Stress concentration for a circular hole in a strip by singular integral equations
type: Item
instance of: scholarly article
title: Stress concentration for a circular hole in a strip by singular integral equations
zbMATH Open document ID: 0625.73114
DOI: 10.1016/0093-6413(86)90024-8
author: E. N. Theotokoglou
author: G. Tsamasphyros
published in: Mechanics Research Communications
publication date: 1986-01-01T00:00:00Z
review text: In recent work [e.g. the authors, Ing.-Arch. 57, 3-15 (1987; Zbl 0598.73102)] the plane elasticity problem of the infinite strip weakened by cracks and/or holes has been considered in general. In this work the method is applied to the problem of a strip weakened by a circular hole. A numerical solution is determined and the maximum stress concentration factor reported for a number of parameter values characterizing the circular hole in the strip. At first the basic principles of the method adopted are explained, and the unknown dislocation density function \(\omega\) (t) is introduced. Then a rather simple study is made and properties derived for the singular integral equation (S.I.E) and the solution (the complex potentials) in the non-physical region, the disc, is added. It is shown that the solution \(\omega\) (t) is defined up to a purely imaginary constant c associated with the solution within the disc (not affecting the solution in the physical region). A further condition is introduced to uniquely determine \(\omega\) (t) and the potentials within the disc. Furthermore using the derived properties of the S.I.E., it is shown that the S.I.E. can be modified in form to include this condition plus the condition of single-valuedness of displacements. Subsequently the modified S.I.E. is numerically solved for the problem and the stress concentration factor determined directly from \(\omega\) (t).
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74G70
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 4016392
zbMATH Keywords: strip weakened by a circular hole
zbMATH Keywords: maximum stress concentration factor
MaRDI profile type: Publication
full work available at URL: 0093-6413(86)90024-8
OpenAlex ID: W2003146579
description: scientific article; zbMATH DE number 4016392