Finite element solutions of two-dimensional contact problems based on a consistent mixed formulation

A consistent mixed finite element method for solving two-dimensional contact problems is presented. Derivations of stiffness equations for contact elements are made from a perturbed Lagrangian variational principle. For a contact element, both the displacement and pressure fields are independently assumed. In order to achieve a consisent formulation, thus avoiding any numerical instability, the pressure function is assumed in such a way that all non-contact modes in deformations must be excluded. Stiffness equations for four-noded and six-noded contact elements are given. Four numerical examples are included to demonstrate the methodology.