An augmented Lagrangian optimization method for contact analysis problems, 2: numerical evaluation

The ALM2 solution procedure is evaluated by solving two simple contact analysis problems for different friction conditions. These example problems are devised to have closed form solutions. This way there is no uncertainty about the target solution for evaluation of the proposed algorithm as well as existing algorithms. The numerical results with ALM2 are compared with the analytical solutions as well as with the penalty, Lagrange multiplier and existing augmented Lagrangian methods. All the algorithms are analysed for stick and slip friction conditions. The example problems are used to show clearly the dependence of the existing solution methods on the number of load steps and penalty values. It is concluded that convergence of incremental solution schemes employed in these methods does not guarantee accuracy of the contact solution even with the use of solution enhancement schemes such as automatic load stepping and contact load prediction. The example problems are also used to demonstrate solution independence of the proposed ALM2 procedure from penalty values, and from the number of load steps. The proposed formulation for calculation of frictional forces and the ALM solution algorithm have worked quite well for the example problems. However, the algorithm needs to be developed and evaluated for more complex contact analysis problems.