M.I.T.'s coursework is available online. Lectures, homework etcetera. Here's the mechanical engineering section...
http://ocw.mit.edu/OcwWeb/Mechanical-Engineering/index.htm
I can't imagine the kind of personal discipline it would take to teach yourself the fundamentals required to have a good grasp of F.E.A. You need some decent calc, difi q's, physics, statics, dynamics and materials coursework under your belt. I seem to recall that my F.E.A. coursework was in my junior year.
-Bernie, P.E.
