A free simulation program
Fusion 360 will do finite element analysis (simulation), although I haven't used it. Whether it will perform the type of analysis that you are looking for, I do not know. Check Autodesk's tutorials.

One problem that you will encounter is that items printed using FDM technology are highly anisotropic. In other words, they have a grain, and are stronger/weaker in some directions than in others. I do not think that Fusion 360 can take account of that in its analysis.

Autodesk: Fusion 360