Comparative analysis of hybrid-trefftz stress and displacement elements

Summary The alternative stress and displacement models of the hybrid-Trefftz finite element formulation for the analysis of linear boundary value problems are derived in parallel form to emphasise the complementary nature of the fundamental concepts they develop from. In the stress model the stresses in the structural domain and the boundary displacements are independently approximated and inter-element stress continuity is enforced explicitly. Conversely, in the displacement model the displacements in the structural domain and the boundary tractions are independently approximated and inter-element linkage is enforced in the form of displacement continuity. In both models the approximation in the domain is constrained to satisfy locally all field equations, a feature typical of the Trefftz method. Duality is used to interpret physically the finite element equations, which are derived from the fundamental relations of elastostatics. Numerical tests are presented to compare the relative performance of the alternative stress and displacement models.