On shakedown of three-dimensional elastoplastic strain-hardening structures

The present article considers the shakedown problem of structures made of either kinematic or mixed strain-hardening materials. Some basic and useful shakedown properties of elastoplastic strain-hardening structures are proved mathematically. It is impossible for a kinematic strain-hardening structure to be involved in incremental plastic collapse, and so its only possible failure mode is that of alternating plasticity. A time-independent self-equilibrium stress field has no influence on the shakedown of a kinematic strain-hardening structure although it contributes to the magnitude of plastic deformation. The sufficient shakedown conditions for either kinematic or mixed strain-hardening structures are deduced, from which the lower bound of shakedown load domain can be obtained via a mathematical programming problem. It should be pointed out that, to guarantee the safety of an elastoplastic strain-hardening structure, the damage analysis is also necessary to determine the maximum load factor the structure can bear. The shakedown analysis of strain-hardening structures can be simplified by the conclusions obtained in this article, as is illustrated by two simple examples.