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FEM with Floquet Theory for Non-slender Elastic Columns Subject to Harmonic Applied Axial Force Using 2D and 3D Solid Elements

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IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 34))

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Abstract

The Rayleigh–Ritz formulation of finite element method using solid elements is implemented for a 2D and 3D clamped-clamped column which is subject to a periodically applied axial force. Non-linear strain is considered. A mass element matrix and two stiffness matrices are obtained. After assembly by elements, the calculated natural frequencies and buckling loads are compared to Euler–Bernoulli beam theory predictions. For 2D triangular and 3D cuboid elements, a large number of degrees of freedom are required for sufficient convergence which adds particular computational costs to applying Floquet theory to determine stability of the harmonically forced column. A method popularised by Hsu et al. is used to reduce the computational load and obtain the full monodromy matrix. The Floquet multipliers are discussed in relation to their bifurcations. The versatile 2D and 3D elements used allows for the discussion of non-slender columns. In addition, the stability of a 3D steel column comprised of impure materials or with changed aspect ratio are investigated.

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Authors and Affiliations

  1. Dynamics and Vibration Group, FNB, Faculty of Mechanical Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293, Darmstadt, Germany

    Eoin Clerkin & Markus Rieken

Authors
  1. Eoin Clerkin
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  2. Markus Rieken
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Correspondence to Eoin Clerkin .

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Editors and Affiliations

  1. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    Stefanie Gutschmidt

  2. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    James N. Hewett

  3. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    Mathieu Sellier

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Clerkin, E., Rieken, M. (2019). FEM with Floquet Theory for Non-slender Elastic Columns Subject to Harmonic Applied Axial Force Using 2D and 3D Solid Elements. In: Gutschmidt, S., Hewett, J., Sellier, M. (eds) IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics. IUTAM Bookseries, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-13720-5_22

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  • DOI: https://doi.org/10.1007/978-3-030-13720-5_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-13719-9

  • Online ISBN: 978-3-030-13720-5

  • eBook Packages: EngineeringEngineering (R0)

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