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.
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.
V. K. Varadan and V. V. Varadan, Acoustic, electro magnetic and elastic wave scattering—Focus on the T-matrix approach, Pergamon, Oxford, 1980.
- 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
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)
T. Mura, Micromechanics of defects in solids, Nijhoff, The Hague, 1982.
R. Burridge and L. Knopoff, Body force equivalents for seismic dislocations, Bulletin of the Seismological Society of America 54, 1875–1888 (1964)
J. D. Achenbach, Wave propagation in elastic solids, North-Holland, Amsterdam, 1973.
- 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
L. M. Brock, Non-uniform edge dislocation motion along an arbitrary path, Journal of the Mechanics and Physics of Solids 31, 123–132 (1983)
I. N. Sneddon, The use of integral transforms, McGraw-Hill, New York, 1972.
- 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
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)
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)
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)
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)
B. A. Bilby and J. D Eshelby, Dislocations and the theory of fracture, in: Fracture, Vol. 1, H. Liebowitz, ed., Academic, New York, 1968..
L. M. Brock, The dynamic stress intensity factor due to arbitrary screw dislocation motion, Journal of Applied Mechanics 50, 383–389 (1983)
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.
V. K. Varadan and V. V. Varadan, Acoustic, electro magnetic and elastic wave scattering—Focus on the T-matrix approach, Pergamon, Oxford, 1980.
I. Stakgold, Green’s functions and boundary value problems, Wiley, New York, 1979.
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)
T. Mura, Micromechanics of defects in solids, Nijhoff, The Hague, 1982.
R. Burridge and L. Knopoff, Body force equivalents for seismic dislocations, Bulletin of the Seismological Society of America 54, 1875–1888 (1964)
J. D. Achenbach, Wave propagation in elastic solids, North-Holland, Amsterdam, 1973.
G. F. Carrier and C. E. Pearson, Partial differential equations, Academic, New York, 1976
L. M. Brock, Non-uniform edge dislocation motion along an arbitrary path, Journal of the Mechanics and Physics of Solids 31, 123–132 (1983)
I. N. Sneddon, The use of integral transforms, McGraw-Hill, New York, 1972.
G. F. Carrier, M. Krook and C. E. Pearson, Functions of a complex variable, McGraw-Hill, New York, 1966
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)
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)
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)
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)
B. A. Bilby and J. D Eshelby, Dislocations and the theory of fracture, in: Fracture, Vol. 1, H. Liebowitz, ed., Academic, New York, 1968..
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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Article copyright:
© Copyright 1985
American Mathematical Society
