TY - JOUR

T1 - Edge singularities and structure of the 3-D Williams expansion

AU - Apel, Thomas

AU - Leguillon, Dominique

AU - Pester, Cornelia

AU - Yosibash, Zohar

PY - 2008/8

Y1 - 2008/8

N2 - 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).

AB - 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).

KW - Edge singularities

KW - Elasticity

KW - Generalized stress intensity factors

UR - http://www.scopus.com/inward/record.url?scp=48549086810&partnerID=8YFLogxK

U2 - 10.1016/j.crme.2008.05.008

DO - 10.1016/j.crme.2008.05.008

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AN - SCOPUS:48549086810

SN - 1631-0721

VL - 336

SP - 629

EP - 635

JO - Comptes Rendus - Mecanique

JF - Comptes Rendus - Mecanique

IS - 8

ER -