A master-surface to master-surface formulation for beam to beam contact. Part I: frictionless interaction

In this paper a surface to surface frictionless contact formulation is presented, which is appropriate to the analysis of beam to beam contact. Parameterized surfaces are assumed to represent the boundaries of the bodies that are candidate to contact. The material points of each surface are described using convective coordinates. No master-slave distinctions are made, once both bodies are parameterized and no slave points are elected. We assume a single point contact interaction, in which the contact point can move along different material points of the surfaces. On the other hand, these surfaces can change since the bodies experience large deformation. To determine the candidate material points to contact, we solve the minimum distance problem between the two surfaces. The equations for obtaining the mechanical contact interaction and the consistent linearization are herewith derived. The proposed formulation can be applied disregarding the nature of the model degrees of freedom. Subsequently one has established the surface parameterizations, the contact formulation can be directly used. As an illustration of the power of our formulation, we present an application for beams with superelliptical cross sections.