TY - JOUR

T1 - A master-surface to master-surface formulation for beam to beam contact

T2 - Part I: Frictionless interaction

AU - Gay Neto, Alfredo

AU - Pimenta, Paulo M.

AU - Wriggers, Peter

N1 - Funding Information: The first author acknowledges FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for the support under the grant 2014/17701-4 . The second author expresses his acknowledgement to CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) under the grant 303091/2013-4 , as well as the Alexander von Humboldt Foundation for the Georg Forster Award that made possible his stay at the Universities of Duisburg–Essen and Hannover in Germany as well as to the French and Brazilian Governments for the Chair CAPES-Sorbonne that made possible his stay at Sorbonne Universités (UTC) on a leave from the University of São Paulo.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Beam

KW - Contact

KW - Superellipse

KW - Surface-to-surface

UR - http://www.scopus.com/inward/record.url?scp=84960801617&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2016.02.005

DO - 10.1016/j.cma.2016.02.005

M3 - Article

AN - SCOPUS:84960801617

VL - 303

SP - 400

EP - 429

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -