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

Abstract Slender structures are commonly represented using beam models. When addressing the contact between them, usually one has to adopt specific formulations, wherein the beam is represented by a 3D curve. Aiming at increasing the geometric details of such formulations, in this work we present a master-surface to master-surface contact formulation, which is adequate for beam-to-beam contact. Particularly, the focus is given to the friction effects. For that, a pointwise interaction is assumed for each contact zone. Then, we establish a special tangential gap function, able to compute not only the relative sliding, but also to consider changes of the material points where contact takes place. Such changes are essential for modeling rolling contact scenarios. We apply the ideas for beam-to-beam contact, considering geometrically-exact beams with superelliptical cross-sections. The proposed model can naturally handle the effects of friction associated with the beam translations and rotations, such as rolling or alternating rolling/sliding. Since the change of material points responsible for contact is included in the tangential gap definition, a single contact zone is able to handle such complex interactions, which is computationally-convenient. We show numerical examples with applications involving sliding, rolling and multiple beam-to-beam contacts.

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