How to model a cap?
I started playing with it and I have the crevisis you are asking about. you should start a project here and upload your file. I saved my version but I am using a SW 2012 so I don't think you will be able to open it so here is how I did it.
I opened a sketch on the plane you created. (the top of the ribs)
created a rectangle the size I wanted and made sure it was large enough to touch both the rim and the inner high part.
extruded to the bottom surface with 5 degrees of draft
created an axis using the front and right plane
did a circular pattern (under the linear pattern button)
did a second circular pattern the other direction (click on the arrows to the left of the axis to change the direction)
added some fillets
and a few more fillets
and this is what we have.