It can be shown theoretically that there is a load magnitude below which a protective residual stress will develop in a rolling and sliding contact of continuum structure, and above which it will undergo an incremental failure. This load is known as the `shakedown limit load’ and the protective residual stresses associated with this shakedown limit load are the optimal residual stresses for the life of the structure.
In his “Contact Mechanics” book, Professor Johnson described an analytical shakedown approach to predict the shakedown load limit and the associated residual stress distribution. This problem will be revisited in this paper using a numerical method proposed in the author’s PhD Thesis. A numerical formulation based on Bleich-Melan shakedown theorem will be discussed by making use of finite element techniques and mathematical programming. The proposed numerical procedure can be used to solve for the shakedown limit load and the associated developed residual stresses of structures subjected to repeated moving surface loads. A series of results on shakedown residual stresses will be examined.