Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The dynamic $ 2$D analysis of a concentrated force near a semi-infinite crack


Author: L. M. Brock
Journal: Quart. Appl. Math. 43 (1985), 201-210
MSC: Primary 73M05; Secondary 73D25
DOI: https://doi.org/10.1090/qam/793528
MathSciNet review: 793528
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Abstract: An exact dynamic 2D solution for a concentrated force near a stationary semi-infinite crack in an unbounded plane can be used in the transient analysis of wave-scattering problems. Direct approaches to obtaining the solution, however, are complicated by the existence of a characteristic length. A less direct approach is used here which circumvents these complications. As an example, the dynamic stress intensity factors are derived and studied for their behavior w.r.t. time and concentrated force-crack edge orientation.


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  • [1] J. D. Achenbach, Y. H. Pao and H. F. Tiersten, Application of elastic waves in electrical devices, non-destructive testing and seismology, Northwestern University, Evanston, 1976.
  • [2] V. K. Varadan and V. V. Varadan, Acoustic, electro magnetic and elastic wave scattering--Focus on the T-matrix approach, Pergamon, Oxford, 1980.
  • [3] Ivar Stakgold, Green’s functions and boundary value problems, John Wiley & Sons, New York-Chichester-Brisbane, 1979. A Wiley-Interscience Publication; Pure and Applied Mathematics. MR 537127
  • [4] J. T. Fokkema and P. M. vandenBerg, Elastodynamic diffraction by a periodic rough surface (stress-free boundary), Journal of the Acoustics Society of America 62, 1095-1101 (1977)
  • [5] T. Mura, Micromechanics of defects in solids, Nijhoff, The Hague, 1982.
  • [6] R. Burridge and L. Knopoff, Body force equivalents for seismic dislocations, Bulletin of the Seismological Society of America 54, 1875-1888 (1964)
  • [7] J. D. Achenbach, Wave propagation in elastic solids, North-Holland, Amsterdam, 1973.
  • [8] George F. Carrier and Carl E. Pearson, Partial differential equations, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Theory and technique. MR 0404823
  • [9] L. M. Brock, Non-uniform edge dislocation motion along an arbitrary path, Journal of the Mechanics and Physics of Solids 31, 123-132 (1983)
  • [10] I. N. Sneddon, The use of integral transforms, McGraw-Hill, New York, 1972.
  • [11] George F. Carrier, Max Krook, and Carl E. Pearson, Functions of a complex variable: Theory and technique, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222256
  • [12] L. B. Freund, The stress intensity factor due to normal impact loading of the faces of a crack, International Journal of Engineering Science 12, 179-190 (1974)
  • [13] L. M. Brock, Shear and normal impact loadings on one face of a narrow slit, International Journal of Solids and Structures 18, 467-477 (1982)
  • [14] H. Lamb, On the propagation of tremors over the surface of an elastic solid, Philosophical Transactions of the Royal Society of London A203, 1-42 (1904)
  • [15] L. M. Brock, The effects of displacement discontinuity derivatives on wave propagation-III. body and point forces in elastic half-spaces, International Journal of Engineering Science 19, 949-957 (1981)
  • [16] B. A. Bilby and J. D Eshelby, Dislocations and the theory of fracture, in: Fracture, Vol. 1, H. Liebowitz, ed., Academic, New York, 1968..
  • [17] L. M. Brock, The dynamic stress intensity factor due to arbitrary screw dislocation motion, Journal of Applied Mechanics 50, 383-389 (1983)

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Additional Information

DOI: https://doi.org/10.1090/qam/793528
Article copyright: © Copyright 1985 American Mathematical Society


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