Hi @tsloan,
if you are concerned about the superficial stress concentrations you are getting because of rigid supports, you can use the remote displacement constraint. If you leave it as deformable the constraint itself won’t add any stiffness to the model. You would need to add a constraint to each one of the fixations and put the remote point at the COG of each of the cylindrical faces. Then you can even constrain the rotations (or leave them free). I would actually leave the rotation free for the cylinder axis rotation and fix it for the other two.
I guess a pressure is fine, as long as this is what actually happens in your real application (like a constant known pressure).
Using second order elements will greatly increase the accuracy of the stress computation. In cases of pure bending this might well be in the range of up to 50% difference. Usually first order elements are approximating the displacements quite good, but are underestimating the stresses (you can also have a look at this forum post which highlights similar projects where second order elements were needed: When should I use a second order mesh?).
Best,
Richard