IMPLEMENTATION OF THE PRE-DISCRETIZATION PENALTY METHOD IN CONTACT PROBLEMS

Summary. A verification of the contact algorithm based on the pre-discretization penalty method was provided by means of numerical examples. It was shown that the proposed algorithm passed the convergence numerical tests including stability and contact patch test. An accuracy of the numerical solution was studied on the Hertz contact problem. More accurate results were obtained for quadratic elements whose incorporation into the contact analysis was granted by the pre-discretization procedure. In the finite element method the contact constraints can be introduced either before or after the finite element discretization has been performed, leading to the so-called pre-discretization or post-discretization techniques1. For example, the standard nodal algorithm belongs to the latter group. In the paper2 we focused on the pre-discretization approach, showing this technique to lead naturally to the use of surface integration points as contactors. The method was shown to be consistent with the variational formulation of the continuum problem, which enabled easy incorporation of higher-order elements with midside nodes to the analysis. Furthermore, the pre-discretization approach preserved the symmetry of the algorithmic approximation with respect to contact boundaries. As a result, there was nothing like a master or slave definition of contact surface. Now, let us briefly summarize the main idea of the pre-discretization method. Consider a system of two contacting bodies coming into contact with each other. The initial configuration is described by open domains Ω01, Ω 0 2 with boundaries