Formulation and comparison of algorithms for frictional contact problems

This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-di erentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-di erentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial nite element code