I don't have an answer for you. But, I will suggest that you clarify a few things. This will help those who can help you.
First, are you doing fluid dynamics or simply mechanical loading of a static system?
" Another pipe with smaller diameter but different material " Is this 2nd pipe made of a different material, or perhaps carrying a different fluid that gets injected into the fluid that exists in the large pipe?
No fluid study in this model, purely static loading. The 2nd pipe is made of a different material ( more elastic) with thinner thickness. both pipes has the same fluid and the annuli between the pipes has the same fluid. Fluid pressure has no effect on any of the pipe loading.
That would be tricky in SWX Sim but it might not be impossible. In Abaqus you can use pipe elements to do this. I have no idea what your situation is or need. I have Abaqus if you want to contract out the job to me we can talk - I don't try tpo sell very often here but this is likely to be pretty challenging in SWX Sim so I thought I would mention it. In SWX Sim you could try it with shell elements but they tend to be a bit finicky with shell on shell contact. Also, you could try using solid elements for the outer pipe which makes the contact more robust when dealing with shells. In 2018 I noticed that displacement control in now supported with contact which might be very helpful. If the pipe length to diameter is large the chances of success seem remote due to the fact that it will drive large element counts, at least to me. Even with Force control if you can get a well behaved solution and get it to fail near the buckling point you might get an estimate of the buckling load at solution failure. Good luck.