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

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.

UDC: 517.382:539.3

Received: 17.05.2018
Revised: 17.05.2018
Accepted: 19.12.2018

DOI: 10.26907/0021-3446-2019-7-65-71

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:7, 56–61

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