Simplified proof of the generalized variational inequality principle for elasto-plastic contact problem with friction

In the case of elasto-plastic contact problem with friction, because the friction law on the contact boundary is expressed by inequalities, the variational formulation of the constraints leads to variational inequalities, instead of variational equalities. In general, the energy functional of variational inequalities problem is obtained by use of Lagrange multipliers method. But the Lagrange multipliers method must be proved by nonlinear functional analysis and convex analysis and it is a complicated process. In this paper, the proving of the generalized variational functional of elasto-plastic contact problem is simplified by use of the vector analysis method.