A finite element formulation for shakedown problems using a yield criterion of the mean

This paper deals with the application of mathematical programming in shakedown problems. After recalling results of some recent works in this field, the authors propose a finite element formulation of the load domain of shakedown. The static approach is utilized together with the yield criterion of the mean. The latter assumption has already given good numerical results in limit analysis applied to plane problems [1]The assumptions on the discrete residual stress field are adopted exactly in the same manner as for elastic asymptotic stress fields in pure equilibrium elements which guarantee the total stress transmission to be perfectly continuous. In this way, nonlinear programming aspects of the shakedown problem are pointed out. Accordingly, it appears that the use of hybrid elements is recommended. A simple and convenient kinematic finite element formulation concludes the work.