Making a 3D system translationally invariant?

Hi,

I have this simple question:
I have a COMSOL model for a physical problem (say a structural mechanics problem)
defined on a 3D prismatic body (say a cylinder with axis coinciding with Z axis).
I want to make this body represent a slice of an infinitely extended translationally invariant
system (therefore the length of my simulated 3D cylinder is arbitrary, but not zero!)
Of course the boundary conditions that I want to apply must also be compatible with
the translational invariance .

Is there any clean way to force my dependent variables (say displacements) to be
EXACTLY independent of the z-coordinate?

My initial guess was to mesh the length of the cylinder with a single element, and
then take periodic boundary conditions between the top and bottom ends
of the cylinder.

Unfortunately the results show indeed equal values of the displacement at the ends of the cylinder
but also some remanent z- dependence along the length of the cylinder, that does not
comply with the desired translational invariance.

Of course, I am perfectly aware that this kind of problem could be best treated by using
a 2D model for the cross section, but for reasons long to explain here, I prefer to implement
it as a 3D problem.

So, any clue on forcing the z-independence in a 3D model?
I would be extremely grateful.

Regards,
Alberto.