Hybrid-equilibrium elements with control of spurious kinematic modes

Abstract

A review is presented of a recent formulation of hybrid-equilibrium elements for modelling planar structural problems. The formulation is based on the use of polynomials of general degree to approximate internal stress fields and bounding side displacements. The existence of hyperstatic stress fields and spurious kinematic modes are considered algebraically for both primitive and macro-elements, the latter providing a means of controlling or removing the spurious modes in the former. Consideration is given to stress fields which are statically admissible, and to Trefftz stress fields which are both statically and kinematically admissible.