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Isogeometric Collocation Methods for the Nonlinear Dynamics of Three-Dimensional Timoshenko Beams

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Proceedings of XXIV AIMETA Conference 2019 (AIMETA 2019)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

In this paper the isogeometric collocation (IGA-C) method is used to solve the dynamic problem of geometrically exact beams. The kinematics of a spatial Timoshenko beam undergoing finite displacements and rotations involves the Lie group \({\mathrm{SO(3)}}\). Most of the computational complexities originate from the presence of such a non-additive and non-commutative rotation group. By employing the incremental rotation vector to describe the evolution of finite rotations, we discuss how the IGA-C method can efficiently be used in both explicit and implicit Newmark-based schemes.

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Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Florence, Via di S. Marta 3, 50139, Firenze, Italy

    Enzo Marino

  2. Department of Marine Technology, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Josef Kiendl

  3. Institute of Applied Mechanics, Technische Universität Braunschweig, Pockelsstraße 3, 38106, Braunschweig, Germany

    Laura De Lorenzis

Authors
  1. Enzo Marino
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  2. Josef Kiendl
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  3. Laura De Lorenzis
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Corresponding author

Correspondence to Enzo Marino .

Editor information

Editors and Affiliations

  1. DIMA, Sapienza University of Rome, Rome, Italy

    Antonio Carcaterra

  2. DISG, Sapienza University of Rome, Rome, Italy

    Achille Paolone

  3. DIMA, Sapienza University of Rome, Rome, Italy

    Giorgio Graziani

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Marino, E., Kiendl, J., De Lorenzis, L. (2020). Isogeometric Collocation Methods for the Nonlinear Dynamics of Three-Dimensional Timoshenko Beams. In: Carcaterra, A., Paolone, A., Graziani, G. (eds) Proceedings of XXIV AIMETA Conference 2019. AIMETA 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-41057-5_96

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  • DOI: https://doi.org/10.1007/978-3-030-41057-5_96

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41056-8

  • Online ISBN: 978-3-030-41057-5

  • eBook Packages: EngineeringEngineering (R0)

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