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Singular Stresses in an Elastic Sphere Having an Annular Crack
Author(s) -
Shindo Y.,
Himemiya T.
Publication year - 1982
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19820620703
Subject(s) - chebyshev polynomials , singular integral , mathematics , singular solution , mathematical analysis , isotropy , polynomial , algebraic equation , regular singular point , integral equation , jacobi polynomials , enhanced data rates for gsm evolution , singular function , geometry , orthogonal polynomials , physics , computer science , nonlinear system , optics , telecommunications , quantum mechanics
This paper concerns the analysis of the singular stresses arising in an isotropic sphere having an annular crack. The analysis is valid not only for an annular crack but also for a penny‐shaped crack and a peripheral edge crack. The problem is first reduced to that of solving a singular integral equation of the first kind. By the way of expanding the unknown function into a Chebyshev polynomial for an annular and a penny‐shaped crack, and into a Jacobi polynomial for an edge crack, respectively, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. The singular stresses are expressed in closed form and clarified numerically in detail.