Hello, Mike, Hello HesamK,
I'm answering so late because I wanted to try different things and read some info in the User Guide. My (apparently) easy simulation had two critical aspects: firstly, the inner cylinder is too "free" to move. Even if there's a force oriented only in x direction, the cylinder must be correctly constrained. That means that no rotation must be possible and no translation in perpendicular directions (y and z) should be possible. ONLY one direction can let be possible, and this one is the direction the force is acting along. For this reason a remote Displacement is the right choice.
Secondly: Contacts. Since the distance between the contact side and target side can be big (the outer cylinder can be much much bigger), the contact can be open (in the beginning, at least). A frictionless, asymmetrical contact can be the right choice but, is MANDATORY to set a form of damping, in order to limit the motion of the inner cylinder during the motus before it touchs the outer cylinder. Stabilization Damping is definitely the right choice. It's difficult to predict the corrisponding value. As perfectly said in the YouTube video "Utilizing Contact Stabilization Damping Properly in Ansys Mechanical" you have to plot, during the computation process, or at the end of it, how big the Stiffness Enery is compared to the Damping dissipation Energy. The damping energy must be 3, 4 orders of magnitude minor than the the Stiffness Energy, since the damping agent, in reality, does not exist, so its energy contribution must be negligible so that it cant alter the essence of the problem you are studying.

I want to thank Mike and HesamK very much for helping me out and Erik for indicating me the video that describes how important the Contact tool is! Thanks so much again, all of you guys!