Years ago my family had a chair that I loved, and I've decided now that I want to get one of my own, There was a stand that was made of wood and then there was a wooden frame that resembled a turtle shell that fit on top of the stand, and there was a big round cushion, practically a mattress, that fit into the shell frame. Could anybody tell me what these chairs are called?

It's called a Papasan Chair.

Check this out

Papasan Chair, double papasan chairs, and swivel rocker chairs and cushions (http://www.papasanfurniture.com/)

The only thing I can think of is papasan chair
Pier One sells them I have a bunch of them but need cushions.

Yes, that's it, thank you for the help