Abstract: In this paper, a new way of combined application of the energy method and the weighted residuals method(called EWR method) to construct finite elements is proposed, Firstlly, the condition of displacement continuity is relaxed using the method of weighted residuals. As a result, only one variable (displacement) remains in the variational principle as the energy item caused by the incompatible displacement no longer exists. Secondly, since the method of weighted residuals used here is considered relating to the element energy functional, it is easy to give a physical explanation to the weighted residual equation. Thus, if the weighted function is chosen properly, the satisfi-cation of the weighted residual equation will be equivalent to the element converglnce criterion. Moreover, changing the weighttd function, various existing displacement-based elements can be derived from the proposed b. VVR method.

Key words: variational principles, finite element method, the method of weighted residuals