Shakedown, Limit, Inadaptation and Post-Yield Analysis

Abstract

An inelastic structure subjected to variable repeated loading may work either in elastic, shakedown (adaptation), inadaptation or limit regime. For the given load variation domain the safety factors against first yielding, inadaptation and limit state can be defined by the shakedown and limit analysis. The classical shakedown and limit analysis can be extended to account for nonlinear geometrical effects as well as material hardening. In this chapter the kinematic approach is described. An uniform formulation of shakedown, limit, inadaptation and post-yield analyses of discrete elastic-plastic structures is presented. Classical limit and shakedown problems are formulated as linear programs, whereas the post-yield and inadaptation as sequences of linear programs. Nonlinear geometric effects, nonlinear strain-hardening as well as material damage may be accounted for.