An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors

Myung-Jin Choi; Sven Klinkel; Roger Sauer

doi:10.1007/s00466-022-02223-5

An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors

Abstract

This paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method is employed. The lateral boundary surface of the beam is parameterized by its axis and cross-sectional boundary curves with NURBS basis functions having at leastC2-continuity,which yields a continuous surface metric and curvature for the closest point projection. Three-dimensional constitutive laws of hyperelastic materials are considered. Several numerical examples verify the accuracy and efficiency of the proposed beam contact formulation in comparison to brick element solutions. The lateral contact pressure distribution of the beam formulation is in excellent agreement with the contact pressure of the brick element formulation while requiring much less degrees-of-freedom.

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DOI:: Digital Object Identifier (open in new tab) 10.1007/s00466-022-02223-5
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Keywords

COSSERAT ROD · CROSS-SECTIONAL DEFORMATION · FRICTIONLESS CONTACT · SURFACE-TO-SURFACE CONTACT · BEAM-TO-BEAM CONTACT · ISOGEOMETRIC ANALYSIS

Details

Category:

Articles

Type:

artykuły w czasopismach

Published in:

COMPUTATIONAL MECHANICS no. 70, pages 1107 - 1144,
ISSN: 0178-7675

Language:

English

Publication year:

2022

Bibliographic description:

Choi M., Klinkel S., Sauer R.: An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors// COMPUTATIONAL MECHANICS -Vol. 70,iss. 6 (2022), s.1107-1144

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