Alternative approach to shakedown as a solution of a min-max problem

Kinematical shakedown analysis with temperature-dependent yield stress

“…It is easy to see from (32) and (34) that the dead (or monotonic) loads have no in uence on the alternating plasticity limit (if these loads do not change the material and the geometry). See also [35] for this conclusion. where t1 y and t2 y are two yield points corresponding to the actual temperature at the beginning and at the end of the half-cycle.…”

Shakedown analysis of spatial frames with parameterized load domain

“…It seems that no further attention has been paid to the inherent bi-level character of Maier's technique, despite its computational potential, since the lower level problems are almost trivial LP problems in case of polyhedral load domains. The minmax approach [35][36][37] to shakedown analysis constitutes another bi-level technique. It has been developed for general yield criteria (linear or nonlinear) and polyhedral load domains.…”

“…Pycko [34] has developed a cycle-oriented incremental analysis of SDA problems with nonlinear variable load domains. His work is based on the minmax approach to SDA problems proposed by Zwoliński and Bielawski [35] and developed by Pycko and Mróz [36]. Load and material uncertainties have been treated by various researchers in a probabilistic framework, in conjunction with reliability considerations.…”

A cycle-oriented incremental analysis of shakedown problems

“…Due to the well-known fact that the elastic locus di ers from the plastic one, an elastic-plastic response is additionally observed besides the purely elastic and plastic cross-sectional behaviour. It was proved by Pycko and Mrà oz 13 that reverse (alternating) plasticity criteria are a ected only by the elastic locus whereas the ratcheting (incremental collapse) depends only on the yield locus. Reverse plasticity can be treated as a local phenomena taking place rather at the cross-sectional but not at the structural level.…”

“…The problem was then rigorously proved by Pycko and Mrà oz. 13 More advanced optimization algorithms were proposed by Zwolià nski 14 and Janas et al 15 The proposed method of a cycle-oriented incremental analysis allows to determine the steadystate response for structures subjected to cyclic (or variable repeated) loading below or at the shakedown limit. It adapts the concept of shakedown analysis centred on the min-max formulation 16; 17 to incremental formulation based on Melan's theorem.…”