Dynamic shakedown in elastoplastic structures with general internal variable constitutive laws

Abstract

The shakedown and nonshakedown theory in elastic-plastic dynamics is dealt with here on the following basis: for the material behaviour a quite general class of internal variables constitutive model is adopted allowing for general nonlinear hardening law; discrete structural models described in terms of generalized stresses and strains are referred to. Some earlier results concerning shakedown are extended to the present more general elastic-plastic models; following the “static” approach a necessary and sufficient condition for adaptation is established; the “dual,” kinematic, approach gives rise to a necessary and sufficient condition for inadaptation; two extremum characterizations of the safety factor are presented.