Extracting generalized edge flux intensity functions with the quasidual function method along circular 3-D edges

Samuel Shannon, Zohar Yosibash, Monique Dauge, Martin Costabel

Research output: Contribution to journalArticlepeer-review

Abstract

Explicit asymptotic series describing solutions to the Laplace equation in the vicinity of a circular edge in a three-dimensional domain was recently provided in Yosibash et al. (Int J Fract 168:31-52, 2011). Utilizing it, we extend the quasidual function method (QDFM) for extracting the generalized edge flux intensity functions (GEFIFs) along circular singular edges in the cases of axisymmetric and non-axisymmetric data. This accurate and efficient method provides a functional approximation of the GEFIFs along the circular edge whose accuracy may be adaptively improved so to approximate the exact GEFIFs. It is implemented as a post-solution operation in conjunction with the p-version of the finite element method. The mathematical analysis of the QDFM is provided, followed by numerical investigations, demonstrating the efficiency, robustness and high accuracy of the proposed quasi-dual function method. The mathematical machinery developed in the framework of the Laplace operator is important to realize its possible extension for the elasticity system.

Original languageEnglish
Pages (from-to)25-50
Number of pages26
JournalInternational Journal of Fracture
Volume181
Issue number1
DOIs
StatePublished - May 2013
Externally publishedYes

Keywords

  • 3-D singularities
  • Edge flux intensity functions
  • Penny-shaped crack
  • Quasi-dual function method

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