Abstract: This paper derives the Ritz method and Trefftz method in linear elastomechanis with the help of general mathematical expressions. Thus it is proved that Ritz method gives the upper bound of the corresponding functional extremurn, while Trefftz method gives its lower bound. At the same time it has been found that the eigenvalue problem (e.g. thenatural frequency problem) concerning the functional variational method in Trefftz method is in concord with the lower bound method of the loosened boundary condition which seeks for the eigenvalue. Of course, the results of this derivation are also applicable to the sort of functional variational method of which Euler’s equation is linear positive definite.

Key words: Q_θ-class, Q_θ-majorized, maximal element, equilibrium, abstract economy