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Mixed antiplane boundary‐value problem for a piecewise‐homogeneous elastic body with a semi‐infinite interfacial crack
Author(s) -
Vasileva Iuliia,
Gürlebeck Klaus,
Silvestrov Vasily
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3869
Subject(s) - mathematics , piecewise , mathematical analysis , stress intensity factor , antiplane shear , boundary value problem , singularity , geometry , finite element method , physics , thermodynamics
Antiplane stress state of a piecewise‐homogeneous elastic body with a semi‐infinite crack along the interface is considered. The longitudinal displacements along one of the crack edges on a finite interval, adjacent to the crack tip, are known. Shear stresses are applied to the body along the crack edges and at infinity. The problem reduces to a Riemann–Hilbert boundary‐value matrix problem with a piecewise‐constant coefficient for a complex potential in the class of symmetric functions. The complex potential is found explicitly using a Gaussian hypergeometric function. The stress state of the body close to the singular points is investigated. The stress intensity factors are determined. Copyright © 2016 John Wiley & Sons, Ltd.