Limit analysis and strain-softening structures

Two simple approaches for investigating the behaviour of strain-softening structures are examined. The first is based on a modified form of the upper bound theorem of limit analysis: whilst the method proves unsuccessful, the theorem being disproved by counter example, useful insight is provided into the behaviour of strain-softening structures. The second approach, which is based on the Galerkin method, is ideally suited to investigating the behaviour of structures which, whilst exhibiting some ductility, do not have sufficient ductility for limit analysis to be applied without concerns for its validity. The equivalence of the latter approach and the standard upper bound theorem, when applied to perfectly plastic structures, is illustrated and examples of its application are presented.