Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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.


References [Enhancements On Off] (What's this?)

  • [1] A. C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves, Internat. J. Engrg. Sci. 10, 233-248 (1972)
  • [2] 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)
  • [3] A. C. Eringen, On the nature of boundary conditions for crack tip stress, Arch. Mech. 33, 937-945 (1981) MR 694737
  • [4] A. C. Eringen, C. G. Speziale, and B. S. Kim, Crack tip problem in nonlocal elasticity, J. Mech. Phys. Solids 25, 339-355 (1977) MR 0475158
  • [5] F. G. Tricomi, Integral Equations, Interscience Pub., New York, 1957. MR 0094665
  • [6] H. Buchholz, The Confluent Hypergeometric Function, Springer-Verlag, New York, 1969 MR 0240343

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Additional Information

DOI: https://doi.org/10.1090/qam/973386
Article copyright: © Copyright 1988 American Mathematical Society

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