As you seeing, there are many different types of nonlinearity; nonlinear material constitutive relationships, nonlinear deformations (such as a end load on a beam causing the beam to wrap around itself), nonlinear kinematics (that is, multi body contact). Each can cause instabilities in the FE solution process. Can you tell me what material you are using--that is, what are using to define the material in the material properties window?
Is there instability problem there when you apply say 100th the force? If not, your analyses appears to be correct, that the force is too large. However, if the force is an input, that is, you have to load this thing with a large force, you might be able with very small load steps to keep the model stable, or in the case of applied displacements, very small displacement increments. Since the problem is nonlinear, you'll have to play around with the inputs until the displacement you input causes the force you need.
I would think all commercial FEA codes have the capability to compute reaction forces someplace in the Results window. Check the FEA help, that might have your answer.
Is it me or is eng-tips squirrely today? 6/20/2007. I am having lots of problems with access.