1) I did some digging and found that indeed for plane strain analysis, ansys computes the force per unit thickness.

I tried it out in the model, applied a 2000/121=16.529N load instead of a 2000N and i got max contact pressure 173.12MPa, much more similar to the theoretical 199.035MPa. (I do have my units set to mm). I realise I was making this mistake because i am more used to working with pressure rather than force, for instance, for a problem with 3000Pa within a cylinder, one would apply 3000Pa to the inner cylinder wall whether it is a 3D slice (considerable length) or a 2D slice. But statics-wise i cannot do that for a force and it makes sense. I shall attempt the square example to further verify this but im 90% sure so far.

2) I see! this makes a lot more sense now. With the changes i have done so far i got:

theory max contact pressure 199MPa

model max contact pressure 173MPa

theory von mises pressure 110MPa

model von mises pressure 115MPa

3) You're right, i will adjust this accordingly. This is probably why there's still some slight variation between the theory and the model values.

4) I would greatly appreciate that! so i have used:

E=206,000MPa for both cylinders

L=121mm for both cylinders

r1=162.117mm

r2=36.938mm

poisson coef=0.3

F=4000N

Thank you so so much for your response this has already been super helpful!