If you have flanged nozzles on the vessels, you should model them accordingly.
Normal practice is to model vessel connections through anchors with CNODES, and loads may be pulled out via the restraint summary. Typically you want the loads at the wall, thus that is where your CNODE anchor will go.
Otherwise, you aren't considering differential growth of the vessels from their support point - i.e. the bottom of the "pipe." You should consider adding rigid elements from CL of the vessel to the bottom of pipe, and anchoring from there.