SOLIDWORKS Simulation Premium can do this. You'll want the Nonlinear package for the elastomeric material. You could then forcibly deflect the green ring and produce the force required to do so. Then just run for different configurations.
Non linear package is also the only one that can trace a time history when you load from 0 to 100% of whatever force you want there, You can schedule the force in time and check the displacements at each time step or you can schedule a displacement of a point on the green surface or the whole surface in time and you can fix the orange surface in three points and probe the reactions, the applied force would be the sum of the reactions.