Geodesic
Generalized surface Green's functions for an elastic half-space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 27-36

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Using generalized functions are constructed Green's functions for homogeneous elastic isotropic half-planes and half-spaces. Airy and Maxwell stress functions to find the Green's functions are used. One-dimensional and two-dimensional integral Fourier transforms to solve the boundary value problems are used. Taking into account the properties of generalized functions with a point support, singular components of displacement images are distinguished. It is shown that they correspond to the displacements of a rigid body. If there are no singular components, then the stresses and displacements coincide with the known classical solutions of the Flaman, Boussinesq and Cerutti problems.
Keywords: elastic half-space, influence functions, Green's functions, stress functions, generalized functions, point support. 
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     author = {A. V. Zemskov and D. V. Tarlakovskii},
     title = {Generalized surface {Green's} functions for an elastic half-space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--36},
     publisher = {mathdoc},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_4_a2/}
}
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A. V. Zemskov; D. V. Tarlakovskii. Generalized surface Green's functions for an elastic half-space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 27-36. http://geodesic.mathdoc.fr/item/IVM_2023_4_a2/