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Symmetries and Fundamental Solutions of Displacement Equations for a Transversely Isotropic Elastic Medium

  • Alexander V. Aksenov
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

A fourth-order linear elliptic partial differential equation describing the displacements of a transversely isotropic linear elastic medium is considered. Its symmetries and the symmetries of an inhomogeneous equation with a delta function on the right-hand side are found. The latter symmetries are used to construct an invariant fundamental solution of the original equation in terms of elementary functions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Alexander V. Aksenov
    • 1
  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation

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