Remarks on Circular Edges and Open Questions

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

Abstract

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
Pages377-393
Number of pages17
DOIs
StatePublished - 2012
Externally publishedYes

Publication series

NameInterdisciplinary Applied Mathematics
Volume37
ISSN (Print)0939-6047
ISSN (Electronic)2196-9973

Keywords

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

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