Without the flexibility factors and SIFs, an elbow would act as two mitered pipes welded together, but without any stress concentrations.
Not to belittle CAESAR, but to simplify the explanation of the process and generally explain how the code works, in CAESAR, we still model two "stick pipes" together. Instructing CAESAR that this is a bend draws it differently and adds nodes in the background to meet code requirements, as well as prescribes an estimate of how much difference there is between two "stick pipes" and an actual elbow, through means of SIFs and flexibility factors.
You can draw correlations between vessel nozzle analysis. My default standard practice (for flanged vessel nozzles) is to add a pipe flange, anchor the pipe flange and CNODE it to another flange, add a pipe element for the nozzle neck, anchor at the base of the neck, CNODE to a location on the shell, which is rigidly connected to the centerline of the vessel.
The assumption here is that there is absolutely no flexibility of the nozzle neck - vessel wall attachment, and generally this is conservative for our intents. The truth, however, is that there is flexibility here, and it can be estimated. For API-650 tanks, there's a module built into CAESAR for this. For pressure vessels, NozzlePro can handle this. Replacing the nozzle neck "anchor" for X/Y/Z and RX/RY/RZ restraints generally reduce loads at the nozzle and make them more realistic.
More realistic? Yes. Fully accurate? No.
In the same way helical physical springs can be approximated to have a single numerical value for its spring constant, this spring constant is averaged over a range of specified conditions.