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Elastic Shells, Material Symmetry Group

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Encyclopedia of Continuum Mechanics

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Synonyms

Constitutive equations of elastic shells; Isotropy group of hyperelastic shells

Definition

Constitutive equations of elastic shells follow by differentiation of the two-dimensional strain energy density as a function of shell strain measures. The material symmetry group of the elastic shell consists of an ordered triple of second-order transformation tensors which make the energy function invariant under changes of reference placement of the shell.

Introduction

The general resultant nonlinear theory of elastic shells discussed here was proposed by Reissner (1974), developed in a number of papers and summarized in monographs by Libai and Simmonds (1998), Chróścielewski et al. (2004), and Eremeyev and Zubov (2008). Basic relations of this version of shell theory are concisely presented by Pietraszkiewicz (2018) in this Encyclopaedia.

The elastic material behavior of the shell is characterized by the two-dimensional (2D) strain energy density being a function of 2D shell strain...

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References

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Author information

Authors and Affiliations

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

    Victor A. Eremeyev & Wojciech Pietraszkiewicz

Authors
  1. Victor A. Eremeyev
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  2. Wojciech Pietraszkiewicz
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Corresponding author

Correspondence to Wojciech Pietraszkiewicz .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Gdańsk, Poland

    Wojciech Pietraszkiewicz

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Eremeyev, V.A., Pietraszkiewicz, W. (2018). Elastic Shells, Material Symmetry Group. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_192-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_192-1

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  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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