INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2014; 97:683–706 Published online 17 December 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.4611 Contact between rolling beams and flat surfaces Alfredo Gay Neto 1, * ,† , Paulo M. Pimenta 1 and Peter Wriggers 2 1 Polytechnic School at University of São Paulo, São Paulo, Brazil 2 Leibniz Universität Hannover, Hannover, Germany SUMMARY This work presents a new approach to model the contact between a circular cross section beam and a flat surface. In a finite element environment, when working with beam elements in contact with surfaces, it is common to consider node or line to surface approaches for describing contact. An offset can be included in normal gap function due to beam cross section dimensions. Such a procedure can give good results in fric- tionless scenarios, but the friction effects are not usually properly treated. When friction plays a role (e.g., rolling problems or alternating rolling/sliding) more elaboration is necessary. It is proposed here a method that considers an offset not only in normal gap. The basic idea is to modify the classical definition of tan- gential gap function in order to include the effect of rigid body rotation that occurs in a rolling scenario and, furthermore, consider the moment of friction force. This paper presents the new gap function definition and also its consistent linearization for a direct implementation in a Newton-Raphson method to solve nonlinear structural problems modeled using beam elements. The methodology can be generalized to any interaction involving elements with rotational degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd. Received 21 July 2013; Revised 5 November 2013; Accepted 6 November 2013 KEY WORDS: contact; rotation; rolling; sliding; beam 1. INTRODUCTION Many engineering applications present components that are naturally modeled using beam or shell elements, instead of solids. Contact interaction between these components in such a modeling has to be considered. As an example, which is the focus of the present paper, one can think of an inter- action between beam-like structures and surfaces. Some practical examples are present in offshore engineering, as long pipelines interaction with the seabed or a rope rolling and sliding in the seabed as a part of an anchoring system of a ship. The fact is that many practical problems present rolling or sliding or both situations occurring in different regions of circular cross section beam-like structures. The rolling/sliding status may even change along time in some transient dynamics problems. Aiming to model such a kind of problem using a FEM environment with beam elements, leads to an issue to consider properly the rolling effect with the classical contact formulations. One could think of modeling everything using solid elements. Then, not only a huge number of degrees of free- dom (DOFs) can be achieved, but also very difficult to find convergence nonlinear models have to be solved, once the nature of rolling includes successive changes of contact points, which is usually a difficult task when solving a nonlinear contact model. This motivates the improvement of a contact formulation to be used together with beam elements or, more generally, with structural elements containing rotation DOFs. For that, it is necessary to include rotations DOFs in a proper way into a contact formulation. Once this is done, structural elements can be used to represent the structure *Correspondence to: Alfredo Gay Neto, Polytechnic School at University of São Paulo, São Paulo, Brazil. † E-mail: alfredo.neto@gmail.com Copyright © 2013 John Wiley & Sons, Ltd.