On singularities in the solution of a problem for an elastic half-plane with a rod emerging orthogonally on the boundary
type: Item
instance of: scholarly article
title: On singularities in the solution of a problem for an elastic half-plane with a rod emerging orthogonally on the boundary
zbMATH Open document ID: 0586.73189
DOI: 10.1016/0021-8928(84)90140-0
author: L. Ya. Tikhonenko
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: An integro-differential equation in the contact stress is investigated for for an elastic half-plane (isotropic and orthotropic) with an extensible rod emerging orthogonally on the boundary. The question of the nature of the contact stress singularity at the point where the rod emerges at the boundary is clarified. It is shown that the asymptotic form of the Cauchy-type integral does not enable a single-valued solution of the question of the nature of the singularity to be obtained if it is assumed to be power-law logarithmic. The true nature of the singularity is determined by an exact solution of the equation constructed using the Mellin integral transform and the Carleman boundary value problem for a strip.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 45E99
zbMATH DE Number: 3940979
zbMATH Keywords: integro-differential equation
zbMATH Keywords: elastic half-plane
zbMATH Keywords: isotropic and orthotropic
zbMATH Keywords: extensible rod
zbMATH Keywords: emerging orthogonally on the boundary
zbMATH Keywords: contact stress singularity
zbMATH Keywords: asymptotic form of the Cauchy-type integral
zbMATH Keywords: not enable a single-valued solution
zbMATH Keywords: power-law logarithmic
zbMATH Keywords: exact solution
zbMATH Keywords: Mellin integral transform
zbMATH Keywords: Carleman boundary value problem
MaRDI profile type: Publication
full work available at URL: 0021-8928(84)90140-0
OpenAlex ID: W1969111935
cites work: Bending of wedgelike plates with elastically-fastened or reinforced edges
cites work: On the Diffusion of Load From a Transverse Tension Bar Into a Semi-Infinite Elastic Sheet
cites work: Q3895765
cites work: Q3892490
description: scientific article; zbMATH DE number 3940979