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A Beam—Just a Beam in Linear Plane Bending

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Recent Developments in the Theory of Shells

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

Abstract

Starting from the equations of the linear, three-dimensional theory of elasticity, the displacements are expanded into power series in the width- and height-coordinates. By invoking the uniform-approximation method in combination with the pseudo-reduction technique, a hierarchy of beam theories of different orders of approximation is established. The first-order approximation coincides with the classical Euler-Bernoulli beam theory, whereas the second-order approximation delivers a Timoshenko-type of shear-deformable beam theory. Differences and implications are discussed.

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Authors and Affiliations

  1. Bremen Institute for Mechanical Engineering (Bime), University of Bremen, Bremen, Germany

    Reinhold Kienzler

  2. Technische Universität Darmstadt, Institute for Lightweight Construction and Design (KLuB), Darmstadt, Germany

    Patrick Schneider

Authors
  1. Reinhold Kienzler
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  2. Patrick Schneider
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Corresponding author

Correspondence to Reinhold Kienzler .

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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Kienzler, R., Schneider, P. (2019). A Beam—Just a Beam in Linear Plane Bending. 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_18

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