Direct evaluation of the limit states of engineering structures exhibiting limited, nonlinear kinematical hardening

The lower bound shakedown analysis is a most convenient tool to determine the load bearing capacity of engineering structures subjected to thermo-mechanical loadings. In order to achieve realistic results, limited nonlinear kinematical hardening needs to be taken into account. Although there exist different formulations incorporating limited kinematical hardening in the literature, it is still not conclusively clarified, whether or not these are applicable to generally-nonlinear hardening laws as well. Thus, the aim of this paper is to propose a method to determine the shakedown limit loads accounting for limited, generally-nonlinear kinematical hardening, and to close the discussion about the effect of the nonlinearity of the hardening law. The proposed method is based on an extension of the statical shakedown theorem by Melan using a two-surface model, which captures both incremental collapse and alternating plasticity. Furthermore, it is implemented into an interior-point algorithm, which is tailored to shakedown analysis and thus capable of handling large-scale problems. The algorithm allows for an arbitrary number of thermo-mechanical loadings. To illustrate the method’s potential, numerical results are shown for several examples from the field of power plant engineering.

► The statical shakedown theorem is extended to limited kinematical hardening.
► Nonlinear hardening is handled for large structures under arbitrary numbers of loads.
► The open discussion on the influence of nonlinear hardening is conclusively closed.
► The method is implemented into an interior-point algorithm.
► The method’s potential is shown by application to several numerical examples.