Non-conventional formulations for the finite element method

Summary This paper reports on hybrid formulations being developed by the Structural Analysis Research Group of Instituto Superior Técnico. Three alternative sets of hybrid finite element formulations are presented. They are termed hybrid-mixed, hybrid and hybrid-Trefftz and differ essentially on the field conditions that the approximation functions are constrained to satisfy locally. Two models, namely the displacement and the stress models, are obtained for each formulation depending on whether the tractions or the boundary displacements are the field chosen to implement inter-element continuity. Because they are derived from a strict hybrid approach released from the conventional node conformity concepts, these formulations allow different fields to be independently approximated, within certain consistency criteria, and enhance the use of a wide range of approximation functions. For simplicity and objectivity, the description of the approach followed in the derivation of the alternative formulations and models is based on the elementary linear elastostatic problem of structural analysis. Their fundamental properties are identified and their patterns of convergence are analysed and compared.