On some issues in shakedown analysis

Shakedown analysis, and its more classical special case of limit analysis, basically consists of "direct" (as distinct from time-stepping) methods apt to assess safety factors for variable repeated external actions and proced ures which provide tipper bounds on history-dependent quantities. The issue s reviewed and briefly discussed herein are: some recent engineering-orient ed and cost-effective methods resting on Koiter's kinematic theorem and app lied to periodic heterogeneous media; recent extensions (after the earlier ones to dynamics and creep) to another area characterized by time derivativ es, namely poroplasticity of fluid-saturated porous media. Links with some classical or more consolidated direct methods are pointed out.