Fundamental solution of the elasticity theory equations in displacements for a transversely isotropic medium. (English. Russian original) Zbl 1433.35052
Differ. Equ. 53, No. 5, 617-622 (2017); translation from Differ. Uravn. 53, No. 5, 624-629 (2017).
Summary: We consider a linear fourth-order elliptic partial differential equation describing the displacements of a transversely isotropic linearly elastic medium. We find the symmetries of this equation and of the inhomogeneous equation with the delta function on the right-hand side. Based on the symmetries of the inhomogeneous equation, we construct an invariant fundamental solution in elementary functions.
MSC:
| 35J40 | Boundary value problems for higher-order elliptic equations |
| 35A08 | Fundamental solutions to PDEs |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74B05 | Classical linear elasticity |
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