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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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. (Arch. Mech. Stos.) 33 (1981), no. 6, 937–945 (1982) (English, with Russian and Polish summaries). MR 694737
  • [4] A. C. Eringen, C. G. Speziale, and B. S. Kim, Crack-tip problem in non-local elasticity, J. Mech. Phys. Solids 25 (1977), no. 5, 339–355. MR 0475158, https://doi.org/10.1016/0022-5096(77)90002-3
  • [5] F. G. Tricomi, Integral equations, Pure and Applied Mathematics. Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665
  • [6] Herbert Buchholz, The confluent hypergeometric function with special emphasis on its applications, Translated from the German by H. Lichtblau and K. Wetzel. Springer Tracts in Natural Philosophy, Vol. 15, Springer-Verlag New York Inc., New York, 1969. MR 0240343

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73C35, 73M05

Retrieve articles in all journals with MSC: 73C35, 73M05

Additional Information

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

American Mathematical Society