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

  • Alexander V. Aksenov
Chapter
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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.

Keywords

Axisymmetric Fundamental Solution Displacement Equilibrium Equations Isotropic Linear Elastic Medium Linear Partial Differential Equations General Symmetry Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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