What is Equilibrium Finite Element Analysis?
Jose Moitinho de Almeida (University of Lisbon)
This article was commissioned for a special edition of the NAFEMS Benchmark Magazine (January 2017) titled Beyond Conventional.
The article compares equilibrium finite elements (EFE) with conventional conforming finite elements (CFE). It draws out the virtues of the EFE formulation for practising engineers in terms of automatic satisfaction of the lower bound theorem of plasticity and demonstrates how safe structural design can be accomplished in a simple manner using equilibrium finite elements.
The design must be regulated by the art of staticks, or invention of the centers of gravity, and the duly poising of all parts to equiponderate; without which, a fine design will fail and prove abortive. Hence I conclude, that all designs must, in the first place, be brought to this test, or rejected. (Sir Christopher Wren 1660s)
The only reason why structural designers sleep soundly is the second [lower bound] theorem of plasticity theory. This theorem says that no matter how I designed my structures, they are safe because everything was in equilibrium, nowhere the stresses were too large and I used ductile components and joints. (Technical University of Delft)