Remarks on Circular Edges and Open Questions

Zohar Yosibash

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This last chapter is devoted to our latest results on circular edges, and some open questions that are the aim and scope of future research. In daily practice, in reality, most edges are curved in three-dimensional domains and therefore these are of utmost engineering interest. Here we concentrate on circular edges (a “penny-shaped crack” being a special renowned case) in a 3-D domain, and derive explicitly a singular series expansion in the vicinity of such an edge for the simplest scalar elliptic operator, the Laplace operator. The displacements and stress fields associated with the elasticity system are provided in a recent paper [208].

Original languageEnglish
Title of host publicationInterdisciplinary Applied Mathematics
PublisherSpringer Nature
Number of pages17
StatePublished - 1 Jan 2012

Publication series

NameInterdisciplinary Applied Mathematics
ISSN (Print)0939-6047
ISSN (Electronic)2196-9973


  • Axisymmetric Case
  • Circumferential Crack
  • Failure Initiation
  • Homogeneous Dirichlet Boundary Condition
  • Shadow Function

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Management Science and Operations Research


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