I use Roark thick cylinder formulas with boundary conditions. So, a given pair is one cylinder under external pressure, the other under internal pressure. The final diameter under load is equal for both parts.
The frictional load is the unit load times the contact area times an assumed coefficient of friction.
You could do it closed form, or use a numerical solver to find a solution.
I know that's kind of general, but in the end, you have a quantity of cylinders that are under external or internal pressure that have a single diameter at each interface.