Improper Double Integrals with a Logarithmic Kernel Calculated by Methods of Elasticity Theory

Abstract

© 2019, Allerton Press, Inc. 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 an improper triple integral with a logarithmic kernel. We give examples of calculating the triple integral for specific loads. As a result, we give the values of five improper double integrals expressed in terms of elementary functions.