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Generalized Surface Green’s Functions for an Elastic Half-Space

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Abstract—

Using generalized functions, Green’s functions for homogeneous elastic isotropic half-planes and half-spaces are constructed. Airy and Maxwell stress functions are used to find Green’s functions. One-dimensional and two-dimensional integral Fourier transforms are used to solve the boundary value problems. 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 rigid-body displacement. If there are no singular components, then the stresses and di-splacements coincide with the known classical solutions of the Flamant, Boussinesq, and Cerutti problems.

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Funding

This study was supported by the Russian Science Foundation, grant no. 20-19-00217, https://rscf.ru/project/20-19-00217/.

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Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), 125993, Moscow, Russia

    A. V. Zemskov & D. V. Tarlakovskii

  2. Research Institute of Mechanics, Lomonosov Moscow State University, 119192, Moscow, Russia

    A. V. Zemskov & D. V. Tarlakovskii

Authors
  1. A. V. Zemskov
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  2. D. V. Tarlakovskii
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Correspondence to A. V. Zemskov or D. V. Tarlakovskii.

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Zemskov, A.V., Tarlakovskii, D.V. Generalized Surface Green’s Functions for an Elastic Half-Space. Russ Math. 67, 22–30 (2023). https://doi.org/10.3103/S1066369X23040084

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