FDM layer bonding strength I'm looking for some advice, rules of thumb, or models for how to design parts for layer bonding strength.

As an example part, lets assume a circular beam in bending (tall cylinder). Depending on how the part is setup on the build platform (tube axis aligned parallel to Z, or setup to lay in the X-Y plane) the layers and internal structure will then be different depending on the orientation chosen at the time of building. Does/has anyone done any investigation to what roles these factors will play on simple shapes like a solid cylinder?

Ideally, with a CNC'd, injection molded part the total strength of a solid part is quite easy to model (mathematically) for strength and flexibility. However, with a 3D printed part the orientation makes the isotropic material properties effectively anisotropic, as layers don't bond perfectly, different cooling rates, and a host of other reasons. 

Ideally I'd love to find a 'simplified' model that can be applied to hand-calculations to come up with rough approximations to part strength and bending. My guess is that these parts would be modeled something similar to an ABD matrix, similar to composite materials, but that's just a guess.
I have not been able to find a simple model for FDM part strength.  FDM parts are pretty complicated as they have a LOT more things that affect their strength than just layer adhesion.  Since any "solid" part will have infill, the part can't really be modeled as a laminant.  There are so many settings you can play with in the slicer that effects part strength, the model would have to have tens (if not hundreds) of parameters.  Also, you would likely have to establish them for your own printer since lots of things can affect them (like room temp, ventilation, humidity, material, material storage, ...)

One empirical example discussing the affects of FDM choices on part strength is a video done by Angus at Marker's Muse.  In the video he discussed how orientation and wall thickness affects strength.  Angus is not a math/ME guy (by his own admission).  FEA or other modeling would not be his approach; but, you can get some insight from his experience.

On the modeling front, I have seen one company that did create an FEA model to test whether their product would be strong enough if they produced it using FDM.  Here is the publication they wrote showing their analysis approach.  It will give you some insight on how they approached what I think you want to do.  

Note: They do offer a service where you can pay to have your part analyzed for a considerable amount of money.  I have no idea how much money; but, based on jobs I have quoted in the past, I would expect it would be a least a few hundreds dollars.

As for me, I really enjoy basing my decisions on models and understanding how a part/process works. In this case; however, an empirical/experimental approach might be more cost effective.  If you really want to take an analytical approach (and have the time to spend doing it), I would recommend choosing several key parameters and run an analysis using DOE (Design of Experiments).

If you come up with something, I would love to see it posted here.

Good luck and happy printing.