A primal-dual active set strategy for unilateral non-linear dynamic contact problems of thin-walled structures

Abstract

The efficient modeling of 3D contact problems is still a challenge in non-linear implicit structural analysis. Most of the existing contact algorithms use penalty methods to satisfy the contact constraints, which necessitates a user defined penalty parameter. As it is well known, the choice of this additional parameter is somehow arbitrary, problem dependent and influences the accuracy of the analysis. We use a primal-dual active set strategy [1], based on dual Lagrange multipliers [4] to handle the nonlinearity of the contact conditions. This allows us to enforce the contact constraints in a weak, integral sense without any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers can be locally eliminated. We perform a static condensation to get a reduced system for the displacements. The Lagrange multipliers, representing the contact pressure, can be easily recovered from the displacements in a variationally consistent way.