Non-localised contact between beams with circular and elliptical cross-sections
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ORIGINAL PAPER
Non-localised contact between beams with circular and elliptical cross-sections Marco Magliulo1 · Jakub Lengiewicz1,2 · Andreas Zilian1 · Lars A. A. Beex1 Received: 19 September 2019 / Accepted: 27 December 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The key novelty of this contribution is a dedicated technique to efficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections. The technique consists of parametrizing the surfaces of the two beams in contact, fixing a point on the centroid line of one of the beams and searching for a constrained minimum distance between the surfaces (two variants are investigated). The resulting unilateral (frictionless) contact condition is then enforced with the Penalty method, which introduces compliance to the, otherwise rigid, beams’ cross-sections. Two contact integration schemes are considered: the conventional slave-master approach (which is biased as the contact virtual work is only integrated over the slave surface) and the so-called two-half-pass approach (which is unbiased as the contact virtual work is integrated over the two contacting surfaces). Details of the finite element formulation, which is suitably implemented using Automatic Differentiation techniques, are presented. A set of numerical experiments shows the overall performance of the framework and allows a quantitative comparison of the investigated variants. Keywords Beams · Contact · Circular and elliptical cross-sections · Rigid cross-sections · Single-pass algorithm · Two-half-pass algorithm
1 Introduction Many engineering materials such as paper, fabrics or opencell high-porosity foams consist of slender fiber-like constituents at the microscopic scale [9,25]. Various approaches to describe their mechanical behavior explicitly incorporate their discrete micro-structure [2,12,17,22,33]. In many cases beam models and beam finite elements (BFEs) are used to represent single fibers, yarns or struts [1,3,16]. It is often crucial to incorporate beam-to-beam contact in order to obtain accurate mechanical predictions. However, due to the specificity of beam kinematics, standard techniques developed to treat contact between 3D solids cannot be directly adopted.
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Lars A. A. Beex [email protected]
1
Institute of Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Maison du Nombre, 6, Avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg
2
Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), ul. Pawinskiego 5B, 02-106 Warsaw, Poland
Thus, special formulations dedicated to beams are developed [5,6,13,19,20,23,24,34,36]. Beam-to-beam contact schemes are in general built upon assumptions on the contacting systems, which restrict their use to specific contact scenarios. The formulation of a particular contact scheme is typically determined by three main issues: (i) whether or not contact remains localized
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