  Mechanics of Solids A Journal of Russian Academy of Sciences   Founded
in January 1966
Issued 6 times a year
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S.A. Lurie and D.B. VolkovBogorodskii, "Green Tensor and Solution of the Boussinesq Problem in the Generalized Theory of Elasticity," Mech. Solids. 53 (4), 440453 (2018) 
Year 
2018 
Volume 
53 
Number 
4 
Pages 
440453 
DOI 
10.3103/S0025654418040106 
Title 
Green Tensor and Solution of the Boussinesq Problem in the Generalized Theory of Elasticity 
Author(s) 
S.A. Lurie (Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Institute of Applied Mechanics of Russian Academy of Sciences, Leningradsky pr. 7, Moscow, 125040, Russia, salurie@mail.ru)
D.B. VolkovBogorodskii (Institute of Applied Mechanics of Russian Academy of Sciences, Leningradsky pr. 7, Moscow, 125040, Russia) 
Abstract 
The fundamental spatial problems of the theory of elasticity such as the problem of constructing Green tensor and the Boussinesq problem of the action of a concentrated force on a halfspace are considered. According to the classical theory of elasticity, these problems are singular. It is shown that an analytical solution of such problems can be constructed by the PapkovichNeuber representation without invoking symmetry conditions. This makes it possible to present the solution of the problems under consideration in a single form and allows us to write an explicit solution of halfspace loaded by a concentrated vectorforce having nonzero projections onto the normal to the plane bounding the halfspace and onto the plane itself.
This paper deals with the generalized regular solutions of the considered fundamental problems of the elasticity. The solutions are limited at a singular point and damp at infinity. 
Keywords 
generalized theory of elasticity, PapkovichNeuber representation, regular solution, Green tensor, Boussinesq problem 
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Received 
02 March 2018 
Link to Fulltext 
https://link.springer.com/article/10.3103/S0025654418040106 
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