Several finite element procedures for frictionless- or friction-contact problems have been proposed for the case in which node-to-node contact no longer holds. One of the typical computational algorithms is the nodal mis-match algorithm in which contact interface is discretized into contact segments. In this paper, the nodal mis-match algorithm to allow arbitrary finite element mesh is generalized by using a perturbed Lagrangian formulation and localized mixed concepts.
A numerical analysis for the excavation problem of shield tunnel was carried out by using the proposed algorithm. The numerical results were well similar to the ground behaviors observed in situ.