A formulation based on localized Lagrange multipliers for BEM–FEM coupling in contact problems

This paper presents a unified formulation for the combination of the finite element method (FEM) and the boundary element method (BEM) in 3D frictional contact problems that is based on the use of localized Lagrange multipliers (LLMs). Resolution methods for the contact problem between non-matching meshes have traditionally been based on a direct coupling of the contacting solids using classical Lagrange multipliers. These methods tend to generate strongly coupled systems that require a deep knowledge of the discretization characteristics on each side of the contact zone complicating the process of mixing different numerical techniques. In this work a displacement contact frame is inserted between the FE and BE interface meshes, discretized and finally connected to the contacting substructures using LLMs collocated at the mesh-interface nodes. This methodology will provide a partitioned formulation which preserves software modularity and facilitates the connection of non-matching FE and BE meshes.