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Moscow University Mechanics Bulletin

, Volume 72, Issue 3, pp 66–69 | Cite as

An eigenvalue problem for tensors used in mechanics and the number of independent Saint-Venant strain compatibility conditions

  • M. U. Nikabadze
Article

Abstract

A number of questions concerning the eigenvalue problem for a tensor \(\mathop A\limits_ \approx\) ∈ ℝ4(Ω) with special symmetries are considered; here Ω is a domain of a four-dimensional (three-dimensional) Riemannian space. It is proved that a nonsingular fourth-rank tensor has no more than six (three) independent components in the case of a four-dimensional (three-dimensional) Riemannian space. It is shown that the number of independent Saint-Venant strain compatibility conditions is less than six.

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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

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