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Quadruple Trigonometrical Series Equations and Their Application to an Inclusion Problem in the Theory of Elasticity
Author(s) -
Singh B. M.,
Rokne J.,
Dhaliwal R. S.
Publication year - 2004
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2004.01468.x
Subject(s) - mathematics , mathematical analysis , stress intensity factor , integral equation , antiplane shear , series (stratigraphy) , shear (geology) , closed form expression , shear stress , elasticity (physics) , trigonometric functions , geometry , mechanics , fracture mechanics , physics , materials science , paleontology , biology , composite material , thermodynamics
Closed form solution of quadruple series equations involving cosine kernels has been obtained by reducing the series equations into triple Abel's type integral equations which in turn are reduced to a single integral equation. Making use of finite Hilbert transforms the solution of the single integral equation is obtained in closed form. This solution is used to solve an electrostatic problem. The results of this paper have also been used in a two‐dimensional elastostatic problem under anti‐plane shear and the effect of rigid line inclusions with thickness on the Griffith cracks has been examined. The expressions for shear stress and stress intensity factor at the tip of the crack are obtained. Finally, some numerical results for the stress intensity factor and shear stress distribution are obtained.