Bounds on plastic strains for elastic plastic structures in plastic shakedown conditions

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

“…In the following section a special bounding principle, analogous to the ones formulated in the context of the elastic shakedown and based on a perturbation method [17], is reported.…”

“…Therefore, taking in mind the unknowledge of the history which describes the load multiplier ξ c (t) variation, and with the aim of obtaining some indication about the elastic plastic response which exhibited by the structure during the transient phase, it is possible to make reference to a suitable bounding principle based on a perturbation method. The bounding technique here reported, which represents a special generalization of analogous principles formulated in the context of the elastic shakedown [28], is devoted to the computation of a bound on a chosen measure of the plastic deformations eventually occurring at the end of the transient phase in condition of plastic shakedown [17]. With this aim, let us consider the relevant elastic perfectly plastic frame subjected to the described combination of amplified fixed and cyclic loads.…”

“…In particular, making reference to a special bounding theorem based on a perturbation method [17], suitable bounds on the plastic deformations related to the transient phase are imposed, whatever the real loading history is during the unknown transient phase; further suitable limits on the alternated plastic deformations related to the known steady-state response are also taken into account, imposing that suitably chosen measure of the plastic deformations occurring in the elements at the limit state of plastic shakedown be not greater than some assigned values.…”