Edge singularities and structure of the 3-D Williams expansion

Thomas Apel, Dominique Leguillon*, Cornelia Pester, Zohar Yosibash

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The elastic solution in a vicinity of a re-entrant wedge can be described by a Williams like expansion in terms of powers of the distance to a point on the edge. This expansion has a particular structure due to the invariance of the problem by translation parallel to the edge. We show here that some terms, so-called primary solutions, derive directly from solutions to the 2-D corner problem posed in the orthogonal cross section of the domain. The others, baptized shadow functions, derive of the primary solutions by integration along the axis parallel to the edge. This 3-D Williams expansion is shown to be equivalent to the edge expansion proposed by Costabel et al. [M. Costabel, M. Dauge, Z. Yosibash, A quasidual function method for extracting edge stress intensity functions, SIAM J. Math. Anal. 35 (5) (2004) 1177-1202]. To cite this article: T. Apel et al., C. R. Mecanique 336 (2008).

Original languageEnglish
Pages (from-to)629-635
Number of pages7
JournalComptes Rendus - Mecanique
Issue number8
StatePublished - Aug 2008
Externally publishedYes


  • Edge singularities
  • Elasticity
  • Generalized stress intensity factors


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