Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Beams, Plates, and Shells

  • Michael KrommerEmail author
  • Yury Vetyukov
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_1-1



In this article we shortly present the fundamental relations of the classical theories for straight and slender beams as well as for thin plates and shells. In particular, Bernoulli-Euler beams, Kirchhoff plates, and Kirchhoff-Love shells are discussed in a geometrically and physically linear regime. Further, we restrict the content to homogenous beams, plates, and shells, for which the material behavior is assumed isotropic. Our presentation rests on the use of a direct tensor notation, which avoids unnecessarily lengthy equations using specific coordinates but rather enables a compact and concise formulation.

Bernoulli-Euler Beams

We study straight and slender beams of length with a solid cross section Ω. The beam is homogenous with isotropic linear elastic material behavior. The position vector of a point P of the undeformed beam is \( \underline {R}_3 = \underline {R}(x) +...
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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mechanics and MechatronicsWienAustria

Section editors and affiliations

  • Franz G. Rammerstorfer
    • 1
  • Melanie Todt
    • 2
  • Isabella C. Skrna-Jakl
    • 3
  1. 1.Institut für Leichtbau und Struktur-BiomechanikTU WienWienAustria
  2. 2.Institut für Leichtbau und Struktur-BiomechanikTU WienWienAustria
  3. 3.Institut für Leichtbau und Struktur-BiomechanikTU WienWienAustria