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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 7, Pages 65–71
DOI: https://doi.org/10.26907/0021-3446-2019-7-65-71 (Mi ivm9483) 		 
Improper double integrals with a logarithmic kernel calculated by methods of elasticity theory

E. V. Skvortsov, T. V. Nikonenkova

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2019-7-65-71
Abstract: The aim of this paper is to calculate some improper double integrals. We consider the plane deformation of an elastic half-space under the action of load applied to its surface. It is shown that a well-known expressions for one of the normal stresses can be represented in another form containing a definite improper triple integral with a logarithmic kernel. We give examples of calculating the triple integral for specific loads. As a result, five improper double integrals are expressed in terms of elementary functions.
Keywords: improper double integral, boundary-value problem, Poisson equation.
Received: 17.05.2018
Revised: 17.05.2018
Accepted: 19.12.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 7, Pages 56–61
DOI: https://doi.org/10.3103/S1066369X19070065
Bibliographic databases:
Document Type: Article
UDC: 517.382:539.3
Language: Russian
Citation: E. V. Skvortsov, T. V. Nikonenkova, “Improper double integrals with a logarithmic kernel calculated by methods of elasticity theory”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 7, 65–71; Russian Math. (Iz. VUZ), 63:7 (2019), 56–61
Citation in format AMSBIB
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\pages 65--71
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