Symmetry limit theory for work-hardening structures in the shakedown region

The symmetry limit theory extended to general discrete structural systems subjected to quasi-static cyclic loading, which has been established by the authors restricted to perfect plasticity, is further extended to hardening plasticity. Constitutive equations for the variation of a steady state are derived by the formulation essentially different from the previous theory, in which basic relations of the plasticity theory, such as a flow rule, a hardening rule and a consistency condition, are applied to each plastic deformation accumulated during the convergent process to an adjacent steady state. The theory is verified through hysteretic response analysis for 2-D finite element models.