DUAL HYBRID-TREFFTZ ELEMENT FORMULATION BASED ON INDEPENDENT BOUNDARYTRACTION FRAME

The paper presents the dual hybrid-Trefftz (HT) element approach devis ed so as to enforce more strongly the reciprocity of boundary traction s at the element interfaces than the interelement conformity of displa cements. As in the standard HT approach,1,2 a complete set of Trefftz functions is used to represent the internal displacement field of the element (and, as a consequence, the governing Navier-Lame differential equations are a priori verified over the element). But rather than em ploying an auxiliary interelement displacement frame field to enforce the conformity on the internal displacements, an auxiliary boundary tr action field is adopted to enforce at the element interfaces the recip rocity of tractions derived from the internal displacement field. Prov ided that the number of Trefftz functions is sufficiently large, this approach yields an opposite bound on the energy in comparison to the s tandard HT approach based on the displacement frame. As in the standar d HT formulation,3 the dual HT formulation is particularly well suited for generation of highly accurate p-version elements. Although presen ted for solid mechanics, the formulation also holds for other problems . Numerical studies which involve comparisons of the two alternative d isplacement and traction frame HT element models have been performed b y considering the Laplace's equation problem in two dimensions.