Non-localised contact between beams withcircular and elliptical cross-sections

Abstract

The key novelty of this contribution is a dedicated technique toefficiently determine the distance (gap) function between parallel or almost parallelbeams with circular and elliptical cross-sections. The technique consists ofparametrizing the surfaces of the two beams in contact, fixing a point on the centroidline of one of the beams and searching for a constrained minimum distance between thesurfaces (two variants are investigated). The resulting unilateral (frictionless)contact condition is then enforced with the Penalty method, which introduces complianceto the, otherwise rigid, beams’ cross-sections. Two contact integration schemes areconsidered: the conventional slave-master approach (which is biased as the contactvirtual work is only integrated over the slave surface) and the so-called two-half-passapproach (which is unbiased as the contact virtual work is integrated over the twocontacting surfaces). Details of the finite element formulation, which is suitablyimplemented using Automatic Differentiation techniques, are presented. A set ofnumerical experiments shows the overall performance of the framework and allows aquantitative comparison of the investigated variants.