Symmetries and Fundamental Solutions of Displacement Equations for a Transversely Isotropic Elastic Medium
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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.
KeywordsAxisymmetric Fundamental Solution Displacement Equilibrium Equations Isotropic Linear Elastic Medium Linear Partial Differential Equations General Symmetry Operator
- 7.Vladimirov, V.S.: Generalized Functions in Mathematical Physics. Mir, Moscow (1979)Google Scholar