Sorry for the late reply but I really had to focus on the assignment. In the end, I derived the equations analytically and then solved them in MatLab to get the answers. I just couldn't find my way around the APDL. I will definitely need some additional courses on that to be able to work with the custom elements. 

I guess I could also try to define the non-linear spring tabular data to model the whole system response, as You proposed in the original post, but that's always the problem with the assignments. If they are interesting, there is always too little time to dig deeper, and now I have another course to take care of the final exam. 

Hopefully, I'll still have some will to come back to that one after I'm done, and then check if Your tips would help, but for now I'd say that I have to survive through the rest of responsibilities.

Thank You so much for the answer any way! It's nice to know there's someone to turn to in case of trouble!

Best regards!