DUAL HYBRID-TREFFTZ ELEMENT FORMULATION BASED ON INDEPENDENT BOUNDARY TRACTION FRAME

The paper presents the dual hybrid-Trefftz (HT) element approach devised so as to enforce more strongly the reciprocity of boundary tractions at the element interfaces than the interelement conformity of displacements. 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 employing an auxiliary interelement displacement frame field to enforce the conformity on the internal displacements, an auxiliary boundary traction field is adopted to enforce at the element interfaces the reciprocity of tractions derived from the internal displacement field. Provided that the number of Trefftz functions is sufficiently large, this approach yields an opposite bound on the energy in comparison to the standard HT approach based on the displacement frame. As in the standard HT formulation,3 the dual HT formulation is particularly well suited for generation of highly accurate p-version elements. Although presented for solid mechanics, the formulation also holds for other problems. Numerical studies which involve comparisons of the two alternative displacement and traction frame HT element models have been performed by considering the Laplace's equation problem in two dimensions.