Fusion360 is free (1). I used it for a while; though I didn't get into all of the features so I didn't really explore the physical simulation capabilities in depth, but I know it's supported to a degree (2). I'd imagine the FEA engine isn't as rigorous as paid software like say, Autodesk Inventor or Solidworks.
As someone who does a fair amount of 3D modeling, I've always thought sketchup was on the right track. It's also available in a free version of course, and the 3D warehouse has a ton of pre-made models in it that I use all the time.
From my experience, I would say the community-built sketchup plug-ins available are decent, but definitely hit-or-miss. I've never found a good (i.e. non-buggy and well-supported) 'physical simulation' plug-in for sketchup, but I haven't checked the plugin store in a while. That, and some plugins require sketchup pro, which isn't free. In the free software domain, I'd say basic Sketchup is good for quick mock-ups, whereas Fusion 360 can be used for higher precision modeling.
1. https://www.autodesk.com/campaigns/fusion-360-for-hobbyists
2. https://www.udemy.com/fea-simulations-with-fusion-360-static...