A try...

I understand that this is probably not even a printable model, but it illustrates some things that could be worth thinking about...

The weaving can definitely be developed more in this one, but I thought this image was worth showing, since it contains another aspect: the folding of the umbrella. The "waves" also work together in another way. One side is more safe, and the other is more exposed (which of course can be developed way further). But I found the folding aspect interesting.

Let me know what you think! Talk to you soon.