I'm triyng to animate an umbrella like a folding fan, i've hooked the cloth to the rods, it follows the rods and makes good folds after the solidify and subdivision modifiers, but the cloth is penetrated by the rods. I don't know how to solve this problem.. i've tried to change some physics value but the bake always went bad. Images https://i.stack.imgur.com/u1R75.jpg
I have been having the same problem, and already spend some nights of the last week on this. The best solution i found was to export and import the cloth simulation as described in this link. After that i put the fabric a little bit higher so that it doesn't collide anymore.
It is the best thing i come up with, but i hope someone comes with a better solution.