Finite element analysis and the stress correspondence paradigm

The underlying mechanics of the finite element method as applied to structural analysis is explored in paradigmatic terms. It is shown that the stress correspondence paradigm has the most explanatory power and that it can be axiomatized from a very basic principle, the Hu-Washizu theorem, which is a variation of the least action principle. Numerical experiments are presented to show that the predictions based on analytical quantification from the stress correspondence paradigm are verifiable.