Stress based finite element methods for solving contact problems: Comparisons between various solution methods

This paper deals with numerical methods for solving unilateral contact problems with friction. Although these problems are usually defined in terms of the displacement, a stress based approach to the problem is developed here. The “equilibrium” finite elements method is therefore used. Using these elements make it possible to satisfy the local equilibrium condition a priori, but on the other hand, prescribed and contact forces have to be introduced using Lagrangian multipliers. The problem obtained is therefore a non-linear, constrained problem and the global system matrix is non-positive definite. Various solution algorithms are thus proposed and compared. Comparisons between the classical method and that developed here show that the stress formulation gives very satisfactory results in terms of the stresses.