Strong equilibrium in FEA – an alternative paradigm?

This paper presents a brief review of some recent and current research in the formulation and application of hybrid equilibrium elements, with emphasis on the design and assessment of structures. The aim is to highlight the means and the benefits of obtaining fully equilibrated solutions from finite element models. The mechanics of the formation of an element stiffness matrix is presented in physical terms, and this is followed by two areas of application: (i) regarding lower bound (safe) limit analysis of plates with particular attention to the use of the von Mises yield criterion for steel; and (ii) the determination of load paths in a masonry arch. The latter is modelled by facetted thick shell equilibrium elements, and a solid hexahedral equilibrium element is also proposed for modelling the voussoirs. We conclude that there is much scope for equilibrium models to be a valuable tool for structural engineers.