Is there a great resource online where I can find an abundance of worked out examples that I can go through? Perhaps specifically about the variational method. Thank you.
There are a lot of worked out examples in Bathe's finite element book, Finite Element Procedures in Engineering Analysis. I don't work for ADINA, but if you are buying the book anyway, you can get a limited capability ADINA FE software when you buy the book at ADINA's website. The license is 900 nodes, and only good for a year. Cost is only $140.
If Clansman's wants to learn to write his own FEM code, then there's no better book than Bathe, but if he wants to learn to use FEM for solving problems, that's the worst book to read. Get a copy of Building Better Products by Vince Adams & Abraham Askenazi, get your university text book on strength of materials and grab any free FEM application on