Limit states of structures in n-dimensional loading spaces with limited kinematical hardening

The load bearing capacity of engineering structures subjected to varying thermo-mechanical loading can be determined most conveniently by shakedown analysis. Admittedly, if limited kinematical hardening is considered, shakedown analysis is, as yet, restricted to either one or two independently varying loads. In consequence, the aim of this paper is to extend existing formulations for arbitrary numbers of loading, which is inevitable for most technical applications. For this, limited kinematical hardening was incorporated into Melan's shakedown theorem by means of a two-surface model covering both alternating plasticity and ratcheting, generalized to n-dimensional loading spaces. As a result, the three-dimensional shakedown domain accounting for hardening is presented for a flanged pipe subjected to thermo-mechanical loading.