# Equilibrium Finite Elements

Presenters - Angus Ramsay & Edward Maunder

### Details

Presented at a Research Seminar at the University of Sheffield, 7th September 2009.

### Abstract

The hybrid-stress or equilibrium finite element formulation offers the practicing engineer a number of advantages over the conventional displacement element used almost exclusively in proprietary finite element software. These advantages stem from the nature of the finite element approximation which, for equilibrium elements, satisfies, a priori, the equations of equilibrium in a strong, point wise, sense. The engineer using equilibrium elements can rest assured that for ductile structures or components, the stress field obtained, irrespective of the level of mesh discretisation, satisfies equilibrium and, in conjunction with an appropriate strength criterion, leads to a safe or lower-bound estimate of the limiting load. This property, which exists for the elastic solution, can be exploited further in limit analysis where the elastic solution may be optimised to maximise the lower-bound.

### Additional Resources

Computational Mechanics and Design Group, Department of Civil & Structural Engineering.