More Equilibrium, More Complementarity!

Abstract

This lecture addresses the relevance of using strong forms of equilibrium, combined with strong forms of compatibility, to assess the quality of finite element solutions.Advocating a more generalised use of equilibrated approaches may be seen, from an historical perspective, as "just" a continuation of the work developed by Fraeijs de Veubeke [1] in the sixties and seventies, which is probably unknown for most members of our community. This raises a question: Are equilibrium approaches nothing more than a footnote in the (distant) history of Computational Mechanics?My answer is a clear no. What is involved is not a race to know which type of formulation, compatibility or equilibrium, leads to better solutions, to smaller systems, is faster to solve, or easier to program. The relevant point is complementarity, a race that requires both contenders crossing the finish line.