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Discretization and numerical realization of contact problems for elastic‐perfectly plastic bodies. PART I – discretization, limit analysis

The paper deals with a static case of discretized contact problems for bodies made of materials obeying Hencky's law of perfect plasticity. The main interest is focused on the analysis of the formulation in terms of displacements. This covers the study of: i) a structure of the solution set in the case when the problem has more than one solution ii) the dependence of the solution set on the loading parameter ζ. The latter is used to give a rigorous justification of the limit load approach based on work of external forces as a function of ζ. A model example illustrates the efficiency of the method.