Admissible traction boundary conditions along the crack line in nonlocal elasticity
Author:
Nasit Ari
Journal:
Quart. Appl. Math. 46 (1988), 727-736
MSC:
Primary 73C35; Secondary 73M05
DOI:
https://doi.org/10.1090/qam/973386
MathSciNet review:
973386
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Abstract: Mixed boundary conditions for integro-differential systems in general lead to overdetermined problems. A specific instance of this problem is encountered in nonlocal elasticity. The ensuing consistency problem is analyzed by utilizing the asymptotic properties of eigenfunctions associated with the kernel of a Fredholm equation of the first kind. Finally as an example, a well-posed set of mixed boundary values are derived for the one-dimensional nonlocal Griffith crack problem.
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A. C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves, Internat. J. Engrg. Sci. 10, 233–248 (1972)
A. A. Maradudin and D. L. Mills, Effect of spatial dispersion on the properties of a semi-infinite dielectric, Phys. Rev. B 7, 2787–2809 (1973)
A. C. Eringen, On the nature of boundary conditions for crack tip stress, Arch. Mech. 33, 937–945 (1981)
A. C. Eringen, C. G. Speziale, and B. S. Kim, Crack tip problem in nonlocal elasticity, J. Mech. Phys. Solids 25, 339–355 (1977)
F. G. Tricomi, Integral Equations, Interscience Pub., New York, 1957.
H. Buchholz, The Confluent Hypergeometric Function, Springer-Verlag, New York, 1969
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Article copyright:
© Copyright 1988
American Mathematical Society
