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Recent Developments in the Theory of Shells pp 43–63Cite as

Subclasses of Mechanical Problems Arising from the Direct Approach for Homogeneous Plates

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

Abstract

Pavel Andreevich Zhilin proposed a theory for deformable directed surfaces which builds a generalized framework in context of linear engineering theories of plates. We introduce this theory axiomatically, delineate the basic ideas and formalize the governing equations. In doing so we present a self-contained set of equations for time-invariant problems. Thereof, subclasses of mechanical problems can be deduced, whereby in present context the main existing theories are derived. These are in-plane and out-of-plane loaded plate problems. Next to the in-plane loaded plate problem, we also distinguish between transverse shear-deformable and transverse shear-rigid out-of-plane loaded plates. Typical representatives are the plate theories by Kirchhoff, Reissner, and Mindlin.

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Acknowledgements

The authors acknowledge support by the German Research Foundation (DFG) within the framework of the Research Training Group Micro-Macro-Interactions of Structured Media and Particle Systems (RTG 1554, grant no. 83477795).

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Authors and Affiliations

  1. Otto von Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany

    Marcus Aßmus, Konstantin Naumenko & Holm Altenbach

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  1. Marcus Aßmus
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  2. Konstantin Naumenko
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  3. Holm Altenbach
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Corresponding author

Correspondence to Marcus Aßmus .

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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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Aßmus, M., Naumenko, K., Altenbach, H. (2019). Subclasses of Mechanical Problems Arising from the Direct Approach for Homogeneous Plates. 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_4

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