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A Non-linear Theory of Thin-Walled Rods of Open Profile Deduced with Incremental Shell Equations

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Recent Developments in the Theory of Shells

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 110))

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Abstract

We study the structural behaviour of rods with thin-walled open cross-sections. Such members are best known for their low torsional rigidity and extensive warping deformation when subjected to twisting. Proceeding to large deformations one needs to account for the geometrically non-linear effects in the cross-section, that affect the structural response and prevent a simple generalisation of the linear theory. We here further elaborate a novel approach that utilizes the equations of incremental shell theory to quantify these non-linear effects and incorporate them into an augmented beam theory, which is then put to test on an example of a circularly curved rod. The linear deformation analysis reveals, that arbitrarily curved and straight rods do not share the same asymptotic behaviour. The torsional-flexural buckling loads obtained with the incremental beam theory correspond well to reference computations with shell finite elements, given that subcritical pre-deformations are negligible. The narration concludes with the post-buckling analysis using shell finite elements.

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Authors and Affiliations

  1. Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060, Vienna, Austria

    Jakob Scheidl & Yury Vetyukov

Authors
  1. Jakob Scheidl
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  2. Yury Vetyukov
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Corresponding author

Correspondence to Jakob Scheidl .

Editor information

Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Jacek Chróścielewski

  3. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  4. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

    Krzysztof Wiśniewski

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Scheidl, J., Vetyukov, Y. (2019). A Non-linear Theory of Thin-Walled Rods of Open Profile Deduced with Incremental Shell Equations. In: Altenbach, H., Chróścielewski, J., Eremeyev, V., Wiśniewski, K. (eds) Recent Developments in the Theory of Shells . Advanced Structured Materials, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-030-17747-8_28

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