Hello,
There are some differences between the analytical method and the FEM. The analytical method is a continuum and normally with stress equally distributed along the object. The FEM considers stress concentration, mainly considering the geometry. The stress concentration factor on ANSYS can give a better estimation than the calculations you are doing. I would check: If you are considering stress concentration points (i.e. Sharp geometric transitions or holes) and if they are considered on the calculations. If the stress concentration factor is exactly for the type of loading you have. I would check also the intensity of loading. The plane stress model may not be the best for this problem. It considers stresses as null in one direction. Check out other stress models, that may be more adequate for your model. I don´t know what the model is, how is loaded, and so on, so this is the best way I can help.
Regards,
Hugo Silva
Mechanical Eng. PhD student
Materials Eng. MSc.