ABSTRACT
This chapter presents an interface treatmentmethod to solve frictional contact problems between 3D elastic bodies using the boundary elementsmethod (BEM), based on localized Lagrangemultipliers (LLM). The connection between solids is done using a displacement frame intercalated between the interfaces meshes, being the LLM collocated at the interface nodes. The BEM is used to compute the influence coefficients of the surface points involved, being the contact conditions imposed using projection functions. The LLM is a powerful tool, developed by Park and Felippa [1-3], for connecting partitioned structural systems. Rebel et al. [4] have applied it to solve 2D contact problems with FEM. The methodology proposed by Rebel has been extended by González et al. [5] to 3D contact problems. The contact problem is solved introducing a contact frame with independent degrees of freedom. The LLM connect the frame with the contacting bodies. As we use the BEM for solid modeling, we will work under the small displacements assumption. This fact simplifies the Jacobian matrix expressions presented by Rebel et al. [4] and González et al. [5]. Another feature presented is the way of finding the contact state; in the present work contact conditions are imposed mathematically using an augmented Lagrangian formulation and a projection function developed by Abascal and Rodríguez-Tembleque [6]. The LLM provide a partitioned formulation which preserve software modularity, facilitate the non-matching meshes treatment and pass the contact patch test [3].
