I contacted COMSOL support about our difficulties with the relative residual error and was told "Typically for solid mechanics this error is because you have not constrained the body enough. So any solution + a rigid body transformation is also a solution. To remove this non-uniqueness, you need a solutions modulo the rigid body transformations. So try and constrain the body somehow." This is what the gravitationally balanced body load was supposed to do, but using the stationary solver has been non-convergent and the eigenfrequency solver has generated odd modes, with the first real modes being sheer modes. These outputs indicate a problem with our model. Matt noticed yesterday that the meshing in our model was slightly non-symmetrical, but we initially dismissed it as not being significant since it was a minor difference which we did not think could account for the large errors we are facing. At further consideration though, if some asymmetry arising from any source, even a numerical or rounding error, were present, that could cause a slight rotation of the object which would cause the object to experience a torque and minor sheer force. The stationary solution would not converge in this case, but the eigenfrequecy solution might, and if it did it would make sense to see sheer modes for some of its low frequency eigenmodes, as we have. One possible solution to this problem is to change the way we mesh the material to ensure a symmetrical distribution of nodes in the x-y plane, probably by extruding lower dimensional meshed systems into our model. I am unsure if we would be able to implement this solution once we start to change the size of the radii of the object's faces. An alternate solution is to find another set of boundary conditions which should be equivalent to the gravitational body load constraint, but which are stable relative to minor perturbations of the system's conditions. I think that I have found another set of boundary conditions which should work and not be too difficult to implement in COMSOL.