of eyelet protector comes to mind, but I'm not sure how to attach one to a pre-made hole. 

Here's a 2-minute diagram of what I'm trying to achieve:



This is the view you would see from the side, once this hammock/shelf is attached to a wall. The brown pieces are the woods sandwiching the blue fabric, and the grey parts are the screws/bolts I will be putting through the wood and fabric. 



For those curious, I have been inspired by some cat shelf/highway products, but am not satisfied with the appearance of them. I want to make something myself that is functional and pretty. But, since living creatures will be playing and sleeping on these modular pieces, safety is of the utmost import.
Instead of securing the fabric with the scews, I'd let the fabric secure itself on the outer edge of the wood. The less holes you poke into a fabric, the stronger it is to withstand tearing or wearing out.

Instead of a simple hem, you could roll and secure the fabric (light blue) around a cord or other thick material (dark blue) to create a bulge that is held by the wood (brown). If the material is somewhat thick and the wood closes well without big gaps, a "simple" hem might even be enough.



Advantages:


Preserves the fabric's strength by avoiding holes
If a weight pulls the fabric down, the force is distributed between all points on the edge instead of single holes. 
You can easily replace one piece of fabric with another one.
No need to sew button holes or inser grommets into the new fabric


Disadvantages:


You need to sew a thick or corded hem on the fabric
The hem is always visible on the "outside" of the wood pieces