Connections / Shells - Solids

Hello,

My question is simple and complicated at the same time. What's the best way to connect shells with solids? Context: I have an office chair and for the part that supports the back of the person, I modeled a surface, and I need to study the stress of the frame of the chair. 

I attached the model, there are MANY errors there (I didn't do it), but I must fix this and I am looking for recommendations. If you need to attach the magenta surface to the frame, how would you do it?

Thanks!