Interior point surrogate dual algorithm for unilateral problems

Summary.

A unilateral problem is one kind of variational inequality problems; it can be discretized with the finite element method and converted to an inequality constrained nonsmooth optimization problem with the potential energy of the structure acting as the objective and unilateralization as the constraints. One characteristic in the optimization problem is that the number of constraints is much smaller than the dimension of the problem; therefore dual methods are often adopted. This paper focuses on the more complicated unilateral problems, the frictional contact problems. First, it is investigated that the value of the Coulomb friction coefficient has great influence on the property of the optimization problem; the friction orientation constraint is accordingly introduced in the solution procedure for treating the problems resulting from the larger friction coefficient. Then, the primal optimization problem is converted to an explicit surrogate dual problem which can be solved by a Karmarkar’s interior point based method. Finally, the method is verified by two typical frictional contact examples.